chars int64 40 24k | content_type stringclasses 9
values | id stringlengths 13 64 | source stringclasses 5
values | subset stringclasses 31
values | text stringlengths 40 24k |
|---|---|---|---|---|---|
6,084 | lean_file_chunk | 4c8a9085948f191badd1fffdf9f380c813cd48667d183fb6ad4443e44cae63ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker
-/
module
public import Mathlib.Probability.CDF
public import Mathlib.Analysis.SpecialFunctions.Gamma.Basic
/-! # Gamma distributions over ℝ
Define the gamma measure over... |
15,028 | lean_file_chunk | 599f7eebbe3fe2298a6e50c401aa8b77c18597cc65b45f23ec14bbbe664e0ef5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker, Devon Tuma, Kexing Ying
-/
module
public import Mathlib.Probability.Density
public import Mathlib.Probability.ConditionalProbability
public import Mathlib.Probability.Prob... |
5,559 | lean_file_chunk | 74e922d8d4777e7eae94b28b4d4c670087426cffbbba910d90a6f7ec391e9d0a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Alvan Caleb Arulandu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alvan Caleb Arulandu
-/
module
public import Mathlib.Probability.CDF
public import Mathlib.Analysis.SpecialFunctions.ImproperIntegrals
/-! # Pareto distributions over ℝ
Define... |
4,825 | lean_file_chunk | 7341c987e24de32feb09d747064080959b2f0b57edc11b66263c0defae08dab9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Probability.ProductMeasure
public import Mathlib.Probability.HasLaw
/-!
# Product of bernoulli distributions on a set
This file defines th... |
6,853 | lean_file_chunk | c81ef067cb38676d0435def5ff1a564750bd94dbc501ab0f01253e75d5082c46 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 David Ledvinka. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Ledvinka
-/
module
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Haar.OfBasis
import Mathlib.Analysis.SpecialFunctions.... |
7,163 | lean_file_chunk | 5a1812628a6eefe6bd4a82013040e9363def67b1a74ae88588c4943f54228f0c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Claus Clausen. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Claus Clausen, Patrick Massot
-/
module
public import Mathlib.Probability.CDF
public import Mathlib.Probability.Distributions.Gamma
/-! # Exponential distributions over ℝ
Define the ... |
23,920 | lean_file_chunk | b37cd1c29aff3d1250d71dde0e47774fb6f7f3a0efc7cf4424e233f3461360cb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Analysis.SpecificLimits.ArithmeticGeometric
public import Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap
public import M... |
6,293 | lean_file_chunk | 203baea7c91a6e14bce03b3e65688fba0faef0d268c1d27768360ef8f8af3f14 | lean_source_file | pkg_mathlib_source_file_chunks | simp only [ha, inv_zero, ne_eq, OfNat.ofNat_ne_zero, not_false_eq_true, zero_pow, mul_zero,
zero_mul, Real.exp_zero, ENNReal.ofReal_one, lintegral_const, measure_univ, mul_one,
ENNReal.toReal_div, neg_mul]
refine le_add_right ?_
rw [← ENNReal.ofReal_one]
gcongr
simp only [Real.one_le_exp_iff... |
3,016 | lean_file_chunk | 59eb784047b16f9fd63c5bd589d3eddcd296cebb9ae8ee0447a7da239a5a5fed | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker
-/
module
public import Mathlib.Probability.ProbabilityMassFunction.Basic
public import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic
/-! # Geometric distributio... |
5,595 | lean_file_chunk | 8d3dc35b9638170c43be082badc627f5660fe39fcd5e45fce1a41214a9dc581c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Tommy Löfgren. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tommy Löfgren
-/
module
public import Mathlib.Analysis.SpecialFunctions.Gamma.Beta
/-! # Beta distributions over ℝ
Define the beta distribution over the reals.
## Main definitions
*... |
3,097 | lean_file_chunk | 51c695ad74fdc10857cc2711e3aa559119a227c9da763289b893aa2b91dc3330 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Probability.CondVar
public import Mathlib.Probability.Distributions.SetBernoulli
public import Mathlib.Probability.Moments.Variance
public i... |
4,310 | lean_file_chunk | 1bc4285ade1473a8f9fc533045a77f833c7d0ffe0f89bb0cbae84c4fe2ab6495 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.Probability.CondVar
import Mathlib.Probability.Notation
/-!
