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 |
|---|---|---|---|---|---|
23,827 | lean_file_chunk | 9441ce175991dcb6a8a2c17f17e5563f02e7d7864d327ddffc246cb6a466cc64 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
module
public import Mathlib.Topology.Order.ProjIcc
public import Mathlib.Topology.CompactOpen
public import Mathlib.Topology.UnitInterval
/-!
# Paths in topologica... |
12,929 | lean_file_chunk | 6d56003ee220cfdf78ee61985cf6f639205ed0985989c58358ccb75a1b3768a8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Topology.Sets.Closeds
public import Mathlib.Topology.Sets.OpenCover
/-!
# Sober spaces
A quasi-sober space is a topological space where ever... |
14,948 | lean_file_chunk | 0f580dc5323481fc279f93a89d3548f9c5f55a9c35a45c497d31a22f45a47589 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Adam Topaz. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Calle Sönne, Adam Topaz
-/
module
public import Mathlib.Data.Setoid.Partition
public import Mathlib.Topology.LocallyConstant.Basic
public import Mathlib.Topology.Separation.Regular
public... |
5,877 | lean_file_chunk | 6ef32adc7225d1099bd7a7dea3bc81d153c87fd3130196310b55815c2f104bca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yaël Dillies, Yury Kudryashov
-/
module
public import Mathlib.Topology.NhdsSet
public import Mathlib.Topology.Inseparable
/-!
# Neighborhoods kernel of a set
In `Mathlib/Topology/Defs... |
10,234 | lean_file_chunk | 5aacb702803e947622d61a97f93e849d7b2797c7c4fb4bd7ab865d84aa7484db | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Topology.Homeomorph.Lemmas
public import Mathlib.Topology.Sets.Closeds
/-!
# Noetherian space
A Noetherian space is a topological space that... |
23,931 | lean_file_chunk | 2cd7380f1a28db9785bc319e41530105d8abe979bc7ed4783635b70cc1a9a8f1 | 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
-/
module
public import Mathlib.Order.Interval.Set.IsoIoo
public import Mathlib.Topology.ContinuousMap.Bounded.Normed
public import Mathlib.Topology.UrysohnsBounded
... |
3,912 | lean_file_chunk | 6f1984b96a8ef0e7d7f00c2d3a7dae9893197101e6ac2c535cc747a4e88fed86 | lean_source_file | pkg_mathlib_source_file_chunks | {t : Set ℝ} [OrdConnected t] (hf : ∀ x, f x ∈ t) (hne : t.Nonempty) :
∃ g : Y →ᵇ ℝ, (∀ y, g y ∈ t) ∧ g.restrict s = f := by
obtain ⟨g, hg, hgf⟩ :=
exists_extension_forall_mem_of_isClosedEmbedding f hf hne hs.isClosedEmbedding_subtypeVal
exact ⟨g, hg, DFunLike.coe_injective hgf⟩
end BoundedContinuousFunctio... |
3,102 | lean_file_chunk | 6306f062b43551827a2ace1d9ce7b98796bdfff3de540de779c1d843446a63ae | 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.Topology.Algebra.Monoid
/-! # Approximate units
An *approximate unit* is a filter `l` such that multiplication on the left (or right) by... |
2,214 | lean_file_chunk | df88b144677a81f510b2cdc35a3259a075175d73737b3e805649314d6a88afa8 | 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, Mario Carneiro, Jeremy Avigad
-/
module
public import Mathlib.Order.Filter.Ultrafilter.Basic
public import Mathlib.Topology.Continuous
/-! # Characterization of basic... |
4,329 | lean_file_chunk | 14b4abc6f55986705355e6ab863480418c30ecd45f4c5dfd49490ed9e12ef8b8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Dagur Asgeirsson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dagur Asgeirsson
-/
module
public import Mathlib.Topology.Compactness.Bases
public import Mathlib.Topology.CompactOpen
public import Mathlib.Topology.Separation.Profinite
public imp... |
2,958 | lean_file_chunk | f0085b2e7f9b3e4bc69c81fa1ad73cdc2fe6860bedb3d6372c616f5de8196ed1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Jujian Zhang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jujian Zhang, Fangming Li, Alessandro D'Angelo
-/
module
public import Mathlib.Order.KrullDimension
public import Mathlib.Topology.Irreducible
public import Mathlib.Topology.Homeomorph.... |
3,957 | lean_file_chunk | 484fbdc0201ecf5cd80d373b95b6c3ff37f089d7a32ee96a23b2f01089f2a0e8 | 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.Topology.Homeomorph.Lemmas
/-!
# Infinite Hausdorff topological spaces
In this file we prove several properties of infinite Hausdorf... |
23,970 | lean_file_chunk | 93cae99622e1782d94832b0f12ba11829a42ded0e280f9fc5c495808d4bf85ed | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Reid Barton. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
module
public import Mathlib.Topology.NhdsWithin
/-!
