measure_theory.covering.density_theorem

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

5f6e827d

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

7e5137f5

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 -/
-import Mathbin.MeasureTheory.Measure.Doubling
-import Mathbin.MeasureTheory.Covering.Vitali
-import Mathbin.MeasureTheory.Covering.Differentiation
+import MeasureTheory.Measure.Doubling
+import MeasureTheory.Covering.Vitali
+import MeasureTheory.Covering.Differentiation
 
 #align_import measure_theory.covering.density_theorem from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"

7e5137f5

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module measure_theory.covering.density_theorem
-! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Measure.Doubling
 import Mathbin.MeasureTheory.Covering.Vitali
 import Mathbin.MeasureTheory.Covering.Differentiation
 
+#align_import measure_theory.covering.density_theorem from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-!
 # Uniformly locally doubling measures and Lebesgue's density theorem

7e5137f5

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -80,6 +80,7 @@ irreducible_def vitaliFamily (K : ℝ) : VitaliFamily μ :=
 #align is_unif_loc_doubling_measure.vitali_family IsUnifLocDoublingMeasure.vitaliFamily
 -/
 
+#print IsUnifLocDoublingMeasure.closedBall_mem_vitaliFamily_of_dist_le_mul /-
 /-- In the Vitali family `is_unif_loc_doubling_measure.vitali_family K`, the sets based at `x`
 contain all balls `closed_ball y r` when `dist x y ≤ K * r`. -/
 theorem closedBall_mem_vitaliFamily_of_dist_le_mul {K : ℝ} {x y : α} {r : ℝ} (h : dist x y ≤ K * r)
@@ -127,7 +128,9 @@ theorem closedBall_mem_vitaliFamily_of_dist_le_mul {K : ℝ} {x y : α} {r : ℝ
     refine' le_mul_of_one_le_left (zero_le _) _
     exact ENNReal.one_le_coe_iff.2 (le_max_right _ _)
 #align is_unif_loc_doubling_measure.closed_ball_mem_vitali_family_of_dist_le_mul IsUnifLocDoublingMeasure.closedBall_mem_vitaliFamily_of_dist_le_mul
+-/
 
+#print IsUnifLocDoublingMeasure.tendsto_closedBall_filterAt /-
 theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type _} {l : Filter ι} (w : ι → α)
     (δ : ι → ℝ) (δlim : Tendsto δ l (𝓝[>] 0)) (xmem : ∀ᶠ j in l, x ∈ closedBall (w j) (K * δ j)) :
     Tendsto (fun j => closedBall (w j) (δ j)) l ((vitaliFamily μ K).filterAt x) :=
@@ -152,6 +155,7 @@ theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type _} {l : Filter
     simp only [mem_closed_ball] at hx hy ⊢
     linarith [dist_triangle_right y x (w j)]
 #align is_unif_loc_doubling_measure.tendsto_closed_ball_filter_at IsUnifLocDoublingMeasure.tendsto_closedBall_filterAt
+-/
 
 end
 
@@ -160,6 +164,7 @@ section Applications
 variable [SecondCountableTopology α] [BorelSpace α] [IsLocallyFiniteMeasure μ] {E : Type _}
   [NormedAddCommGroup E]
 
+#print IsUnifLocDoublingMeasure.ae_tendsto_measure_inter_div /-
 /-- A version of *Lebesgue's density theorem* for a sequence of closed balls whose centers are
 not required to be fixed.
 