# Distributions on ... |
7,332 | lean_file_chunk | fdaf7b0f2e04efce4af04b51eefdadfb63570af8cce872740d38554fa7212c58 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Integral.DominatedConvergence
public import Mathlib.Probability.Kernel.MeasurableLIntegral
/-!
# Measurability of the integra... |
3,956 | lean_file_chunk | 56e78ee393aa84eea05c6f2e20c30ed4c502a3033809e1f73d1eb378f70be4a3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.Probability.Kernel.Basic
/-!
# Bochner integrals of kernels
-/
public section
... |
15,572 | lean_file_chunk | bd0b033c703dd321350d857d2c7e57a5eb536e90385335ba148e229ccfe98aea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Composition.MeasureComp
public import Mathlib.Probability.Kernel.CondDistrib
public import Mathlib.Probability.Conditiona... |
23,978 | lean_file_chunk | d5e6e677c05714fff8c2bcfc6177312354ab8f1aaebb40d86da1c6dc55bef208 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Composition.Lemmas
public import Mathlib.Probability.Kernel.Disintegration.Unique
/-!
# Regular conditional probability ... |
904 | lean_file_chunk | 12c012c7e83e5d4a873d5af2d7572058053a23e916a9c9e59032e05d527e81d8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.MeasureTheory.Integral.Bochner.Set
public import Mathlib.Probability.Kernel.Integral
/-! # Integral against a kernel over a set
This f... |
8,039 | lean_file_chunk | b25edc8c17c6655ace2798a675026d5615c3afc6456e24d18b77304349512cbe | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.MeasurableSpace.Prod
public import Mathlib.Probability.Kernel.Basic
/-!
# Measurability of the integral against a kernel
The... |
17,907 | lean_file_chunk | fe48cf73ab80918481c7924ec55ffda926c7d247d47cebb4f849802b8aaa1e18 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Defs
/-!
# Basic kernels
This file contains basic results about kernels in general and definitions of some particular
k... |
23,984 | lean_file_chunk | 16540a92f3e718081502aae5c25be308aaef235be98103f97f50919c3e80251c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Disintegration.Density
public import Mathlib.Probability.Kernel.WithDensity
/-!
# Radon-Nikodym derivative and Lebesgue ... |
6,386 | lean_file_chunk | a21eab285866cf8d0b0b695ddec765e73744676b194347c1c97175da18361319 | lean_source_file | pkg_mathlib_source_file_chunks | variable [IsFiniteKernel κ] {a : α}
lemma rnDeriv_eq_rnDeriv_measure : rnDeriv κ η a =ᵐ[η a] ∂(κ a)/∂(η a) :=
eq_rnDeriv_measure (rnDeriv_add_singularPart κ η).symm (measurable_rnDeriv κ η) a
(mutuallySingular_singularPart κ η a)
lemma singularPart_eq_singularPart_measure : singularPart κ η a = (κ a).singularPa... |
3,049 | lean_file_chunk | de28fc2f2252fe6f0b141177c2d83b53a7a8f6fe544cb1595e11e8083e4e06e2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Composition.AbsolutelyContinuous
/-!
# Condition for two kernels to be equal almost everywhere
We prove that two finite... |
12,709 | lean_file_chunk | 5db9100e769a695abf0dde381921028c18f35f14232e1336a59cb8e02a49c9c3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap
public import Mathlib.Probability.Kernel.MeasurableLIntegral
/-!
# With Density
For an ... |
6,537 | lean_file_chunk | 886ca67522a15dbbea3d2e5bb60e89d9e34ec9e551f0ed9f682acbe307a3f971 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies, Kalle Kytölä, Kin Yau James Wong. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Kalle Kytölä, Kin Yau James Wong
-/
module
public import Mathlib.Probability.Kernel.Composition.CompNotation
/-!
# Proper kernels
This ... |
16,453 | lean_file_chunk | 86cc303952224106142f80852a6bb21ace9705f7913da1210853314e04227403 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Measure.GiryMonad
/-!
# Markov Kernels
A kernel from a measurable space `α` to another measurable space `β` is a measurable ... |
5,660 | lean_file_chunk | a5c9b0a3b939ca727a0fdd52156472079aa4a214ce75b2d12561a81482a21eeb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Gaëtan Serré. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gaëtan Serré, Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Constructions.Polish.Basic
public import Mathlib.MeasureTheory.Constructions.UnitInterval
public import Mathlib.... |
2,716 | lean_file_chunk | d7729227a099d1508f95f720dff9d5a52d424486af4a83b26c27c22cd27331ae | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Bryan Wang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bryan Wang
-/
module
public import Mathlib.Probability.Kernel.Composition.Comp
/-!