# Neighborhoods and continuity relative to a subset
This file develops API on the relative versions
* `Contin... |
20,762 | lean_file_chunk | df7e9007e6927b077465c0a34458a0b435031c59013e1838b863b8cdcda21021 | lean_source_file | pkg_mathlib_source_file_chunks | haveI := mem_closure_iff_nhdsWithin_neBot.1 hx
mem_closure_of_tendsto h <| mem_of_superset self_mem_nhdsWithin (subset_preimage_image f s)
theorem ContinuousWithinAt.mem_closure {t : Set β}
(h : ContinuousWithinAt f s x) (hx : x ∈ closure s) (ht : MapsTo f s t) : f x ∈ closure t :=
closure_mono (image_subset_i... |
17,036 | lean_file_chunk | 0f52c5913a4c51a1c5d3a61006a6cd0fd1c4262ef25989f7981e28983f26f016 | 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, Reid Barton
-/
module
public import Mathlib.Topology.Separation.Regular
/-!
# The shrinking lemma
In this file we prove a few versions of the shrinking lemma. The ... |
23,918 | lean_file_chunk | 0fdf57cbab1646a1262acd4a4a7186cb8cf56fb34bdc06096a7625cd50d2b57f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jeremy Avigad. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jeremy Avigad, Sébastien Gouëzel
-/
module
public import Mathlib.Topology.Constructions
/-!
# Neighborhoods relative to a subset
This file develops API on the relative versions `nhds... |
2,930 | lean_file_chunk | 0c591c4f0cbd1a6e060364748d9fbe211ee301a6d2c1ff2fedfe0e717a8f9a87 | lean_source_file | pkg_mathlib_source_file_chunks | lemma mem_nhdsSetWithin {s t u : Set α} : u ∈ 𝓝ˢ[t] s ↔ ∃ v, IsOpen v ∧ s ⊆ v ∧ v ∩ t ⊆ u := by
simpa [and_assoc] using (nhdsSetWithin_basis_open s t).mem_iff
@[simp]
lemma nhdsSetWithin_singleton {x : α} {s : Set α} : 𝓝ˢ[s] {x} = 𝓝[s] x := by
simp [nhdsSetWithin, nhdsWithin]
@[simp]
lemma nhdsSetWithin_univ {... |
19,908 | lean_file_chunk | 4da743814deea0e62956e9b2da4280debbe90c0ce30049fc986493074e14a742 | 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, Mario Carneiro, Jeremy Avigad
-/
module
public import Mathlib.Topology.ClusterPt
/-!
# Continuity in topological spaces
For topological spaces `X` and `Y`, a functio... |
23,986 | lean_file_chunk | 19ad410fc598fe2e6e983c230666267192a827c8ad7750040482afcdde85f165 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Stefan Kebekus. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefan Kebekus
-/
module
public import Mathlib.Algebra.BigOperators.Finprod
public import Mathlib.Algebra.Group.Subgroup.Defs
public import Mathlib.Algebra.Group.Support
public import... |
1,284 | lean_file_chunk | dd5f895f855c8a41a18473f375c3f14766474dd1880a2ec92f617cff3b6cab27 | lean_source_file | pkg_mathlib_source_file_chunks | by_cases hz : z ∈ F.support
· aesop
· aesop
/-- Restriction as a lattice morphism -/
noncomputable def restrictLatticeHom [AddCommGroup Y] [Lattice Y] {V : Set X} (h : V ⊆ U) :
LatticeHom (locallyFinsuppWithin U Y) (locallyFinsuppWithin V Y) where
toFun D := D.restrict h
map_sup' D₁ D₂ := by
ext x
... |
1,179 | lean_file_chunk | 526a952567d978a70cf70bf3add0ba637b28bdf72a2fbc646674b71dc113580b | 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.Order.Restriction
public import Mathlib.Topology.Constructions
/-!
# Continuity of the restriction function for functions indexed by a ... |
2,280 | lean_file_chunk | 726d7e6b05846ce88d0166abc27d98a04e53d3ec4362dd2c1b7ad776d19f4713 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Order.OmegaCompletePartialOrder
public import Mathlib.Topology.Order.ScottTopology
/-!
# Scott Topological Spaces
A type of topological spac... |
8,206 | lean_file_chunk | 167960c3917727a145ea33063d0d373c517a53e012d4e71f42baaaa58076ea73 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Patrick Massot
-/
module
public import Mathlib.Topology.Neighborhoods
/-!
# Neighborhoods of a set
In this file we define the filter `𝓝ˢ s` or `nhdsSet s` consi... |
23,999 | lean_file_chunk | 06a4851f0397849ee44cda0e4ea9dad54b677631e54fddc7c4a911ab80e8e2c5 | 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, Mario Carneiro, Yury Kudryashov
-/
module
public import Mathlib.Order.Minimal
public import Mathlib.Order.Zorn
public import Mathlib.Topology.ContinuousOn
public impor... |
178 | lean_file_chunk | 962828ca2cb73fba89fff33291a3ae7d79d67bc6241d0e777b09dad503af0753 | lean_source_file | pkg_mathlib_source_file_chunks | (e : X ≃ₜ Y) : IrreducibleSpace X ↔ IrreducibleSpace Y :=
⟨fun _ ↦ e.surjective.irreducibleSpace e.continuous,
fun _ ↦ e.symm.surjective.irreducibleSpace e.symm.continuous⟩ |
15,622 | lean_file_chunk | b349b10f309f2feeca867d420f6bb97d643c61ea6cf392df20511ec891dbb4ca | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
module
public import Mathlib.Topology.Homeomorph.Lemmas
public import Mathlib.Topology.Compactification.StoneCech
/-!