@@ -173,7 +178,9 @@ theorem ae_tendsto_measure_inter_div (S : Set α) (K : ℝ) :
   filter_upwards [(VitaliFamily μ K).ae_tendsto_measure_inter_div S] with x hx ι l w δ δlim
     xmem using hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
 #align is_unif_loc_doubling_measure.ae_tendsto_measure_inter_div IsUnifLocDoublingMeasure.ae_tendsto_measure_inter_div
+-/
 
+#print IsUnifLocDoublingMeasure.ae_tendsto_average_norm_sub /-
 /-- A version of *Lebesgue differentiation theorem* for a sequence of closed balls whose
 centers are not required to be fixed. -/
 theorem ae_tendsto_average_norm_sub {f : α → E} (hf : Integrable f μ) (K : ℝ) :
@@ -185,7 +192,9 @@ theorem ae_tendsto_average_norm_sub {f : α → E} (hf : Integrable f μ) (K : 
   filter_upwards [(VitaliFamily μ K).ae_tendsto_average_norm_sub hf] with x hx ι l w δ δlim
     xmem using hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
 #align is_unif_loc_doubling_measure.ae_tendsto_average_norm_sub IsUnifLocDoublingMeasure.ae_tendsto_average_norm_sub
+-/
 
+#print IsUnifLocDoublingMeasure.ae_tendsto_average /-
 /-- A version of *Lebesgue differentiation theorem* for a sequence of closed balls whose
 centers are not required to be fixed. -/
 theorem ae_tendsto_average [NormedSpace ℝ E] [CompleteSpace E] {f : α → E} (hf : Integrable f μ)
@@ -198,6 +207,7 @@ theorem ae_tendsto_average [NormedSpace ℝ E] [CompleteSpace E] {f : α → E}
   filter_upwards [(VitaliFamily μ K).ae_tendsto_average hf] with x hx ι l w δ δlim xmem using
     hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
 #align is_unif_loc_doubling_measure.ae_tendsto_average IsUnifLocDoublingMeasure.ae_tendsto_average
+-/
 
 end Applications

7e5137f5

bump to nightly-2023-06-09-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

fe176e9b

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 
 ! This file was ported from Lean 3 source module measure_theory.covering.density_theorem
-! leanprover-community/mathlib commit 5f6e827d81dfbeb6151d7016586ceeb0099b9655
+! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.MeasureTheory.Covering.Differentiation
 /-!
 # Uniformly locally doubling measures and Lebesgue's density theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Lebesgue's density theorem states that given a set `S` in a sigma compact metric space with
 locally-finite uniformly locally doubling measure `μ` then for almost all points `x` in `S`, for any
 sequence of closed balls `B₀, B₁, B₂, ...` containing `x`, the limit `μ (S ∩ Bⱼ) / μ (Bⱼ) → 1` as

5f6e827d

bump to nightly-2023-06-07-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/58a272265b5e05f258161260dd2c5d247213cbd3

c2a08841

Diff

@@ -49,6 +49,7 @@ variable [SecondCountableTopology α] [BorelSpace α] [IsLocallyFiniteMeasure μ
 
 open scoped Topology
 
+#print IsUnifLocDoublingMeasure.vitaliFamily /-
 /-- A Vitali family in a space with a uniformly locally doubling measure, designed so that the sets
 at `x` contain all `closed_ball y r` when `dist x y ≤ K * r`. -/
 irreducible_def vitaliFamily (K : ℝ) : VitaliFamily μ :=
@@ -74,6 +75,7 @@ irreducible_def vitaliFamily (K : ℝ) : VitaliFamily μ :=
     (Vitali.vitaliFamily μ (scaling_constant_of μ (max (4 * K + 3) 3)) A).enlarge (R / 4)
       (by linarith)
 #align is_unif_loc_doubling_measure.vitali_family IsUnifLocDoublingMeasure.vitaliFamily
+-/
 
 /-- In the Vitali family `is_unif_loc_doubling_measure.vitali_family K`, the sets based at `x`
 contain all balls `closed_ball y r` when `dist x y ≤ K * r`. -/