# Irreducibility of kernels
A kernel `κ : Kernel α α` is `φ`-irreducible, for a given measure `φ` on `... |
2,311 | lean_file_chunk | 77d604a862a582e3b93dc5cbd343960f33fcfd3c5b6f9313fc79b043c32f2787 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Matteo Cipollina
-/
module
public import Mathlib.Probability.Kernel.Composition.MeasureComp
/-!
# Invariance of measures along a kernel
We say that a measure `μ` is invari... |
15,461 | lean_file_chunk | 5374ca0da2227a337c375466f3345a8528eebd4fd4dfea4b6a204f524c573d1f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.CompProdEqIff
public import Mathlib.Probability.Kernel.Composition.Lemmas
public import Mathlib.Probability.Kernel.Disint... |
9,085 | lean_file_chunk | 98e5d7129dd593220293084d3798aca8a3c4a1024313bddb8bc349e3fd023f86 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying
-/
module
public import Mathlib.Probability.Process.Adapted
/-!
# Predictable σ-algebra
This file defines the predictable σ-algebra associated to a filtration, as well as t... |
12,445 | lean_file_chunk | c5215080aadb074921213d73de8e6242bebc872f6e12cf32a3a15f51b5be3cfd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
module
public import Mathlib.Probability.Process.Filtration
public import Mathlib.Topology.Instances.Discrete
/-!
# Adapted and progressively measurable pro... |
21,451 | lean_file_chunk | 02761d81fc892ab34d195538d2a0215d09aa227a1d574b7cf05dfbb4dcb533ee | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Constructions.Cylinders
public import Mathlib.MeasureTheory.Function.ConditionalExpectation.Real
public import Mat... |
23,985 | lean_file_chunk | 6432c0d5cb29c578be6b8c9f23843c2dc9cdcb68610de0d027ae4ec91e9454f6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
module
public import Mathlib.Probability.Process.Adapted
public import Mathlib.MeasureTheory.Constructions.BorelSpace.WithTop
public import Mathlib.Data.ENat... |
23,980 | lean_file_chunk | cd00c4f2455665cc451bb1576795e331e6ff45afa5f5de96b2c0168a2fa0c135 | lean_source_file | pkg_mathlib_source_file_chunks | rw [@eq_comm _ i, or_comm]
rw [this]
exact (hτ.measurableSet_eq' i).union (hτ.measurableSet_gt' i)
protected theorem measurableSet_lt' [TopologicalSpace ι] [OrderTopology ι]
[FirstCountableTopology ι] (hτ : IsStoppingTime f τ) (i : ι) :
MeasurableSet[hτ.measurableSpace] {ω | τ ω < i} := by
have : {ω | τ ... |
12,920 | lean_file_chunk | 62dc7810ad865a86583927ce46bd016557ab1b51f0df92c3f6b1e050c069aa7b | lean_source_file | pkg_mathlib_source_file_chunks | lift τ ω to ι using h_top with i hi
exact ⟨i, mod_cast hbdd, rfl⟩
theorem integrable_stoppedValue_of_mem_finset (hτ : IsStoppingTime ℱ τ)
(hu : ∀ n, Integrable (u n) μ) {s : Finset ι} (hbdd : ∀ ω, τ ω ∈ WithTop.some '' s) :
Integrable (stoppedValue u τ) μ := by
simp_rw [← memLp_one_iff_integrable] at hu ⊢
... |
15,236 | lean_file_chunk | a2d42ba8f16bf7f01609e2066cc5a18a98e51cddf47e5f693616fd8b82284c31 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Rémy Degenne, Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Kexing Ying
-/
module
public import Mathlib.Probability.Process.Stopping
/-! # Local properties of processes
This file defines local and stable properties o... |
6,272 | lean_file_chunk | c66adb8c51754d30591c309028fb9b3ac64d0867ed33659cf8a231a50f4e81ea | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated
public import Mathlib.Probability.Process.Filtration
/-!
# Filtration built from the finit... |
7,919 | lean_file_chunk | ec2fcfea791f5b6a5feeb9785a7e763261c39d4ead97156933f69a3347bed1cd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Function.SpecialFunctions.Basic
public import Mathlib.MeasureTheory.Function.StronglyMeasurable.AEStronglyMeasurable
public im... |
23,218 | lean_file_chunk | 5f78627b8fabd8bd061ffc3640f41a14434d0acc175eb5833ddad8b902190418 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
module
public import Mathlib.Probability.Process.Stopping
public import Mathlib.Tactic.AdaptationNote
/-!