# Extremally disconnected spaces
An extremall... |
136 | lean_file_chunk | d5fd2e7e3ef9f880363b2d56f67eb406e822d6d3efe544c9ba11d19fad1b5d60 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Topology.OpenPartialHomeomorph.Constructions
deprecated_module (since := "2025-12-08") |
8,492 | lean_file_chunk | 9394a66650106282e82fbcb05663def60dc25fd3ae4e6d528da692936ddd7faa | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Sebastian Kumar. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sebastian Kumar
-/
module
public import Batteries.Data.Fin.Fold
public import Mathlib.AlgebraicTopology.FundamentalGroupoid.Basic
/-!
# Subpaths and concatenation of paths
This fil... |
7,770 | lean_file_chunk | 5f4e9b1aed9b00a4062e2549be857db68abb499ef275fb1b27244c16f47ab823 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Topology.Compactness.Bases
public import Mathlib.Topology.NoetherianSpace
/-!
# Quasi-separated spaces
A topological space is quasi-separate... |
11,729 | lean_file_chunk | 043e5bef82827e95216eb28d856ff67a1444f956722d6976702ea510b5e76f0f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Andrew Yang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Andrew Yang
-/
module
public import Mathlib.Topology.Homeomorph.Lemmas
public import Mathlib.Topology.Sets.OpenCover
public import Mathlib.Topology.LocallyClosed
public import Mathlib.To... |
23,973 | lean_file_chunk | fc725ff56920256dbfdc66cda62324b2aa922838d6cebd8b6f207b1964c847b2 | 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
-/
module
public import Mathlib.Algebra.BigOperators.Finprod
public import Mathlib.Topology.ContinuousMap.Algebra
public import Mathlib.Topology.Compactness.Paracompa... |
7,668 | lean_file_chunk | db144584aecc71a9422192dcf482694342289343c7d625ce98c73148b12aeddf | lean_source_file | pkg_mathlib_source_file_chunks | theorem toPOUFun_eq_mul_prod (i : ι) (x : X) (t : Finset ι)
(ht : ∀ j, WellOrderingRel j i → f j x ≠ 0 → j ∈ t) :
f.toPOUFun i x = f i x * ∏ j ∈ t with WellOrderingRel j i, (1 - f j x) := by
refine congr_arg _ (finprod_cond_eq_prod_of_cond_iff _ fun {j} hj => ?_)
rw [Ne, sub_eq_self] at hj
rw [Finset.mem_... |
17,044 | lean_file_chunk | f03dd9266fa2027c644dcb4c7dd3b0ef681dee6f2b16bb5e5d3ff8242187e2ed | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash, Bhavik Mehta, Daniel Weber, Stefan Kebekus
-/
module
public import Mathlib.Tactic.TautoSet
public import Mathlib.Topology.Constructions
public import Mathlib.Data.Set.Subset... |
23,961 | lean_file_chunk | 80a2f98b58c7ece3ccd7fa895ddbf3c6e3b50d767c5a527befde35803c45da5b | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Antoine Chambert-Loir. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, Anatole Dedecker
-/
module
public import Mathlib.Analysis.Convex.Quasiconvex
public import Mathlib.Order.SaddlePoint
public import Mathlib.Topology.Insta... |
823 | lean_file_chunk | 8fab108c6c4062d6dea49cff2e7a8c873243ce1da5c7022e626d0849bd9c47a9 | lean_source_file | pkg_mathlib_source_file_chunks | (ne_X : X.Nonempty) (cX : Convex ℝ X) (kX : IsCompact X)
(hfy : ∀ y ∈ Y, LowerSemicontinuousOn (fun x : E ↦ f x y) X)
(hfy' : ∀ y ∈ Y, QuasiconvexOn ℝ X fun x => f x y)
variable [TopologicalSpace F] [AddCommGroup F] [Module ℝ F]
[IsTopologicalAddGroup F] [ContinuousSMul ℝ F]
(cY : Convex ℝ Y) (ne_Y : Y.Non... |
18,159 | lean_file_chunk | 92413e8cf2452020c2145fc2d73b18af38c4d1d83771e0204fdb45996228eed2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Jan-David Salchow. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jan-David Salchow, Patrick Massot, Yury Kudryashov
-/
module
public import Mathlib.Topology.Defs.Sequences
public import Mathlib.Topology.Metrizable.Basic
/-!