5f6e827d

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -45,7 +45,7 @@ variable {α : Type _} [MetricSpace α] [MeasurableSpace α] (μ : Measure α)
 
 section
 
-variable [SecondCountableTopology α] [BorelSpace α] [LocallyFiniteMeasure μ]
+variable [SecondCountableTopology α] [BorelSpace α] [IsLocallyFiniteMeasure μ]
 
 open scoped Topology
 
@@ -128,7 +128,7 @@ theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type _} {l : Filter
     Tendsto (fun j => closedBall (w j) (δ j)) l ((vitaliFamily μ K).filterAt x) :=
   by
   refine' (VitaliFamily μ K).tendsto_filterAt_iff.mpr ⟨_, fun ε hε => _⟩
-  · filter_upwards [xmem, δlim self_mem_nhdsWithin]with j hj h'j
+  · filter_upwards [xmem, δlim self_mem_nhdsWithin] with j hj h'j
     exact closed_ball_mem_vitali_family_of_dist_le_mul μ hj h'j
   · by_cases l.ne_bot
     swap; · simp [not_ne_bot.1 h]
@@ -152,7 +152,7 @@ end
 
 section Applications
 
-variable [SecondCountableTopology α] [BorelSpace α] [LocallyFiniteMeasure μ] {E : Type _}
+variable [SecondCountableTopology α] [BorelSpace α] [IsLocallyFiniteMeasure μ] {E : Type _}
   [NormedAddCommGroup E]
 
 /-- A version of *Lebesgue's density theorem* for a sequence of closed balls whose centers are
@@ -165,8 +165,8 @@ theorem ae_tendsto_measure_inter_div (S : Set α) (K : ℝ) :
         (xmem : ∀ᶠ j in l, x ∈ closedBall (w j) (K * δ j)),
         Tendsto (fun j => μ (S ∩ closedBall (w j) (δ j)) / μ (closedBall (w j) (δ j))) l (𝓝 1) :=
   by
-  filter_upwards [(VitaliFamily μ K).ae_tendsto_measure_inter_div
-      S]with x hx ι l w δ δlim xmem using hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
+  filter_upwards [(VitaliFamily μ K).ae_tendsto_measure_inter_div S] with x hx ι l w δ δlim
+    xmem using hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
 #align is_unif_loc_doubling_measure.ae_tendsto_measure_inter_div IsUnifLocDoublingMeasure.ae_tendsto_measure_inter_div
 
 /-- A version of *Lebesgue differentiation theorem* for a sequence of closed balls whose
@@ -177,8 +177,8 @@ theorem ae_tendsto_average_norm_sub {f : α → E} (hf : Integrable f μ) (K : 
         (xmem : ∀ᶠ j in l, x ∈ closedBall (w j) (K * δ j)),
         Tendsto (fun j => ⨍ y in closedBall (w j) (δ j), ‖f y - f x‖ ∂μ) l (𝓝 0) :=
   by
-  filter_upwards [(VitaliFamily μ K).ae_tendsto_average_norm_sub
-      hf]with x hx ι l w δ δlim xmem using hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
+  filter_upwards [(VitaliFamily μ K).ae_tendsto_average_norm_sub hf] with x hx ι l w δ δlim
+    xmem using hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
 #align is_unif_loc_doubling_measure.ae_tendsto_average_norm_sub IsUnifLocDoublingMeasure.ae_tendsto_average_norm_sub
 
 /-- A version of *Lebesgue differentiation theorem* for a sequence of closed balls whose
@@ -190,8 +190,8 @@ theorem ae_tendsto_average [NormedSpace ℝ E] [CompleteSpace E] {f : α → E}
         (xmem : ∀ᶠ j in l, x ∈ closedBall (w j) (K * δ j)),
         Tendsto (fun j => ⨍ y in closedBall (w j) (δ j), f y ∂μ) l (𝓝 (f x)) :=
   by
-  filter_upwards [(VitaliFamily μ K).ae_tendsto_average
-      hf]with x hx ι l w δ δlim xmem using hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
+  filter_upwards [(VitaliFamily μ K).ae_tendsto_average hf] with x hx ι l w δ δlim xmem using
+    hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
 #align is_unif_loc_doubling_measure.ae_tendsto_average IsUnifLocDoublingMeasure.ae_tendsto_average
 
