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 |
|---|---|---|---|---|---|
18,265 | lean_file_chunk | 572b9c3ca45cf2a550bd400398533f81b68ad2f9a5d0c12c30100da0d5bfd440 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández
-/
module
public import Mathlib.Analysis.Normed.Unbundled.RingSeminorm
/-!
# seminormFromBounded
In this file, we prove [BGR, Propositi... |
15,333 | lean_file_chunk | d40f0682bf6c3ea7fdd19a50a4e1fe2ca51b1db0823218ebe31f99abe761cbdc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 María Inés de Frutos-Fernández. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández, Yaël Dillies
-/
module
public import Mathlib.Algebra.Order.Ring.IsNonarchimedean
public import Mathlib.Analysis.Normed.Field.Lemmas
pub... |
7,665 | lean_file_chunk | a62abf371d1a431d940e19a8a3194e03d6df5d98bb012af623953613abe4fe19 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
module
public import Mathlib.Analysis.Normed.Group.Uniform
public import Mathlib.Analysis.Normed.MulAction
public import Mathlib.Li... |
12,023 | lean_file_chunk | a18f88b1c8870774ae65d594f3714a15e7e3a3fa0f0e32594ecc332fd2337793 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Bhavik Mehta. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Bhavik Mehta
-/
module
public import Mathlib.Algebra.Order.Ring.Star
public import Mathlib.Analysis.Normed.Module.RieszLemma
public import Mathlib.Analysis.Normed.Operator.Banach
public... |
16,901 | lean_file_chunk | b38df96a84d2bc39f3cc91fd91928cff18a57e60e8cd7d16d57a8c7945e76c06 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
module
public import Mathlib.Analysis.Normed.Operator.Basic
public import Mathlib.Analysis.Normed.Operator.LinearIsometry
public im... |
2,480 | lean_file_chunk | bf06640a8a2dc55b28981357f24e4599bbdf1a5f4940723c74fd551c28bf0475 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
module
public import Mathlib.Analysis.Normed.Operator.Basic
public import Mathlib.Analysis.Asymptotics.Defs
/-!
# Asymptotic statem... |
21,702 | lean_file_chunk | 1e1af6baa2c7c504d69103f22c49dd0b508cddb5985a203607494cbf238a8f31 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
module
public import Mathlib.Analysis.LocallyConvex.Bounded
public import Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap
/-!
# Compact operators
In... |
6,365 | lean_file_chunk | ed4deb91f31b4c70f933679296a90583ac87d55972b6a4ced4ef81b702df4a11 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
module
public import Mathlib.Analysis.Normed.Operator.Bilinear
/-!
# Operator norm: Cartesian products
Interaction of operator no... |
3,663 | lean_file_chunk | 0a9ca11f596c919281377d3345eb14aec8319ed24b1150571b2ed464ddea6bc6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Algebra.Central.Defs
public import Mathlib.Analysis.LocallyConvex.SeparatingDual
public import Mathlib.Analysis.Normed.Module.Mult... |
9,324 | lean_file_chunk | 109eb45c4ba8f15a82eb5466818a0d4ec6d5b19044f2e63cecdc7d3e6cd97386 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
module
public import Mathlib.Analysis.Normed.Operator.Basic
public import Mathlib.Analysis.Normed.Module.RCLike.Real
/-!
# Operato... |
9,096 | lean_file_chunk | 327ebc3553152b9a7c91e108c037e24045fb20a2323f517a3178382fcc83e239 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
module
public import Mathlib.Algebra.Algebra.Bilinear
public import Mathlib.Analysis.Normed.Operator.NormedSpace
/-!
# Results abo... |
21,633 | lean_file_chunk | 0b5b07e4af5e652b2a5fe8cee5ba4629a4aecaad2481939fe0dfb264bc5baebf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
module
public import Mathlib.Algebra.Algebra.Tower
public import Mathlib.Analysis.LocallyConvex.WithSeminorms
public import Mathlib... |
12,150 | lean_file_chunk | 628b31e78c75da0125c10d56104b43de24c9066e2eb2bc3ac137849d23fcd604 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Monica Omar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Monica Omar
-/
module
public import Mathlib.Analysis.InnerProductSpace.Adjoint
public import Mathlib.Analysis.InnerProductSpace.Positive
public import Mathlib.Analysis.LocallyConvex.Sepa... |
9,256 | lean_file_chunk | 0c3a87b82c43e5434c5dfd0712dc691bc92ae02b9e0dbaec20cd36fc98cb3823 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
module
public import Mathlib.Analysis.Normed.Operator.Bilinear
public import Mathlib.Analysis.Normed.Operator.NNNorm
/-!