# Sequences in topol... |
6,584 | lean_file_chunk | c3d0f8736e6b17246b44272070c8e5e10a9dcd798032eb57fdc6a79c2a94eb88 | 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, Peter Pfaffelhuber
-/
module
public import Mathlib.Topology.Maps.Proper.Basic
/-! # Restriction of a closed compact set in a product space to a set of coordinates
We sho... |
23,987 | lean_file_chunk | 8475f3e94d5c5e9653bf2cbf7430ac44e640840e9dfa711ceb4d6abffdda8822 | 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.Order.BooleanSubalgebra
public import Mathlib.Topology.Compactness.Bases
public import Mathlib.Topology.LocalAtTarget
public import Mathlib.... |
2,191 | lean_file_chunk | 5644b668c02eeaedd705859382d04fd3f0092d70e09c5a41513ecc4b37be6cf7 | lean_source_file | pkg_mathlib_source_file_chunks | lemma IsLocallyConstructible.inter_of_isOpen_isCompact
[PrespectralSpace X] [QuasiSeparatedSpace X]
(hs : IsLocallyConstructible s) (ht : IsOpen t) (ht' : IsCompact t) :
IsConstructible (s ∩ t) :=
(hs.inter (ht'.isConstructible ht).isLocallyConstructible).isConstructible_of_subset_of_isCompact
Set.int... |
10,747 | lean_file_chunk | f56ee200c0001c6567b95dbce60ec3e2cf1b54f1910c893e1a2530e53754392a | 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
-/
module
public import Mathlib.Order.Filter.SmallSets
public import Mathlib.Topology.ContinuousOn
/-!
### Locally finite families of sets
We say that a family of s... |
3,828 | lean_file_chunk | e7e46d0b0cde037d4d5878eed6f668e5330930eafc5d0c7ade5d87d8af2fce33 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Anatole Dedecker
-/
module
public import Mathlib.Topology.Separation.Regular
/-!
# Extending a function from a subset
The main definition of this file is `extendFr... |
436 | lean_file_chunk | e3ca508471175c75b472b58915210f9a02410a5ad032d82375761d63f1166e50 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
module
public import Mathlib.Init
public import Lean.ScopedEnvExtension
/-!
# Helper function for environment extensions and attributes.
-/
@[expose] public se... |
998 | lean_file_chunk | cd10d8b68034a7a963295ca95739766297e8185fb2e716e35ef07ce08dfd15b2 | 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: Kim Morrison
-/
module
public import Mathlib.Init
public import Lean.LocalContext
public import Batteries.Control.AlternativeMonad
/-!
# Additional methods about `LocalContext`
-/
pub... |
4,144 | lean_file_chunk | 7a296a163d5f10d3aaabc8c80b237a4bf7fc2ca751d9c53fc4c70149c4e44bcb | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2026 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
module
public import Lean.Meta.Basic
public import Mathlib.Init
/-!
# Folding through the environment efficiently
This file defines `foldImportedDecls`, a func... |
1,086 | lean_file_chunk | 7e77fce70e710190c55b8a3c5299b87f32fef4dcfc95a2add5a9450598f47585 | 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.Init
/-!
# Json serialization typeclass for `PUnit` & `Fin n` & `Subtype p`
-/
@[expose] public section
universe u
namespace Lean
derivi... |
1,264 | lean_file_chunk | 21bc39ee0ff8cae191ce8f5d31c9344f0b67a82241084e7254d59cba0ff657a0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Edward Ayers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Edward Ayers
-/
module
public import Mathlib.Init
public import Lean.Exception
/-!
# Additional methods for working with `Exception`s
This file contains two additional methods for wor... |
900 | lean_file_chunk | e43403d859db8b1281279dc700716ef09bc9e8037996801fc83a534b1008cf23 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Init
/-!
# Additional functions using `CoreM` state.
-/
@[expose] public section
open Lean Core
/--
Run a `CoreM α` in a fresh `Environm... |
1,200 | lean_file_chunk | 8295ead17082660bd9b374bceccb21b7938548accdd441062f96574b8862ad2a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2018 Simon Hudon. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Simon Hudon
-/
module
public import Mathlib.Init
/-!
# Basic facts about `Thunk`.
-/
@[expose] public section
namespace Thunk
@[simp] theorem get_pure {α} (x : α) : (Thunk.pure x).ge... |
1,310 | lean_file_chunk | f4b948e81410497e852aa9a640a7996be0a564c00bf0b077b747fe36401e92d8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Jovan Gerbscheid. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jovan Gerbscheid
-/
module
public import Mathlib.Init
public import Lean.Meta.Tactic.Util
public import Lean.SubExpr
/-! This file defines some functions for dealing with `SubExpr.... |
1,965 | lean_file_chunk | 6d220a6ff91dfa92cc78647e7e692c98f7ed55994208ef1a4d947028f08d0784 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Thomas R. Murrills. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas R. Murrills
-/
module
public import Lean.Environment
-- Import this linter explicitly to ensure that
-- this file has a valid copyright header and module docstring.