 end Applications

5f6e827d

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -144,7 +144,7 @@ theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type _} {l : Filter
     rintro j ⟨⟨hjε, hj₀ : 0 < δ j⟩, hx⟩ y hy
     replace hjε : (K + 1) * δ j < ε := by
       simpa [abs_eq_self.mpr hj₀.le] using (lt_div_iff' hK).mp hjε
-    simp only [mem_closed_ball] at hx hy⊢
+    simp only [mem_closed_ball] at hx hy ⊢
     linarith [dist_triangle_right y x (w j)]
 #align is_unif_loc_doubling_measure.tendsto_closed_ball_filter_at IsUnifLocDoublingMeasure.tendsto_closedBall_filterAt

5f6e827d

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -36,7 +36,7 @@ noncomputable section
 
 open Set Filter Metric MeasureTheory TopologicalSpace
 
-open NNReal Topology
+open scoped NNReal Topology
 
 namespace IsUnifLocDoublingMeasure
 
@@ -47,7 +47,7 @@ section
 
 variable [SecondCountableTopology α] [BorelSpace α] [LocallyFiniteMeasure μ]
 
-open Topology
+open scoped Topology
 
 /-- A Vitali family in a space with a uniformly locally doubling measure, designed so that the sets
 at `x` contain all `closed_ball y r` when `dist x y ≤ K * r`. -/

5f6e827d

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -131,8 +131,7 @@ theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type _} {l : Filter
   · filter_upwards [xmem, δlim self_mem_nhdsWithin]with j hj h'j
     exact closed_ball_mem_vitali_family_of_dist_le_mul μ hj h'j
   · by_cases l.ne_bot
-    swap
-    · simp [not_ne_bot.1 h]
+    swap; · simp [not_ne_bot.1 h]
     have hK : 0 ≤ K := by
       skip
       rcases(xmem.and (δlim self_mem_nhdsWithin)).exists with ⟨j, hj, h'j⟩
@@ -140,8 +139,7 @@ theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type _} {l : Filter
       exact (mul_nonneg_iff_left_nonneg_of_pos (mem_Ioi.1 h'j)).1 this
     have δpos := eventually_mem_of_tendsto_nhdsWithin δlim
     replace δlim := tendsto_nhds_of_tendsto_nhdsWithin δlim
-    replace hK : 0 < K + 1
-    · linarith
+    replace hK : 0 < K + 1; · linarith
     apply (((metric.tendsto_nhds.mp δlim _ (div_pos hε hK)).And δpos).And xmem).mono
     rintro j ⟨⟨hjε, hj₀ : 0 < δ j⟩, hx⟩ y hy
     replace hjε : (K + 1) * δ j < ε := by

5f6e827d

bump to nightly-2023-05-09-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

244524af

Diff

@@ -45,7 +45,7 @@ variable {α : Type _} [MetricSpace α] [MeasurableSpace α] (μ : Measure α)
 
 section
 
-variable [SecondCountableTopology α] [BorelSpace α] [IsLocallyFiniteMeasure μ]
+variable [SecondCountableTopology α] [BorelSpace α] [LocallyFiniteMeasure μ]
 
 open Topology
 
@@ -154,7 +154,7 @@ end
 
 section Applications
 
-variable [SecondCountableTopology α] [BorelSpace α] [IsLocallyFiniteMeasure μ] {E : Type _}
+variable [SecondCountableTopology α] [BorelSpace α] [LocallyFiniteMeasure μ] {E : Type _}
   [NormedAddCommGroup E]
 
 /-- A version of *Lebesgue's density theorem* for a sequence of closed balls whose centers are

5f6e827d

bump to nightly-2023-04-03-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/d95bef0d215ea58c0fd7bbc4b151bf3fe952c095