# Operato... |
23,986 | lean_file_chunk | a2bab3e48e767262b1ae859a0ec218b1c3d678e0b030bd77c34ed56ace368f35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Algebra.Algebra.Spectrum.Basic
public import Mathlib.Topology.Baire.Lemmas
public import Mathlib.Topology.Baire.CompleteMetrizable... |
2,903 | lean_file_chunk | 5fb20804491c54cd6110cd1d805606ffd11b1906696979d16e3fbbe534093a85 | lean_source_file | pkg_mathlib_source_file_chunks | refine hg (Prod.fst ∘ φ) x y ((continuous_fst.tendsto _).comp hφ) ?_
have : g ∘ Prod.fst ∘ φ = Prod.snd ∘ φ := by
ext n
exact (hφg n).symm
rw [this]
exact (continuous_snd.tendsto _).comp hφ
variable {g}
namespace ContinuousLinearMap
/-- Upgrade a `LinearMap` to a `ContinuousLinearMap` using the **close... |
3,283 | lean_file_chunk | d218d347ac2eae0693d1256e5a85ea88a8e30902ccf846d75ebcf0918b398c8b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
module
public import Mathlib.Analysis.Normed.Module.Basic
public import Mathlib.Analysis.Normed.Operator.LinearIsometry
/-!
# Conformal Linear Maps
A continuous linear... |
15,986 | lean_file_chunk | a283ecd26f3da5ac89fa4213659783ae24c963e381a63cc7c2281cbee9dd7b8f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Sébastien Gouëzel, Jean Lo
-/
module
public import Mathlib.Analysis.Normed.Module.Span
public import Mathlib.Analysis.Normed.Operator.Bilinear
public import Math... |
2,232 | lean_file_chunk | 07cd12191832afa3fb12b9240d625e07b7bd9cdc25001a31948850c1008308b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Analysis.Normed.Operator.NormedSpace
public import Mathlib.Analysis.LocallyConvex.Barrelled
public import Mathlib.Topology.Baire.CompleteM... |
15,298 | lean_file_chunk | 7c43be9503fee61144ea0f8bf86e0668d7f5970c4b6d38f0642045dbb61def9d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Zhouhang Zhou
-/
module
public import Mathlib.Analysis.Normed.Operator.Basic
public import Mathlib.LinearAlgebra.Isomorphisms
/-!
# Extension of continuous linear maps on ... |
23,043 | lean_file_chunk | 4b31a165517a82551a6ee9034d2a9923451002405d9e2a363f48809884ffb7d6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
module
public import Mathlib.Analysis.Normed.Module.Multilinear.Basic
public import Mathlib.Analysis.Normed.Ring.Units
public import Mathlib.Analysis... |
23,949 | lean_file_chunk | 69a4214cf5a257a684fd6110f276c6471ff7b8c3ed9a90faad483af7d110fd7f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Frédéric Dupuis, Heather Macbeth
-/
module
public import Mathlib.Algebra.Star.Basic -- shake: keep (used in `notation` only)
public import Mathlib.Analysis.Normed.G... |
14,242 | lean_file_chunk | 83f81a4b2d7fdf9b8f062f4bb632786700032c2d64ddd5292cc660dda947c268 | lean_source_file | pkg_mathlib_source_file_chunks | e.symm.toContinuousLinearEquiv = e.toContinuousLinearEquiv.symm := rfl
@[simp]
theorem coe_symm_toContinuousLinearEquiv : ⇑e.toContinuousLinearEquiv.symm = e.symm :=
rfl
@[simp]
theorem toIsometryEquiv_symm : e.symm.toIsometryEquiv = e.toIsometryEquiv.symm :=
rfl
@[simp]
theorem coe_symm_toIsometryEquiv : ⇑e.toI... |
7,209 | lean_file_chunk | 486491da54a82fd448e0d2b6b5f94c0226139f818db049aae7456b32cc3f0b8f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Analysis.Normed.Algebra.Exponential
public import Mathlib.Analysis.Matrix.Normed
public import Mathlib.LinearAlgebra.Matrix.ZPow
public import... |
1,980 | lean_file_chunk | 4e4bcda9b74c4c24beedb3a375a75ec396b98fb838a13ddae05d8bcc78c80213 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jiedong Jiang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiedong Jiang
-/
module
public import Mathlib.Analysis.Normed.Field.Ultra
public import Mathlib.Analysis.Normed.Module.Basic
/-!