import ... |
3,714 | lean_file_chunk | 4d5cb6ee01390901935e86bfadd04d4c0f26eb7c6f059ad1336708fb66b306b1 | 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
-/
module
public import Mathlib.Init
public import Lean.Elab.Term
public import Lean.Elab.Tactic.Basic
public import Lean.Meta.Tactic.Assert
public import Lean.Meta.Tac... |
6,713 | lean_file_chunk | 1babe7e2890900385aa3b96598b1cd4de342ce6e1714794dd683dfe168fae839 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Lean FRO, LLC. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anne Baanen
-/
module
public meta import Mathlib.Lean.Elab.Tactic.Meta
-- Import this linter explicitly to ensure that
-- this file has a valid copyright header and module docstring.
p... |
2,418 | lean_file_chunk | 99c35c464df3deaa400b2ea1b1836850d4187e4612a05d69d2fd6343a29c4fe8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Thomas R. Murrills. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas R. Murrills
-/
module
public meta import Lean.Elab.Command
public meta import Lean.Linter.Basic
-- Import this linter explicitly to ensure that
-- this file has a valid cop... |
390 | lean_file_chunk | 939c2d27478d38a1e8cb926af75230d8df815690398b1ab0f1bbdaac9ff26dc6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Robert Y. Lewis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Mario Carneiro, Simon Hudon, Kim Morrison, Keeley Hoek, Robert Y. Lewis, Floris van Doorn
-/
module -- shake: keep-all
public import Mathlib.Lean.Expr.Basic
public import Mathlib.Tac... |
3,806 | lean_file_chunk | 1ca79407cafac9a4153f19d59fab3e40a5cefce27ca6201e1d86f7b8b29e3b44 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Kim Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kim Morrison
-/
module
public import Mathlib.Init
public import Lean.Meta.Match.MatcherInfo
public import Std.Data.HashMap.Basic
/-!
# Additional functions on `Lean.Name`.
We provide ... |
11,093 | lean_file_chunk | dc956b924a4d155ec9447f90e884b871bd13379cb4ffc7490f1c6407385df221 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo
-/
module
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Topology.Algebra.Monoid
public import Mathlib.Topology.Algebra.Group.Defs
public import Mathlib.Algebra.O... |
6,160 | lean_file_chunk | 648f6d7830822de8b31ed0fbab6dd8333d39adc79b18e6fab854d67908fa0280 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Daniel Figueroa. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Figueroa
-/
module
public import Mathlib.Dynamics.Minimal
/-!
# Topologically transitive monoid actions
In this file we define an action of a monoid `M` on a topological spa... |
15,528 | lean_file_chunk | 76d3704320984ffa92656c511c3155deef6a9a9b231bc69d14c2f4e154f95b29 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo
-/
module
public import Mathlib.Dynamics.Flow
public meta import Mathlib.Tactic.ToAdditive
/-!
# ω-limits
For a function `ϕ : τ → α → β` where `β` is a topological space, we
define... |
3,812 | lean_file_chunk | f2800e58a8f531e18e6de9001187d646b44c4f6b2325984d9029e03d9216079b | 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
-/
module
public import Mathlib.Topology.Algebra.ConstMulAction
/-!
# Minimal action of a group
In this file we define an action of a monoid `M` on a topological sp... |
5,965 | lean_file_chunk | c4e682cdcac601ba29e30cb77544a74785449795affa8157d28ab0f630b5d3d9 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Antoine Chambert-Loir, Oliver Nash
-/
module
public import Mathlib.Algebra.Polynomial.AlgebraMap
public import Mathlib.Algebra.Polynomial.Identities
public import Mathlib.RingTheory.Nilp... |
3,978 | lean_file_chunk | 7bd295259d7e7e7b1b3706e1be516a3fc685a66730b62f3b12e4040ad00dfec0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2020 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
module
public import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Hofer's lemma
This is an elementary lemma about complete metric spaces. It is motivated by an
appl... |
3,235 | lean_file_chunk | 686ae1f67f014f02d49626ae29fa1232727d798aaf6ea10f8f4cd3706a144c7f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Pietro Monticone
-/
module
public import Mathlib.Analysis.SpecialFunctions.Gamma.Basic
public import Mathlib.Analysis.SumIntegralComparisons
/-!