# Hitting times
Given a stochastic process, the h... |
4,976 | lean_file_chunk | 34494a733634055be0eb8d8fbb74e04f5710e4a6d9094ae9e323efc300c91d34 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Jonas Bayer
-/
module
public import Mathlib.MeasureTheory.Constructions.Projective
public import Mathlib.Probability.IdentDistrib
/-!
# Finite-dimensional distributions o... |
23,946 | lean_file_chunk | 562ce48dbd20a01c7deab022657354540590da55bb62fefcde257ac70d03124a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Independence.Kernel.Indep
public import Mathlib.MeasureTheory.MeasurableSpace.Pi
public import Mathlib.Probability.ConditionalPr... |
10,865 | lean_file_chunk | aa76ef152968d5d85fd4732ef50f9adc12b1172600fd86ae498f40221d15216d | lean_source_file | pkg_mathlib_source_file_chunks | exact iIndepFun.congr' hf_indep fun i ↦ Measure.ae_ae_of_ae_comp (hf_meas i).ae_eq_mk
refine IndepFun.congr' h ?_ ?_
· filter_upwards [Measure.ae_ae_of_ae_comp (hf_meas i).ae_eq_mk,
Measure.ae_ae_of_ae_comp (hf_meas j).ae_eq_mk] with a hi hj
filter_upwards [hi, hj] with ω hωi hωj
rw [← hωi, ← hωj]
·... |
23,930 | lean_file_chunk | b4a0316d06c20f5d9fb7c0dabf058cea279257206d4e1dcf1bb66f0b75690717 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Basic
public import Mathlib.Tactic.Peel
public import Mathlib.Analysis.Normed.Group.Basic
/-!
# Independence of families... |
14,040 | lean_file_chunk | b7148f0c53e97821df991242160f9f1eea325806f1abb3197a36f164127081a1 | lean_source_file | pkg_mathlib_source_file_chunks | ⋂ i ∈ p1 ∪ p2, ite (i ∈ p1) (f1 i) Set.univ ∩ ite (i ∈ p2) (f2 i) Set.univ := by
ext1 x
simp only [Set.mem_ite_univ_right, Set.mem_inter_iff, Set.mem_iInter, Finset.mem_union]
exact
⟨fun h i _ => ⟨h.1 i, h.2 i⟩, fun h =>
⟨fun i hi => (h i (Or.inl hi)).1 hi, fun i hi => (h i (Or.inr h... |
302 | lean_file_chunk | 57697b5ca267da9da953be2345c9a0c1e47505423cf75649ecb6c7269ba3d784 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion, Joris van Winden
-/
module
public import Mathlib.Probability.Independence.Process.HasIndepIncrements.Basic
deprecated_module (since := "2026-03-30") |
23,976 | lean_file_chunk | 6d1609939ed4de3468908884464a27821edb5da7a822622d52180ec04450a373 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.MeasureTheory.Constructions.Cylinders
public import Mathlib.Probability.Independence.Basic
/-!
# Independence of stochastic processes
... |
71 | lean_file_chunk | 547e4a7a0777b7993394118687b2ecf3f4240bb51c2ed8513e8257334750c919 | lean_source_file | pkg_mathlib_source_file_chunks | Kernel.iIndepFun.iIndepFun_process₀ (by simpa) h
end ProbabilityTheory |
5,132 | lean_file_chunk | d7cc17de4655ebd243fe4665cde202c79a955a1beef06d45910df9c16cbedb6f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion, Joris van Winden
-/
module
public import Mathlib.Probability.Independence.Basic
import Mathlib.MeasureTheory.Constructions.BorelSpace.ContinuousLinearMap
/-!
# Stoch... |
6,211 | lean_file_chunk | 30faca09fc5bbf15dcad91df4edd2cfd6e1e19fc7a368fdd6db69c49c5a89834 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Def
public import Mathlib.Probability.Independence.Process.HasIndepIncrements.Basic... |
3,857 | lean_file_chunk | bd112dda6ea59ff07f9f1688a8a63289b5444a04e7cfa5af48cf0f99b834382c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies
-/
module
public import Mathlib.Data.Sym.Card
public import Mathlib.MeasureTheory.Constructions.SimpleGraph
public import Mathlib.Probability.Distributions.SetBernoulli
/-... |
11,478 | lean_file_chunk | fc0792c1e66be6d4b755c424b9029ae0ae32879ea969098248cf0377c3bec402 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.Probability.Decision.Risk.Defs
public import Mathlib.Probability.Kernel.Composition.MeasureComp
/-!