# Normed algebra preserves ultrametricity
This file c... |
5,373 | lean_file_chunk | 05063f01279ee5913058c071663bdc434e0e528f4c8e944a648343db8fad33e1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Algebra.Algebra.TransferInstance
public import Mathlib.Algebra.Algebra.Unitization
public import Mathlib.Analysis.Normed.Lp.ProdLp
/-! # ... |
23,970 | lean_file_chunk | 95777bd3785a1af551afde39a498f07015fa0d8133eda6b6d48a3d34816d20b3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Eric Wieser, Yuyang Zhao
-/
module
public import Mathlib.Algebra.Algebra.TransferInstance
public import Mathlib.Algebra.Ring.Action.ConjAct
public import Mathlib.A... |
5,424 | lean_file_chunk | afb1726e8a2b5b9909771d883dc46b0fe918e8b859c6c6d155fbc37c0d74c340 | lean_source_file | pkg_mathlib_source_file_chunks | induction s using Finset.induction_on with
| empty => simp
| insert a s ha ih =>
rw [Finset.noncommProd_insert_of_notMem _ _ _ _ ha, Finset.sum_insert ha, exp_add_of_commute,
ih (h.mono <| Finset.subset_insert _ _)]
refine Commute.sum_right _ _ _ fun i hi => ?_
exact h.of_refl (Finset.mem_insert_s... |
21,365 | lean_file_chunk | 3edda197d2f2547f6afedbf85ffd3bf7eb9358e95629ad89a63aff74a5eb6170 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Michael Stoll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Michael Stoll
-/
module
public import Mathlib.Analysis.Polynomial.Factorization
/-!
# A (new?) proof of the Gelfand-Mazur Theorem
We provide a formalization of proofs of the followin... |
1,970 | lean_file_chunk | 5414a2965e603695ea63435739a892164daf88d0054ff2dacbd764221c696840 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
module
public import Mathlib.Topology.Algebra.Module.Spaces.CharacterSpace
public import Mathlib.Analysis.Normed.Module.WeakDual
public import Mathlib.Analysis.Nor... |
10,376 | lean_file_chunk | 0e5ee5d2e8e6174cfe8368f10498130a49afa2a2abf965a665e4f75501368106 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Analysis.Normed.Algebra.Spectrum
public import Mathlib.Analysis.Calculus.Deriv.Basic
public import Mathlib.Analysis.Normed.Operator.Mul
im... |
5,824 | lean_file_chunk | 454812d82308d69a7edf1e66cb1e92a78f94e55d7882d991040998cc910fe05a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Analysis.Quaternion
public import Mathlib.Analysis.Normed.Algebra.Exponential
public import Mathlib.Analysis.SpecialFunctions.Trigonometric.Se... |
13,224 | lean_file_chunk | 91607e1607353c0f11e48774f4a201c2641a7ce4856bcca7c74adcc2629f5e71 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Algebra.Algebra.Unitization
public import Mathlib.Analysis.Normed.Operator.Mul
/-!
# Unitization norms
Given a not-necessarily-unital no... |
11,951 | lean_file_chunk | 12daf3931f2b32e425019fc1bb2735b53277799aef5dd034879497657b29612e | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Analysis.Normed.Algebra.Exponential
public import Mathlib.Analysis.Normed.Lp.ProdLp
public import Mathlib.Topology.Instances.TrivSqZeroExt
/-... |
855 | lean_file_chunk | a481ed2bc987cd5667683692abf9b53624ebd29e6c47e23f5ea10a96b736880d | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
module
public import Mathlib.Algebra.DualNumber
public import Mathlib.Analysis.Normed.Algebra.TrivSqZeroExt
/-!
# Results on `DualNumber R` related to the norm
These are... |
23,991 | lean_file_chunk | 95302daef64f1942a2d595913ea5c496231e68eec8e1c2cef451dc32b4bd80cd | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
module
public import Mathlib.Algebra.Algebra.Spectrum.Quasispectrum
public import Mathlib.Analysis.Real.Spectrum
public import Mathlib.Analysis.Normed.Algebra.Exponent... |
8,539 | lean_file_chunk | 7537b59420ea3c72cf46fe19bdaa5127f2e0659b864d97de60d654937e3f2d13 | lean_source_file | pkg_mathlib_source_file_chunks | /-- Let `S` be a closed subalgebra of a Banach algebra `A`, and let `x : S`. If `z` is in the
spectrum of `x`, then the connected component of `z` in the complement of the spectrum of `↑x : A`
is bounded (or else `z` actually belongs to the spectrum of `↑x : A`). -/
lemma Subalgebra.spectrum_isBounded_connectedComponen... |
1,690 | lean_file_chunk | 81cb5dc2b3b9567e75a0b7bd8211d891687d74b2f4e9cc98fe085fa9524470a0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Analysis.Normed.Order.Hom.Basic
public import Mathlib.Topology.MetricSpace.Ultra.Basic
/-!
# Constructing nonarchimedean (ultrametric... |
3,376 | lean_file_chunk | 7a041661c82a434dd4eecc9134667d68505c881ef96216edfefb30e7edf766ef | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Yakov Pechersky. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yakov Pechersky
-/
module
public import Mathlib.Algebra.Order.Hom.Basic
public import Mathlib.Analysis.Normed.Group.Basic
/-!