# Bounds for su... |
23,989 | lean_file_chunk | 6b3eaf6656f616b697b6a5c7dae2cea681b28ede87d1d7ea86947352468d0ce8 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn
-/
module
public import Mathlib.MeasureTheory.Integral.Prod
public import Mathlib.MeasureTheory.Function.LocallyIntegrable
public import Mathlib.MeasureTheory.Group... |
23,491 | lean_file_chunk | 6a0c8d21e7c53e05515d7692d9ada99fb7baee62c765e70905b7c1cc92ae680a | lean_source_file | pkg_mathlib_source_file_chunks | variable [TopologicalSpace G]
variable [IsTopologicalAddGroup G]
protected theorem _root_.HasCompactSupport.convolution [T2Space G] (hcf : HasCompactSupport f)
(hcg : HasCompactSupport g) : HasCompactSupport (f ⋆[L, μ] g) :=
(hcg.isCompact.add hcf).of_isClosed_subset isClosed_closure <|
closure_minimal
... |
114 | lean_file_chunk | 27a7356a7656349c9916f7c2879bb0dac4053f177f0b8617fe0627fc4794d5c6 | lean_source_file | pkg_mathlib_source_file_chunks | module -- shake: keep-all
public import Mathlib.Analysis.Matrix.Normed
deprecated_module (since := "2025-11-03") |
4,019 | lean_file_chunk | aa6d9540a9051abf4bdeccaff7d8ff562333e4053a8068a869630fbb6aeb4ad0 | 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
-/
module
public import Mathlib.Order.Filter.AtTopBot.Archimedean
public import Mathlib.Order.Filter.AtTopBot.Finite
public import Mathlib.Order.Filter.AtTopBot.P... |
23,963 | lean_file_chunk | 6076fc827b5201db5664de94a6660edf20b7a8ccbced846a2def732e41ac353a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.SpecialFunctions.ImproperIntegrals
public import Mathlib.Analysis.Calculus.ParametricIntegral
public import Mathlib.MeasureTheo... |
501 | lean_file_chunk | 8c40322a9243fef49d432645687ca3dd93b184710646e7eb8bcde74fba4450e2 | lean_source_file | pkg_mathlib_source_file_chunks | ofReal_zero, ofReal_one, one_cpow, zero_cpow aux2, sub_zero]
/-- The Mellin transform of a power function restricted to `Ioc 0 1`. -/
theorem hasMellin_cpow_Ioc (a : ℂ) {s : ℂ} (hs : 0 < re s + re a) :
HasMellin (indicator (Ioc 0 1) (fun t => ↑t ^ a : ℝ → ℂ)) s (1 / (s + a)) := by
have := hasMellin_one_Ioc (by r... |
21,687 | lean_file_chunk | 7f2b8793cebfc83f641b2aa1e2eca75726e9a99dd1747a72979de1ba85849505 | 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
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.NNReal
public import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
public import Mathlib.Analysis.Sum... |
23,988 | lean_file_chunk | 7af4e5c64d67092b2a6a7ad2e9d8f5f930027ce2390f28c79cba539a85b0b8d0 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne, Jireh Loreaux
-/
module
public import Mathlib.Algebra.BigOperators.Expect
public import Mathlib.Algebra.BigOperators.Field
public im... |
23,960 | lean_file_chunk | 685323c1ce8d88e738efe7320b165fdc6339fc463a3185b50f43841a0ae7cc55 | lean_source_file | pkg_mathlib_source_file_chunks | /-- **Weighted Hölder inequality**. -/
lemma inner_le_weight_mul_Lp (s : Finset ι) {p : ℝ} (hp : 1 ≤ p) (w f : ι → ℝ≥0) :
∑ i ∈ s, w i * f i ≤ (∑ i ∈ s, w i) ^ (1 - p⁻¹) * (∑ i ∈ s, w i * f i ^ p) ^ p⁻¹ := by
obtain rfl | hp := hp.eq_or_lt
· simp
calc
_ = ∑ i ∈ s, w i ^ (1 - p⁻¹) * (w i ^ p⁻¹ * f i) := ?_... |
6,144 | lean_file_chunk | 15d103b0048461211db532c2c6acf07e9523969441fa0dd4b37915f4bf02080c | lean_source_file | pkg_mathlib_source_file_chunks | sums are not already expressed as `p`-th powers, see `Lp_add_le_tsum_of_nonneg`. -/
theorem Lp_add_le_hasSum_of_nonneg (hp : 1 ≤ p) (hf : ∀ i, 0 ≤ f i) (hg : ∀ i, 0 ≤ g i) {A B : ℝ}
(hA : 0 ≤ A) (hB : 0 ≤ B) (hfA : HasSum (fun i => f i ^ p) (A ^ p))
(hgB : HasSum (fun i => g i ^ p) (B ^ p)) :
∃ C, 0 ≤ C ∧ C... |
12,296 | lean_file_chunk | ace1ab5647cd89673695341c28e6652b7e1d030fbb433e3fac221e0abc2e2ec6 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2023 Rémi Bottinelli. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rémi Bottinelli
-/
module
public import Mathlib.Data.Set.Function
public import Mathlib.Analysis.RCLike.Basic
public import Mathlib.Topology.EMetricSpace.BoundedVariation
/-!
# Cons... |
6,982 | lean_file_chunk | c5df00e7bdd1c28af3f887cb46c1e109d61f287489152e046aae34281a99562f | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 James Sundstrom. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: James Sundstrom
-/
module
public import Mathlib.Data.ENNReal.Real
public import Mathlib.Order.WellFoundedSet
public import Mathlib.Topology.EMetricSpace.Diam
/-!