8477bcac

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
 
 ! This file was ported from Lean 3 source module measure_theory.covering.density_theorem
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 5f6e827d81dfbeb6151d7016586ceeb0099b9655
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,19 +13,21 @@ import Mathbin.MeasureTheory.Covering.Vitali
 import Mathbin.MeasureTheory.Covering.Differentiation
 
 /-!
-# Doubling measures and Lebesgue's density theorem
+# Uniformly locally doubling measures and Lebesgue's density theorem
 
 Lebesgue's density theorem states that given a set `S` in a sigma compact metric space with
-locally-finite doubling measure `μ` then for almost all points `x` in `S`, for any sequence of
-closed balls `B₀, B₁, B₂, ...` containing `x`, the limit `μ (S ∩ Bⱼ) / μ (Bⱼ) → 1` as `j → ∞`.
+locally-finite uniformly locally doubling measure `μ` then for almost all points `x` in `S`, for any
+sequence of closed balls `B₀, B₁, B₂, ...` containing `x`, the limit `μ (S ∩ Bⱼ) / μ (Bⱼ) → 1` as
+`j → ∞`.
 
-In this file we combine general results about existence of Vitali families for doubling measures
-with results about differentiation along a Vitali family to obtain an explicit form of Lebesgue's
-density theorem.
+In this file we combine general results about existence of Vitali families for uniformly locally
+doubling measures with results about differentiation along a Vitali family to obtain an explicit
+form of Lebesgue's density theorem.
 
 ## Main results
-  * `is_doubling_measure.ae_tendsto_measure_inter_div`: a version of Lebesgue's density theorem for
-  sequences of balls converging on a point but whose centres are not required to be fixed.
+  * `is_unif_loc_doubling_measure.ae_tendsto_measure_inter_div`: a version of Lebesgue's density
+  theorem for sequences of balls converging on a point but whose centres are not required to be
+  fixed.
 
 -/
 
@@ -36,9 +38,10 @@ open Set Filter Metric MeasureTheory TopologicalSpace
 
 open NNReal Topology
 
-namespace IsDoublingMeasure
+namespace IsUnifLocDoublingMeasure
 
-variable {α : Type _} [MetricSpace α] [MeasurableSpace α] (μ : Measure α) [IsDoublingMeasure μ]
+variable {α : Type _} [MetricSpace α] [MeasurableSpace α] (μ : Measure α)
+  [IsUnifLocDoublingMeasure μ]
 
 section
 
@@ -46,8 +49,8 @@ variable [SecondCountableTopology α] [BorelSpace α] [IsLocallyFiniteMeasure μ
 
 open Topology
 
-/-- A Vitali family in a space with a doubling measure, designed so that the sets at `x` contain
-all `closed_ball y r` when `dist x y ≤ K * r`. -/
+/-- A Vitali family in a space with a uniformly locally doubling measure, designed so that the sets
+at `x` contain all `closed_ball y r` when `dist x y ≤ K * r`. -/
 irreducible_def vitaliFamily (K : ℝ) : VitaliFamily μ :=
   by
   /- the Vitali covering theorem gives a family that works well at small scales, thanks to the
@@ -70,10 +73,10 @@ irreducible_def vitaliFamily (K : ℝ) : VitaliFamily μ :=
   exact
     (Vitali.vitaliFamily μ (scaling_constant_of μ (max (4 * K + 3) 3)) A).enlarge (R / 4)
       (by linarith)
-#align is_doubling_measure.vitali_family IsDoublingMeasure.vitaliFamily
+#align is_unif_loc_doubling_measure.vitali_family IsUnifLocDoublingMeasure.vitaliFamily
 