# Constructing (semi)normed groups from (semi)normed ho... |
4,394 | lean_file_chunk | d6e2e306ccc9028316b70a8c686645932b90246c31c9611eee9be92919165d42 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Johan Commelin
-/
module
public import Mathlib.Analysis.Normed.Group.SemiNormedGrp
public import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
public import Mat... |
13,033 | lean_file_chunk | 97ca8f095eb0674d4563ea1c8a8723c223ac2b9f9ba4eb0181d4468c5f4edde3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Johan Commelin, Kim Morrison
-/
module
public import Mathlib.Analysis.Normed.Group.SemiNormedGrp
public import Mathlib.Analysis.Normed.Group.Quotient
public import Math... |
5,010 | lean_file_chunk | 9fca0f4f71e98ff4ee52f39c63f0ab3aedce519d0497310672604c5c17d0977b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä
-/
module
public import Mathlib.Analysis.RCLike.Basic
public import Mathlib.Analysis.Normed.Module.RCLike.Real
public import Mathlib.Analysis.Normed.Module.Span
public impo... |
2,387 | lean_file_chunk | 68b7eef775482c7085b94e7f33f3a6d2bd11d1db6e848ec335a3b1eac32b62c2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Ruben Van de Velde. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ruben Van de Velde
-/
module
public import Mathlib.Analysis.RCLike.Extend
public import Mathlib.Analysis.Normed.Operator.Basic
/-!
# Norm properties of the extension of continuou... |
6,244 | lean_file_chunk | 25f83570d73d1b6fda557efba9ec00e07e7e2b69088c06593dc425f14c4e7917 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Patrick Massot, Eric Wieser, Yaël Dillies
-/
module
public import Mathlib.Analysis.Normed.Module.Basic
/-!
# Basic facts about real (semi)normed spaces
In this fil... |
23,979 | lean_file_chunk | 9c09280867b281b46567d83bff76e32f03f6a010fc7bd8a71ed89398834b91c4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Analysis.Normed.Module.Multilinear.Basic
public import Mathlib.LinearAlgebra.Multilinear.Curry
public import Mathlib.Analysis.Norm... |
6,014 | lean_file_chunk | 9696f933fd80b2c69a1fea702bd534fea0ef2c205b16d4072b3f44a735fab9cb | lean_source_file | pkg_mathlib_source_file_chunks | (ContinuousMultilinearMap 𝕜 (fun _ : ι' => G) G')) :
ContinuousMultilinearMap 𝕜 (fun _ : ι ⊕ ι' => G) G' :=
MultilinearMap.mkContinuous
(toMultilinearMapLinear.compMultilinearMap f.toMultilinearMap).uncurrySum ‖f‖ fun m => by
simpa [Fintype.prod_sum_type, mul_assoc] using
(f (m ∘ Sum.inl)).le_of_o... |
23,966 | lean_file_chunk | 689077ad3df6ab1c54ead559547f6cea2e50e4e2eee1fbcf56a6d54a8f114f1f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Sophie Morel, Yury Kudryashov
-/
module
public import Mathlib.Logic.Embedding.Basic
public import Mathlib.Data.Fintype.CardEmbedding
public import Mathlib.Topolo... |
23,951 | lean_file_chunk | 97abcf6d78bc52e5c9f107df3ab05e122626d13516710d900dcbcf68bc092ce1 | lean_source_file | pkg_mathlib_source_file_chunks | /-- An alias of `ContinuousMultilinearMap.normedSpace` with non-dependent types to help typeclass
search. -/
instance normedSpace' : NormedSpace 𝕜' (ContinuousMultilinearMap 𝕜 (fun _ : ι => G') G) :=
ContinuousMultilinearMap.normedSpace
end NormedField
/-- The fundamental property of the operator norm of a contin... |
10,710 | lean_file_chunk | 1bd6893f1110151e66cffdd4b2f6b6d02a138acae26bb023c3daaf70e2203cbc | lean_source_file | pkg_mathlib_source_file_chunks | simp only [compContinuousLinearMap_apply, smul_apply]
convert g.map_update_smul (fun j ↦ f j (x j)) i a (f₀ (x i)) <;>
exact apply_update (fun (i : ι) (f : E i →L[𝕜] E₁ i) ↦ f (x i)) f i _ _ }
(‖g‖) (fun f ↦ by simp [norm_compContinuousLinearMap_le])
@[simp]
theorem compContinuousLinearMapLRight... |
5,605 | lean_file_chunk | 08ca82bcdace97c711060d54030acb2ed6bf13c32ab997b5f61e1d7b39a737a7 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel
-/
module
public import Mathlib.Analysis.Normed.Module.Multilinear.Basic
public import Mathlib.LinearAlgebra.PiTensorProduct
/-!
# Projective seminorm on the tensor of a f... |
18,430 | lean_file_chunk | 0ae19630c7730379115e91e5a0dd5f530dce6db663dc11b2879808767f25ad84 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sophie Morel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sophie Morel
-/
module
public import Mathlib.Analysis.Normed.Module.PiTensorProduct.ProjectiveSeminorm
import Mathlib.LinearAlgebra.Isomorphisms
/-!