# Basic properties of... |
4,899 | lean_file_chunk | aabadfb5cb2e1409d47da700ccb7e9163b2cdce3f0347bcd12f90af7e26d75c1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.Probability.Kernel.Composition.Comp
/-!
# Risk of an estimator
An estimation problem is defined by a parameter space `Θ`... |
11,316 | lean_file_chunk | 7a96cd37992534a344bc3ca4e8f72242f7ca0ae1d3bf892bfac91149f7d1db36 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Distributions.Gaussian.Real
/-!
# Gaussian distributions in Banach spaces
We introduce a predicate `IsGaussian` for measures o... |
11,626 | lean_file_chunk | 642e713dff8cfc719f2796c78fec5fe6ea31031ea63aae86a0067bd7c826b9ac | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Distributions.Fernique
public import Mathlib.Probability.Distributions.Gaussian.Basic
/-!
# Fernique's theorem for Gaussian mea... |
8,848 | lean_file_chunk | 6a66083230f8ba1caa5248ff99fb46b2be8aa921a0495094b473ad3d9150fbb9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Probability.Distributions.Gaussian.Basic
public import Mathlib.Probability.Moments.CovarianceBilin
import Mathlib.Probability.Distribut... |
12,474 | lean_file_chunk | ef43c1b9bac4a4af8b21a007e7198e7d93bb435774f0970cff3e996a80a1eaa3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Etienne Marion
-/
module
public import Mathlib.Analysis.CStarAlgebra.Matrix
public import Mathlib.MeasureTheory.Measure.CharacteristicFunction.Basic
public import Mathlib.... |
23,939 | lean_file_chunk | 7b7cc529a39576c1f92a2f067c4ff493661dd914fab757622af5ee5296ce9d46 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lorenzo Luccioli, Rémy Degenne, Alexander Bentkamp
-/
module
public import Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform
public import Mathlib.Probability.HasLaw
public im... |
3,995 | lean_file_chunk | b9afd9335be76354dab1f0f5a0c8a84b89ea6e1c40e6c617ddef7122b97b0cd5 | lean_source_file | pkg_mathlib_source_file_chunks | /-- The variance of a real Gaussian distribution `gaussianReal μ v` is
its variance parameter `v`. -/
@[simp]
lemma variance_id_gaussianReal : Var[id; gaussianReal μ v] = v :=
variance_fun_id_gaussianReal
/-- All the moments of a real Gaussian distribution are finite. That is, the identity is in Lp for
all finite `p... |
6,091 | lean_file_chunk | e864a88cea91eec471d780ac22778931dda1669d27612ec9a677d303db5bcf29 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Josha Dekker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Josha Dekker, Etienne Marion
-/
module
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.Probability.ProbabilityMassFunction.Basic
import Mathlib.Analysi... |
4,258 | lean_file_chunk | 4e8249249bbeba76db6e2c253607aaddb95a70600cbe4f30d237c7e9d82ccdb1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Yi Yuan. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yi Yuan
-/
module
public import Mathlib.Probability.Distributions.Poisson.Basic
public import Mathlib.Probability.ProbabilityMassFunction.Binomial
import Mathlib.Algebra.Order.Ring.Star
imp... |
1,015 | lean_file_chunk | afc8c7785165247b9455adb5e4e0fcd7ad10b9687c628e91ef82d70b0eedf169 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Probability.Distributions.Gaussian.Basic
/-!
# Gaussian random variables
In this file we define a predicate `HasGaussianLaw X P`, whic... |
19,980 | lean_file_chunk | a441866b226b6142efeb29115cabae123cb2246d0556efaf5f7231bfb57fe0c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Def
public import Mathlib.Probability.HasLaw
import Mathlib.Probability.Distributions.... |
9,067 | lean_file_chunk | 89fbe8ec2efa34b6eab50795b6ee932bbfa963fea9b87319da424b768d91a6fb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Def
public import Mathlib.Probability.HasLaw
import Mathlib.Probability.Distributions... |
985 | lean_file_chunk | ddaa10a5df972370bcc1d137c39410437c0d623b49fa7daeac705ee989d0012e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Def
/-!