# Oscillation
In t... |
7,224 | lean_file_chunk | 362ca8e8bc1120a54231dcb60de12503dd17f18fdb81811861c79f6c6fcb1c43 | 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, Eric Wieser
-/
module
public import Mathlib.Algebra.Quaternion
public import Mathlib.Analysis.InnerProductSpace.Continuous
public import Mathlib.Analysis.InnerProduc... |
16,503 | lean_file_chunk | f6acd563d4a2ae8474d838bc8576cc1efdab63b113ae6ace1001aa5da46af480 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Sébastien Gouëzel, Rémy Degenne
-/
module
public import Mathlib.Analysis.Convex.Jensen
public import Mathlib.Analysis.Convex.Mul
public import Mathlib.Analysis.Conve... |
6,796 | lean_file_chunk | 054a0faab21a361b7a03f6d9112e85f453c13594b2573acea1f5fde268d5fb90 | 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
-/
module
public import Mathlib.Analysis.Calculus.FDeriv.Equiv
public import Mathlib.Analysis.Calculus.FDeriv.Prod
public import Mathlib.Analysis.Calculus.Monoton... |
1,002 | lean_file_chunk | 4047492e3dc063f898ed532a00ee16c08dea55a1777857f33d73fc6c18cbb0a1 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
module
public import Mathlib.Analysis.Normed.Module.FiniteDimension
public import Mathlib.Analysis.PSeries
public import Mathlib.LinearAlgebra.Complex.FiniteDimensio... |
11,724 | lean_file_chunk | b689fd352f128423d57ff70353e294149b1acadeaf8a351c6aaa7ae76c7f20c5 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Kevin H. Wilson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kevin H. Wilson
-/
module
public import Mathlib.MeasureTheory.Integral.IntervalIntegral.Basic
public import Mathlib.Data.Set.Function
/-!
# Comparing sums and integrals
## Summary
... |
23,962 | lean_file_chunk | 47b44f7c9cc34a798c83734c6adad19fd64019cad61f4df058bdb1f595bc49e2 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2019 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo, Yaël Dillies, Moritz Doll
-/
module
public import Mathlib.Algebra.Order.Pi
public import Mathlib.Analysis.Convex.Function
public import Mathlib.Analysis.LocallyConvex.Basic
public i... |
23,927 | lean_file_chunk | 6e52e0d6f5ac543c25a4a43ee863e5d163470e325f3073d6b127fecda0eb49d3 | lean_source_file | pkg_mathlib_source_file_chunks | eq_univ_of_subset (ball_subset_closedBall _ _ _) (ball_zero' x hr)
theorem ball_smul (p : Seminorm 𝕜 E) {c : NNReal} (hc : 0 < c) (r : ℝ) (x : E) :
(c • p).ball x r = p.ball x (r / c) := by
ext
rw [mem_ball, mem_ball, smul_apply, NNReal.smul_def, smul_eq_mul, mul_comm,
lt_div_iff₀ (NNReal.coe_pos.mpr hc)]... |
9,138 | lean_file_chunk | 11ce69664e7be8335c0d7b08ba6a95260ee6863b63f44d36b0fe554928b63bc2 | lean_source_file | pkg_mathlib_source_file_chunks | · rw [← @comap_norm_nhds_zero E p.toAddGroupSeminorm.toSeminormedAddGroup, ← tendsto_iff_comap]
suffices Continuous p from this.tendsto' 0 _ (map_zero p)
rcases h₁ with ⟨r, hr⟩
exact p.continuous' hr
· rw [(@NormedAddGroup.nhds_zero_basis_norm_lt E
p.toAddGroupSeminorm.toSeminormedAddGroup).le_basis... |
5,528 | lean_file_chunk | 6eb4110e4ac435d96af00c9f5a9a078ba082450bdf83a3e1ec2108d09f2fdb35 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 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.Normed.Group.Real
public import Mathlib.Data.ZMod.Basic
public import Mathlib.Topology.Algebra.InfiniteSum.ENNReal
/-!
# Sums ov... |
5,700 | lean_file_chunk | e66802cc8b6806dce4ed1b7bb0081653acd5f7556648b44416fb94a09e8acbbc | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Lawrence Wu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Lawrence Wu
-/
module
public import Mathlib.Analysis.Fourier.Inversion
public import Mathlib.Analysis.MellinTransform
/-!
# Mellin inversion formula
We derive the Mellin inversion form... |
5,834 | lean_file_chunk | 0cf5d44d997c2312365dcca147277a6058932de755e5242da9e3dad2d76c726a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 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.Group.Prod
public import Mathlib.MeasureTheory.Group.LIntegral
/-!
# Convolution of functions using the Lebesgue integral... |
7,235 | lean_file_chunk | a916d8d6e4a272ea0e100d435b7caa8999d0922d8a8cc8bd77f335b8ec348d02 | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2024 Thomas Zhu. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Zhu, Etienne Marion
-/
module
public import Mathlib.Probability.Distributions.Gaussian.Real
public import Mathlib.MeasureTheory.Function.ConvergenceInDistribution
import Mathlib.M... |
4,654 | lean_file_chunk | 8fc6e10d88169459992f20dbbd248e7f031eb28fb908a2d9360af83cf8152872 | 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.Martingale.BorelCantelli
public import Mathlib.Probability.ConditionalExpectation
public import Mathlib.Probability.Independence.B... |
6,191 | lean_file_chunk | a854910ec72e58a9a268af3e77d1aea028cb0fd2a78d35678f683db4a48e3717 | 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.Density
public import Mathlib.Probability.Moments.Variance
/-!