# Injective seminorm on the tensor ... |
3,596 | lean_file_chunk | 148a4ac5b81ce914fd8d999511ad152ed09cf2c64cbf8700013a6bce2b73a006 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Eric Wieser
-/
module
public import Mathlib.LinearAlgebra.Alternating.Curry
public import Mathlib.Analysis.Normed.Module.Alternating.Basic
public import Mathlib.Anal... |
23,976 | lean_file_chunk | 9e2bef9fc1ef6777a28795cfcb91d2841d4edbfb4cfd2ac87bdbd67c487b1ab9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yury Kudryashov, Heather Macbeth, Patrick Massot
-/
module
public import Mathlib.Topology.Algebra.Module.Alternating.Topology
public import Mathlib.Analysis.Norm... |
3,714 | lean_file_chunk | 3cf8a3021970006b99794e454cc9e25ae700872b6de16237a2b3dea501dfdc1b | lean_source_file | pkg_mathlib_source_file_chunks | theorem mkContinuousLinear_norm_le (f : F →ₗ[𝕜] E [⋀^ι]→ₗ[𝕜] G) {C : ℝ} (hC : 0 ≤ C)
(H : ∀ x m, ‖f x m‖ ≤ C * ‖x‖ * ∏ i, ‖m i‖) : ‖mkContinuousLinear f C H‖ ≤ C :=
(mkContinuousLinear_norm_le_max f C H).trans_eq (max_eq_left hC)
variable {ι' : Type*} [Fintype ι']
/-- Given a map `f : E [⋀^ι]→ₗ[𝕜] (F [⋀^ι']→... |
6,364 | lean_file_chunk | 172035614ec30c89a223de801d362ed2a1a6288f516fa1617e894fd57eb5a619 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Oliver Nash
-/
module
public import Mathlib.Topology.OpenPartialHomeomorph.Composition
public import Mathlib.Analysis.Normed.Group.AddTorsor
public import Mathlib.An... |
4,165 | lean_file_chunk | b57b98521dcabfbf24ae7305a5fbadf9abf300ddccae87308b367761319942bf | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.Normed.Module.Basic
public import Mathlib.Algebra.Ring.Action.Pointwise.Set
/-!
# Homeomorphism between a normed space and s... |
17,613 | lean_file_chunk | ac4aab983e172b1d38638f7037e8fecfcb13bb371cb9c16dd805433c777c44a9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yaël Dillies
-/
module
public import Mathlib.Analysis.Normed.Group.Pointwise
public import Mathlib.Analysis.Normed.Module.RCLike.Real
/-!
# Properties of pointw... |
7,667 | lean_file_chunk | d9f41be82e5da2cf71c8f0c8a22aabe0ec05deb9881e256d5fb8c2ccbe5605af | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
module
public import Mathlib.Analysis.Normed.Field.UnitBall
public import Mathlib.Analysis.Normed.Module.Basic
/-!
# Multiplicative actions of/on... |
10,910 | lean_file_chunk | 92f562f4ee26d9a529fb31a8b837837f63c5cc699a5c3c5b158247622873f199 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
module
public import Mathlib.Analysis.Normed.Module.Alternating.Curry
public import Mathlib.LinearAlgebra.Alternating.Uncurry.Fin
/-!
# Uncurrying continuous alte... |
2,210 | lean_file_chunk | a63d17f11bdad4bfeb97af155842e3ae5cbb5f3f0a7ab7c89008b006455ed684 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joachim Breitner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joachim Breitner
-/
module
public import Mathlib.Probability.ProbabilityMassFunction.Basic
public import Mathlib.Probability.ProbabilityMassFunction.Constructions
public import Math... |
11,577 | lean_file_chunk | 5615f7fdc6f4870912c7eed80efb1c18d0f0330ef435fb3a646e6c340be34836 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Devon Tuma
-/
module
public import Mathlib.Probability.ProbabilityMassFunction.Basic
/-!
# Monad Operations for Probability Mass Functions
This file constructs two opera... |
14,393 | lean_file_chunk | 60ee32cc250387c3122f2999d80484d61797f8cbac8708d7cbea1ea0d95462da | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Devon Tuma
-/
module
public import Mathlib.Topology.Instances.ENNReal.Lemmas
public import Mathlib.MeasureTheory.Measure.Dirac
/-!
# Probability mass functions
This ... |
10,828 | lean_file_chunk | d0391e07df1ae594406cf8ea9f03e5292ea24e7810a8287df6fb198646851aa3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2017 Johannes Hölzl. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johannes Hölzl, Devon Tuma
-/
module
public import Mathlib.Probability.ProbabilityMassFunction.Monad
public import Mathlib.Control.ULiftable
/-!