# Gaussian processes
In this file we define a **Gaussian process** as a stoc... |
8,328 | lean_file_chunk | 176a3701cd09019852b41c95156b1e34b6eb453d821171af074fd04cf8b53fa9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Def
import Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic
import ... |
6,404 | lean_file_chunk | 0e4869d4f1cc20e1b67c8d4a262c13be95f8f96ba41db69204ca1c6887ebf156 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.Probability.Distributions.Gaussian.IsGaussianProcess.Def
import Mathlib.Probability.Distributions.Gaussian.HasGaussianLaw.Basic
import ... |
2,430 | lean_file_chunk | cecf90b355046d49f8023cafc6f90426e755c7648eba94bfaf3870f52c8ad1ed | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Gaëtan Serré. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gaëtan Serré
-/
module
public import Mathlib.CategoryTheory.MarkovCategory.Basic
public import Mathlib.CategoryTheory.CopyDiscardCategory.Widesubcategory
public import Mathlib.Probabil... |
9,043 | lean_file_chunk | 4c5abfdd63c63917ecbe11ee2d565d72ebd557d249c8a840f2e887e12dd46017 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Gaëtan Serré. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Gaëtan Serré
-/
module
public import Mathlib.CategoryTheory.CopyDiscardCategory.Basic
public import Mathlib.Probability.Kernel.Composition.KernelLemmas
/-!
# SFinKer
The category of m... |
6,880 | lean_file_chunk | bb2ac90d2e859b65b841cd6a2035f667d2af6198477db9767a280bcf4e462d9d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.MeasureTheory.MeasurableSpace.Embedding
public import Mathlib.Order.Restriction
/-! # Auxiliary maps for Ionescu-Tulcea theorem
This f... |
23,952 | lean_file_chunk | 0b7f6bb297358b44f191d3c361007b94f8006c3d803fbf11880aa51557a8aea9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.MeasureTheory.Constructions.ProjectiveFamilyContent
public import Mathlib.MeasureTheory.Function.FactorsThrough
public import Mathlib.Me... |
14,825 | lean_file_chunk | 96e64c72aa96f51fc66a0bf6ace69bbde165bb6b4c4006beca0a095150e56528 | lean_source_file | pkg_mathlib_source_file_chunks | rw [Measure.map_apply (measurable_frestrictLe n) ms, trajFun, AddContent.measure_eq, trajContent,
projectiveFamilyContent_congr _ (frestrictLe n ⁻¹' s) rfl ms]
· exact generateFrom_measurableCylinders.symm
· exact cylinder_mem_measurableCylinders _ _ ms
variable {κ} in
theorem measurable_trajFun (a : ℕ) : Meas... |
20,811 | lean_file_chunk | 586258c7ceb8e87e0ef5d719f859304cf7bd454fb5da0363dcd25f00f0f9040c | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Etienne Marion. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Etienne Marion
-/
module
public import Mathlib.MeasureTheory.MeasurableSpace.PreorderRestrict
public import Mathlib.Probability.Kernel.Composition.Prod
public import Mathlib.Probabili... |
23,986 | lean_file_chunk | e67ad4de15f0551be7ad0b8d5a9709c8f17608dd4e830ee4f1e1a9ac712b5257 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Function.AEEqOfIntegral
public import Mathlib.Probability.Kernel.Composition.CompProd
public import Mathlib.Probability.Kernel... |
7,024 | lean_file_chunk | 11179fa68c1e27d87e0229b44a62ca949741ea98a2d6ad8f55122cab86ed443a | lean_source_file | pkg_mathlib_source_file_chunks | (a : α) {s : Set β} (hs : MeasurableSet s) :
∫⁻ b in s, hf.toKernel f (a, b) univ ∂(ν a) = κ a (s ×ˢ univ) := by
rw [← Real.iUnion_Iic_rat, prod_iUnion]
have h_dir : Directed (fun x y ↦ x ⊆ y) fun q : ℚ ↦ Iic (q : ℝ) := by
refine Monotone.directed_le fun r r' hrr' ↦ Iic_subset_Iic.mpr ?_
exact mod_cast ... |
22,110 | lean_file_chunk | 33b085738e10e7940b06f22fe153f98b671747f4db9f442c429ba9638f2a014e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Measure.GiryMonad
public import Mathlib.MeasureTheory.Measure.Stieltjes
public import Mathlib.Analysis.Normed.Order.Lattice
pu... |
10,752 | lean_file_chunk | dafd3ea2d3f669532f39a549af9b4a7c4fd7a6abf9208e3b2cea83090ce520aa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Composition.IntegralCompProd
public import Mathlib.Probability.Kernel.Disintegration.StandardBorel
/-!