# Law of a random variable
We introduce a predicate `HasLaw... |
23,980 | lean_file_chunk | b8e47af04b0a5fce6450c89356f2f56a264134a6da4017507b4ade729c8c5d42 | 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.Kernel.Composition.MeasureComp
public import Mathlib.Probability.Kernel.IonescuTulcea.Traj
/-!
# Infinite product of probab... |
5,258 | lean_file_chunk | e87b03c63c327ee07181ae992c2e736c1738dea05a2db75809e91b3fd7beda06 | lean_source_file | pkg_mathlib_source_file_chunks | /-- If we push the product measure forward by a reindexing equivalence, we get a product measure
on the reindexed product. -/
theorem infinitePi_map_piCongrLeft {α : Type*} (e : α ≃ ι) :
(infinitePi (fun i ↦ μ (e i))).map (piCongrLeft X e) = infinitePi μ := by
refine eq_infinitePi μ fun s t ht ↦ ?_
conv_lhs => ... |
7,671 | lean_file_chunk | a148f23c5326157bd2aa801a30792b175792dcf1cb6bf6fe0f496a354b025137 | 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.MeasureTheory.Function.ConditionalExpectation.PullOut
public import Mathlib.MeasureTheory.Integral.Average
public import Mathlib.Probability... |
17,056 | lean_file_chunk | 6e948eac874429a32680cdf4106685bf88d47323fa6331315e8e765a98108d31 | 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
-/
module
public import Mathlib.MeasureTheory.Measure.Decomposition.RadonNikodym
public import Mathlib.MeasureTheory.Measure.Haar.OfBasis
public import Mathlib.Probability.In... |
23,993 | lean_file_chunk | c4ebc1a15a2a296987db1605f750e976c5e2c23980c3719b89a5240b49fd4cfc | 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
-/
module
public import Mathlib.Probability.IdentDistrib
public import Mathlib.Probability.Independence.Integrable
public import Mathlib.MeasureTheory.Integral.Do... |
19,967 | lean_file_chunk | 89d82d11cd576dbe81cf46038814402d341a470575d4cd01bc71d1216c904323 | lean_source_file | pkg_mathlib_source_file_chunks | exists_seq_strictAnti_tendsto (0 : ℝ)
have := fun i => strong_law_aux1 X hint hindep hident hnonneg c_one (v_pos i)
filter_upwards [ae_all_iff.2 this] with ω hω
apply Asymptotics.isLittleO_iff.2 fun ε εpos => ?_
obtain ⟨i, hi⟩ : ∃ i, v i < ε := ((tendsto_order.1 v_lim).2 ε εpos).exists
filter_upwards [hω i] w... |
16,851 | lean_file_chunk | 41dc2a1a975e342e2d259bdf20b2d0375fcc2a9b2bc898dddf537491eab36e29 | 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
-/
module
public import Mathlib.Probability.HasLaw
public import Mathlib.Probability.Moments.Variance
public import Mathlib.MeasureTheory.Function.UniformIntegrab... |
1,918 | lean_file_chunk | e03790d8d725be49242bb19e034177ff1e3160d7850fa9403cb3bf5faf18ba5a | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2025 David Ledvinka. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Ledvinka
-/
module
public import Mathlib.Probability.HasLaw
public import Mathlib.Probability.Independence.InfinitePi
/-!
# Existence of Random Variables
This file contains le... |
3,030 | lean_file_chunk | e36f9b96acabf75b74255a93868fff2afa0a4403f60bceed7f55b28efcb466fb | 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.MeasureTheory.Function.ConditionalExpectation.Basic
public import Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue
/-! # Notations for ... |
10,466 | lean_file_chunk | 4b77d8911158eb72754137894333ea662823a1fdf78cbebd58c0f5d369794857 | 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, Bhavik Mehta
-/
module
public import Mathlib.Probability.ConditionalProbability
public import Mathlib.MeasureTheory.Measure.Count
public import Mathlib.MeasureTheory.Constru... |
3,357 | lean_file_chunk | 733ad479bed2bccfb03ab8426563df9a198ab029d8cd8280d1b7f87e55e9aab8 | 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.IdentDistrib
import Mathlib.Probability.Independence.InfinitePi
/-!
# Results about identically distributed random variables an... |
12,579 | lean_file_chunk | aaacb745e66cf97a7692d5c390d80c903e06742bd2f1fa7062267b90a05eb2ec | lean_source_file | pkg_mathlib_source_file_chunks | /-
Copyright (c) 2022 Rishikesh Vaishnav. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Rishikesh Vaishnav
-/
module
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
/-!
# Conditional Probability
This file defines conditional probability and incl... |
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