# Specific Constructions of Probabili... |
2,601 | lean_file_chunk | aaf2c59f51223d8ceaaaaa27a3e0d6cdc8f662358978416a62027145f669dfb6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Joachim Breitner. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joachim Breitner
-/
module
public import Mathlib.Data.Nat.Choose.Sum
public import Mathlib.Probability.ProbabilityMassFunction.Constructions
public import Mathlib.Tactic.FinCases
/... |
14,386 | lean_file_chunk | 5533accbd52d9ab6092847c14c5b0d919876e07e6e7e5ba6edc4084237ff550e | 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.LocallyConvex.ContinuousOfBounded
public import Mathlib.LinearAlgebra.BilinearForm.Properties
public import Mathlib.MeasureTheory.C... |
23,975 | lean_file_chunk | c433dd8980fccf5d16b1e6710b132819a9426013665cc40f8b9a5c7b3f0a965b | 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.Condexp
public import Mathlib.Probability.Moments.MGFAnalytic
public import Mathlib.Probability.Moments.Tilted
/-!
# Sub... |
18,977 | lean_file_chunk | 6f9fc1afa3b88325c903c2fb6b837cb9e1b2505301ee47c5e057ede8410f18d3 | lean_source_file | pkg_mathlib_source_file_chunks | HasSubgaussianMGF (fun p ↦ X p.1 + Y p.2) (c + cY) (κ ⊗ₖ prodMkLeft Ω' η) ν :=
hX.add_compProd hY.prodMkLeft_compProd
end Add
end Kernel.HasSubgaussianMGF
end Kernel
section Conditional
/-! ### Conditionally sub-Gaussian moment-generating function -/
variable {Ω : Type*} {m mΩ : MeasurableSpace Ω} {hm : m ≤ mΩ}... |
6,975 | lean_file_chunk | 952a01572740964d7ad25473b1fa1afe1491c04cc79f182bf908c4f94bc61f13 | 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.Measure.Tilted
public import Mathlib.Probability.Moments.MGFAnalytic
/-!
# Results relating `Measure.tilted` to `mgf` and `cg... |
23,949 | lean_file_chunk | 88fdb52d6da12b74f221d711220429517e013cb1f93e6ffa3814c1b26956c082 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Kexing Ying
-/
module
public import Mathlib.Probability.Moments.Covariance
public import Mathlib.Probability.Notation
import Mathlib.MeasureTheory.Function.LpSem... |
143 | lean_file_chunk | 1c15c1a4d13c85e36531d00a706955513abcdbb366ce1e54f2ee3b58dcd0f2aa | lean_source_file | pkg_mathlib_source_file_chunks | variance_dual_prod' (ContinuousLinearMap.comp_memLp' _ hLμ)
(ContinuousLinearMap.comp_memLp' _ hLν)
end NormedSpace
end ProbabilityTheory |
12,677 | lean_file_chunk | 85009ced36a92068d0a4e40921b72e1b60b8d5638d05912532d6f1404476494e | 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.Moments.ComplexMGF
public import Mathlib.Analysis.SpecialFunctions.Complex.Analytic
public import Mathlib.Analysis.Calculus.Tayl... |
22,510 | lean_file_chunk | e85e9ee895ef46f4df064fd68b0065adb89cca6ae72d6f7d2602851e659304a6 | 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.IdentDistrib
import Mathlib.Probability.Independence.Integration
/-!
# Moments and moment-generating function
## Main definiti... |
14,870 | lean_file_chunk | 1e39086c381ebcc1c6ffde49637ec0be13f600351001319ead1dc405be45129e | 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.Calculus.ParametricIntegral
public import Mathlib.Analysis.Complex.CauchyIntegral
public import Mathlib.MeasureTheory.Measure.Chara... |
12,913 | lean_file_chunk | 9d059d4c4ab3f2016540662b61cdf1fbd542737561d4f627a0853262368dc438 | 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, Etienne Marion
-/
module
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.Probability.Independence.Basic
import Mathlib.Probability.Indepen... |
23,964 | lean_file_chunk | 50cc50e4aa7159113fcef6052bd9a5f789e3b59f8d2c91b1e0847d1e0abbaa92 | 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.L1Space.Integrable
public import Mathlib.MeasureTheory.Order.Group.Lattice
/-!
# Domain of the moment-generating fun... |
3,093 | lean_file_chunk | 27d6ba83924126497e47247c2590adf5c0e8ea700625fe7875c76bad7639afbf | lean_source_file | pkg_mathlib_source_file_chunks | have hX : AEMeasurable X μ := aemeasurable_of_mem_interior_integrableExpSet h
by_cases hp_zero : p = 0
· simp only [hp_zero, ENNReal.coe_zero, memLp_zero_iff_aestronglyMeasurable]
exact hX.aestronglyMeasurable
rw [← integrable_norm_rpow_iff hX.aestronglyMeasurable (mod_cast hp_zero) (by simp)]
simp only [no... |
10,034 | lean_file_chunk | 34a7b3b9fdee52ef40d70b908ba4796feb87443aea236299e2d26c74222bf264 | 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, Etienne Marion
-/
module
public import Mathlib.Analysis.InnerProductSpace.Positive
public import Mathlib.Analysis.Normed.Lp.MeasurableSpace
public import Mathlib.MeasureTh... |
21,347 | lean_file_chunk | 330c2ce71811199de0c0de439654eeaa5c1deb24b6a31f369f06a36554854152 | 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.Measure.HasOuterApproxClosedProd
public import Mathlib.Probability.Independence.Process.Basic
public import Mathlib.Probab... |
9,025 | lean_file_chunk | 6489a41b5e70157d899293d2641c169d62ea185d4768ebd8bac58934d6129556 | 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.Independence.Basic
public import Mathlib.Probability.ProductMeasure
/-!