# Lebesgue and Bo... |
23,980 | lean_file_chunk | 040eee304cf843ea1d2cfc8e35f9be11c8cc347305cd10a49e84f1131efbda45 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Composition.MapComap
public import Mathlib.Probability.Martingale.Convergence
public import Mathlib.Probability.Process.P... |
13,765 | lean_file_chunk | d9fd8891614c6105909c6c55cdb84096133e8e48c966691c7870ee79bb6c74f0 | lean_source_file | pkg_mathlib_source_file_chunks | · exact Eventually.of_forall (fun n ↦ densityProcess_mono_set hκν n a x h)
· exact isCoboundedUnder_le_of_le atTop (fun i ↦ densityProcess_nonneg _ _ _ _ _ _)
· exact isBoundedUnder_of ⟨1, fun n ↦ densityProcess_le_one hκν _ _ _ _⟩
lemma density_nonneg (hκν : fst κ ≤ ν) (a : α) (x : γ) (s : Set β) :
0 ≤ densit... |
9,415 | lean_file_chunk | 405cadd882fe26286ad64efdf422cb33fe741002b8311ccfb1cb750dad6ae45b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yaël Dillies, Kin Yau James Wong. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Kin Yau James Wong, Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Function.AEEqOfLIntegral
public import Mathlib.Probability.Kernel.Compos... |
8,107 | lean_file_chunk | cc6c047f4a64aa5d55cab193cfbee50ce58a7d2c54d0caa6881dc835bcce3d98 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kexing Ying. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kexing Ying, Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Disintegration.Integral
/-!
# Uniqueness of the conditional kernel
We prove that the conditional kernels `P... |
15,524 | lean_file_chunk | ad8b0700828fb8daae7bafba26d0fbfe8e1f2fb046fb0fcb0df48e2a5d0340ec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym
public import Mathlib.MeasureTheory.Measure.Prod
public import Mathlib.Probability.Kernel.D... |
19,468 | lean_file_chunk | 0fbb3d2336abb23367dd87260b2cca5171ec2c31dcc38ee75de94037968abf83 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Composition.MeasureCompProd
public import Mathlib.Probability.Kernel.Disintegration.Basic
public import Mathlib.Probabili... |
9,563 | lean_file_chunk | f05d1124f7560a9604cd6dd1f5033732a3790417b14b59e27e123b640ce137e4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Etienne Marion
-/
module
public import Mathlib.Probability.Kernel.MeasurableLIntegral
/-!
# Composition of kernels
We define the composition `η ∘ₖ κ` of kernels `κ : Ker... |
6,310 | lean_file_chunk | 0e0d273705ffa0068d4c7fe6c53a7013e746809796556431d5783a5df3738e29 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.Probability.Kernel.Composition.MeasureComp
/-!
# Lemmas relating different ways to compose measures and kernels
This fil... |
10,753 | lean_file_chunk | 015d28363f0979ac0d7682dc55f8cc941db7695972fd3fdbe063c8cc4eb562d9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Composition.CompMap
public import Mathlib.Probability.Kernel.Composition.ParallelComp
/-!
# Product and composition of k... |
17,144 | lean_file_chunk | 207bd3fdd28c5516e66406413106b963a20e0005b211016624ac8bc854ee0a7a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue
public import Mathlib.MeasureTheory.Measure.Prod
public import Mathlib.Probability.Kernel.Compo... |
23,944 | lean_file_chunk | aacb4da4dd6405feaaa82902e76eef328b2ec7c72f36b7990d48c1f76678d32b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.Probability.Kernel.Basic
/-!
# Map of a kernel by a measurable function
We define the map and comap of a kernel along a ... |
2,811 | lean_file_chunk | 106b9f67ab4e158b915e60b56f46ef0651be41ac39e7a188366dea234e0757b4 | lean_source_file | pkg_mathlib_source_file_chunks | lemma sectL_prodMkLeft (α : Type*) [MeasurableSpace α] (κ : Kernel β γ) (a : α) {b : β} :
sectL (prodMkLeft α κ) b a = κ b := rfl
@[simp]
lemma sectL_prodMkRight (β : Type*) [MeasurableSpace β] (κ : Kernel α γ) (b : β) :
sectL (prodMkRight β κ) b = κ := rfl
/-- Define a `Kernel β γ` from a `Kernel (α × β) γ` ... |
5,123 | lean_file_chunk | 4d5c7a26ff2682e7cdfe78a8326a189006e76fce1c02ea2ceb2451375c9ff8e0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Composition.MeasureCompProd
import Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym
/-!