# Independence of an infinite family of random vari... |
16,653 | lean_file_chunk | d4f23b9da46ed843d376eef43569f078bb55ee82edf2e9d46d52e0be16a00f3f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.Basic
public import Mathlib.Probability.Independence.Conditional
/-!
# Kolmogorov's 0-1 law
Let `s : ι → Measurab... |
16,185 | lean_file_chunk | 1f2c9b3e43ec7fc65d42f7ef4a4c88296f0e47ed20991ad2a6f849ed05f82930 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Martin Zinkevich. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Martin Zinkevich, Vincent Beffara, Etienne Marion
-/
module
public import Mathlib.MeasureTheory.Integral.Pi
public import Mathlib.Probability.Independence.Integrable
public import M... |
11,895 | lean_file_chunk | 8aadbbc051866c0c832ce3901e9df96c0741ad4916ff5044b31b4efe74591a89 | 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.Measure.CharacteristicFunction.Basic
public import Mathlib.Probability.Independence.Basic
/-!
# Links between independenc... |
23,962 | lean_file_chunk | 6f52f51309e5d18b3ba7069bedde80945784e69d3a1f89d5bf2c5d83d65ca2a3 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 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.IndepFun
public import Mathlib.MeasureTheory.Constructions.Pi
public import Mathlib.MeasureTheory.Group.Conv... |
23,996 | lean_file_chunk | 09f3b48149439bb2cec56632bc176f20ca6435078852083a27f5faf536564ae9 | lean_source_file | pkg_mathlib_source_file_chunks | theorem iIndepSet.indep_generateFrom_le_nat {s : ℕ → Set Ω}
(hsm : ∀ n, MeasurableSet (s n)) (hs : iIndepSet s μ) (n : ℕ) :
Indep (generateFrom {s (n + 1)}) (generateFrom { t | ∃ k ≤ n, s k = t }) μ :=
Kernel.iIndepSet.indep_generateFrom_le_nat hsm hs n
theorem indep_iSup_of_monotone [SemilatticeSup ι] [IsZe... |
2,370 | lean_file_chunk | 99a598f931a621e6211648dceecc9626cf6c184516b2bd766447a8be8cdbaab7 | lean_source_file | pkg_mathlib_source_file_chunks | rw [Finset.prod_mul_distrib, ENNReal.prod_inv_distrib]
exact fun _ _ i _ _ ↦ .inr <| measure_ne_top _ _
_ = ∏ i, if i ∈ s then μ[f i | Y i ⁻¹' t i] else 1 := by
refine Finset.prod_congr rfl fun i _ ↦ ?_
by_cases hi : i ∈ s
· simp only [hi, ↓reduceIte, g, cond_apply (hY i (ht i))]
· sim... |
23,989 | lean_file_chunk | f858a1fca9895e3ebefa1e9e2528ee9c57581c99dab49b771909b677fbf09cd3 | 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.IndepFun
public import Mathlib.Probability.Kernel.CompProdEqIff
public import Mathlib.Probability.Kernel.Com... |
23,969 | lean_file_chunk | 86b6844f2635634e1f12a2731bec6c684784f7b68ff5e7adaa2fc746da26d700 | lean_source_file | pkg_mathlib_source_file_chunks | Kernel.Indep.indepSets h_indep
end FromMeasurableSpacesToSetsOfSets
section FromPiSystemsToMeasurableSpaces
/-! ### Conditional independence of generating π-systems implies conditional independence of
σ-algebras -/
variable {m' m₁ m₂ : MeasurableSpace Ω} {mΩ : MeasurableSpace Ω} [StandardBorelSpace Ω]
{hm' : m'... |
523 | lean_file_chunk | fccbe1e9f95c1002f9ab64e87127175cae80f60722967b274567ab5c227978dc | lean_source_file | pkg_mathlib_source_file_chunks | (hf_Indep : iCondIndepFun m' hm' f μ) (hf_meas : ∀ i, Measurable (f i)) (n : ℕ) :
CondIndepFun m' hm' (∏ j ∈ Finset.range n, f j) (f n) μ :=
Kernel.iIndepFun.indepFun_prod_range_succ hf_Indep hf_meas n
end CommMonoid
theorem iCondIndepSet.iCondIndepFun_indicator [Zero β] [One β] {m : MeasurableSpace β}
{s :... |
282 | lean_file_chunk | 3e3504cc43ceeaa81d1f0b0aabce7c209cb4e92e76561b4ec47f673d3e4be267 | 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 -- shake: keep-all
public import Mathlib.Probability.Independence.Kernel.IndepFun
deprecated_module (since := "2025-12-01") |
2,419 | lean_file_chunk | 5f7f0e2aed0c7a816c1ad2eeaea14a4787f63b2c3ea370235234e8246c143793 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.MeasureTheory.Function.L1Space.Integrable
public import Mathlib.Probability.Independence.Basic
/-!