# Radon-Nikodym derivat... |
23,935 | lean_file_chunk | 7a4ce806831568c0732b8a0c8dbfbcb8261d8837953e54355dddd5f64fdd93b9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Etienne Marion
-/
module
public import Mathlib.Probability.Kernel.Composition.MeasureComp
public import Mathlib.Probability.Kernel.MeasurableIntegral
/-!
# Bochner integr... |
711 | lean_file_chunk | 40553e507a6f04a9e46a54b933a94d43775d6ffc1a925cefb09e6205ee85e2d6 | lean_source_file | pkg_mathlib_source_file_chunks | Integrable (fun p ↦ f p.2) (μ ⊗ₘ κ) ↔ Integrable f (κ ∘ₘ μ) := by
rw [← Measure.snd_compProd, Measure.snd, integrable_map_measure _ measurable_snd.aemeasurable,
Function.comp_def]
rwa [← Measure.snd, Measure.snd_compProd]
lemma ae_integrable_of_integrable_comp (h_int : Integrable f (κ ∘ₘ μ)) :
∀ᵐ x ∂μ, Int... |
3,773 | lean_file_chunk | 6ef09b9ea2183ec95a77d8db816f04806f4dd7d89d8e81c9e10253f23981e3bc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.Probability.Kernel.Composition.MeasureCompProd
public import Mathlib.Probability.Kernel.RadonNikodym
/-!
# Absolute conti... |
6,070 | lean_file_chunk | 0cd46ba9610de191245bac2ed788af178e39b8aa4673047f22b0fbfa59fc5033 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.Probability.Kernel.Composition.CompProd
public import Mathlib.Probability.Kernel.Composition.Prod
/-!
# Lemmas relating d... |
6,711 | lean_file_chunk | c137b9a19a2ea520cc12b0b53afe63e0026ded89cd96f400dcc152bd29effa3d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.MeasureTheory.Measure.Prod
public import Mathlib.Probability.Kernel.Composition.MapComap
public import Mathlib.Probability... |
1,942 | lean_file_chunk | 435648ef6fb7ff9058febacead571d60e67d5c7e2ec2da9a0f190c032a937f20 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.Probability.Kernel.Basic
/-!
# Notation for the composition of a measure and a kernel
This operation, for which we intro... |
23,905 | lean_file_chunk | 8d9a53f0d5409d2c0228d255cc8cb69331af21a30224f7a83612970ed5353ec5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Composition.Comp
public import Mathlib.Probability.Kernel.Composition.ParallelComp
/-!
# Composition-product of kernels
... |
216 | lean_file_chunk | 5b2a816a6aa9b4f4b4e2ded5fa4cf2d49d50788e3c4ace294c6df93f2f5bbd54 | lean_source_file | pkg_mathlib_source_file_chunks | lemma fst_compProd (κ : Kernel α β) (η : Kernel (α × β) γ) [IsSFiniteKernel κ] [IsMarkovKernel η] :
fst (κ ⊗ₖ η) = κ := by
ext x s hs; simp [fst_compProd_apply, hs]
end FstSnd
end Kernel
end ProbabilityTheory |
2,853 | lean_file_chunk | fa16d9a4048e5d9a07ce150b44c00a9ca71adef0953cb8fdafe79346b56f759b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne
-/
module
public import Mathlib.Probability.Kernel.Composition.Comp
public import Mathlib.Probability.Kernel.Composition.MapComap
/-!
# Lemmas about compositions and maps ... |
8,187 | lean_file_chunk | 4543c963fc26954aab0f785170bde7d903518aa63daf84b0c3b4b1091e05b035 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Lorenzo Luccioli
-/
module
public import Mathlib.Probability.Kernel.Composition.CompNotation
public import Mathlib.Probability.Kernel.Composition.KernelLemmas
public impor... |
6,021 | lean_file_chunk | 7b64281a1211d9b24492890528ad82624c0552b8229510a939ea9e9a21961ba2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Mario Carneiro. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Heather Macbeth
-/
module
public import Mathlib.Util.AtomM
/-!
# Running `AtomM` metaprograms recursively
Tactics such as `ring` and `abel` are implemented using the... |
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