# Independence of functions im... |
12,145 | lean_file_chunk | 5346497a2f57e76c7e93d91c733f0918f3105ec69b13fb6c52ee303cfda92eb0 | 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
-/
module
public import Mathlib.Probability.Notation
public import Mathlib.Probability.Process.HittingTime
public import Mathlib.Probability.Martingale.Basic
/-! # Optional ... |
16,708 | lean_file_chunk | 5d76f72438251ab402aaab38a5f9542f6fa3bb6f71510546fc3f9c7383bcf5df | 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
-/
module
public import Mathlib.Algebra.Order.Archimedean.IndicatorCard
public import Mathlib.Probability.Martingale.Centering
public import Mathlib.Probability.Martingale.Co... |
23,973 | lean_file_chunk | 17bbcf62216c43c3b46b672a7e6c6d3e03738bbc6f9081921dd523dd4168f2d4 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Rémy Degenne. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémy Degenne, Kexing Ying
-/
module
public import Mathlib.MeasureTheory.Function.ConditionalExpectation.PullOut
public import Mathlib.Probability.Process.Predictable
public import Mathl... |
4,470 | lean_file_chunk | 1e086a29ff72424e8d79beb54fe586cf05e205d0110d8709ad5fa30e705f9a41 | lean_source_file | pkg_mathlib_source_file_chunks | {f : ℕ → Ω → E} (hfmgle : Supermartingale f 𝒢 μ) (hfadp : IsPredictable 𝒢 f)
(n : ℕ) : f n ≤ᵐ[μ] f 0 :=
le_zero_of_predictable hfmgle (fun _ ↦ (hfadp.measurable_add_one _).stronglyMeasurable) n
/-- A predictable martingale is a.e. equal to its initial state.
In contrast to the non-primed version, this result ... |
11,818 | lean_file_chunk | 6bd6b4e824c76214e5eb63d17373ce65c18e36facae8a59b508130f11fc2659a | 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.Order.SuccPred.LinearLocallyFinite
public import Mathlib.Probability.Martingale.Basic
/-!
# Optional sampling theorem
If `τ` is a bounded ... |
8,481 | lean_file_chunk | 5451b280e3d795cdb0adc1db70aa425abb5e8dae67a7fb5d830ca1b4b77f3ff1 | 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.Martingale.Basic
/-!
# Centering lemma for stochastic processes
Any `ℕ`-indexed stochastic process which is strongly adapted a... |
23,976 | lean_file_chunk | fb8a607e56bf52ccd6c2355e2a0c710827177c0923dd87852d2a35080cd15f23 | 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
-/
module
public import Mathlib.MeasureTheory.Constructions.Polish.Basic
public import Mathlib.MeasureTheory.Function.UniformIntegrable
public import Mathlib.Probability.Mart... |
68 | lean_file_chunk | aa19e84635f8bb38f3e4ccf0c1903c780b490ce7447314ab17ccea674b2459f0 | lean_source_file | pkg_mathlib_source_file_chunks | simp only [hxeq, Pi.sub_apply]
end L1Convergence
end MeasureTheory |
23,982 | lean_file_chunk | bb5a24bb79085be65e445ce69d25549428b79cb6888f0f3296d2257993ea2733 | 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
-/
module
public import Mathlib.Order.Interval.Set.Monotone
public import Mathlib.Probability.Notation
public import Mathlib.Probability.Process.HittingTime
public import Mat... |
15,594 | lean_file_chunk | d86838fa9014458ea34833d433ded9ec2615d987f3cf679928543e43c1808ea7 | lean_source_file | pkg_mathlib_source_file_chunks | gcongr sSup {n | ?_} with n
· exact upperCrossingTime_lt_bddAbove hab
intro hn
rw [upperCrossingTime_eq_upperCrossingTime_of_lt hNM hn]
exact lt_of_lt_of_le hn hNM
theorem upcrossingsBefore_lt_of_exists_upcrossing (hab : a < b) {N₁ N₂ : ℕ} (hN₁ : N ≤ N₁)
(hN₁' : f N₁ ω < a) (hN₂ : N₁ ≤ N₂) (hN₂' : b < f N₂... |
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