-/-- In the Vitali family `is_doubling_measure.vitali_family K`, the sets based at `x` contain all
-balls `closed_ball y r` when `dist x y ≤ K * r`. -/
+/-- In the Vitali family `is_unif_loc_doubling_measure.vitali_family K`, the sets based at `x`
+contain all balls `closed_ball y r` when `dist x y ≤ K * r`. -/
 theorem closedBall_mem_vitaliFamily_of_dist_le_mul {K : ℝ} {x y : α} {r : ℝ} (h : dist x y ≤ K * r)
     (rpos : 0 < r) : closedBall y r ∈ (vitaliFamily μ K).setsAt x :=
   by
@@ -118,7 +121,7 @@ theorem closedBall_mem_vitaliFamily_of_dist_le_mul {K : ℝ} {x y : α} {r : ℝ
     apply (measure_mono this).trans _
     refine' le_mul_of_one_le_left (zero_le _) _
     exact ENNReal.one_le_coe_iff.2 (le_max_right _ _)
-#align is_doubling_measure.closed_ball_mem_vitali_family_of_dist_le_mul IsDoublingMeasure.closedBall_mem_vitaliFamily_of_dist_le_mul
+#align is_unif_loc_doubling_measure.closed_ball_mem_vitali_family_of_dist_le_mul IsUnifLocDoublingMeasure.closedBall_mem_vitaliFamily_of_dist_le_mul
 
 theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type _} {l : Filter ι} (w : ι → α)
     (δ : ι → ℝ) (δlim : Tendsto δ l (𝓝[>] 0)) (xmem : ∀ᶠ j in l, x ∈ closedBall (w j) (K * δ j)) :
@@ -145,7 +148,7 @@ theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type _} {l : Filter
       simpa [abs_eq_self.mpr hj₀.le] using (lt_div_iff' hK).mp hjε
     simp only [mem_closed_ball] at hx hy⊢
     linarith [dist_triangle_right y x (w j)]
-#align is_doubling_measure.tendsto_closed_ball_filter_at IsDoublingMeasure.tendsto_closedBall_filterAt
+#align is_unif_loc_doubling_measure.tendsto_closed_ball_filter_at IsUnifLocDoublingMeasure.tendsto_closedBall_filterAt
 
 end
 
@@ -166,7 +169,7 @@ theorem ae_tendsto_measure_inter_div (S : Set α) (K : ℝ) :
   by
   filter_upwards [(VitaliFamily μ K).ae_tendsto_measure_inter_div
       S]with x hx ι l w δ δlim xmem using hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
-#align is_doubling_measure.ae_tendsto_measure_inter_div IsDoublingMeasure.ae_tendsto_measure_inter_div
+#align is_unif_loc_doubling_measure.ae_tendsto_measure_inter_div IsUnifLocDoublingMeasure.ae_tendsto_measure_inter_div
 
 /-- A version of *Lebesgue differentiation theorem* for a sequence of closed balls whose
 centers are not required to be fixed. -/
@@ -178,7 +181,7 @@ theorem ae_tendsto_average_norm_sub {f : α → E} (hf : Integrable f μ) (K : 
   by
   filter_upwards [(VitaliFamily μ K).ae_tendsto_average_norm_sub
       hf]with x hx ι l w δ δlim xmem using hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
-#align is_doubling_measure.ae_tendsto_average_norm_sub IsDoublingMeasure.ae_tendsto_average_norm_sub
+#align is_unif_loc_doubling_measure.ae_tendsto_average_norm_sub IsUnifLocDoublingMeasure.ae_tendsto_average_norm_sub
 
 /-- A version of *Lebesgue differentiation theorem* for a sequence of closed balls whose
 centers are not required to be fixed. -/
@@ -191,9 +194,9 @@ theorem ae_tendsto_average [NormedSpace ℝ E] [CompleteSpace E] {f : α → E}
   by
   filter_upwards [(VitaliFamily μ K).ae_tendsto_average
       hf]with x hx ι l w δ δlim xmem using hx.comp (tendsto_closed_ball_filter_at μ _ _ δlim xmem)
-#align is_doubling_measure.ae_tendsto_average IsDoublingMeasure.ae_tendsto_average
+#align is_unif_loc_doubling_measure.ae_tendsto_average IsUnifLocDoublingMeasure.ae_tendsto_average
 
 end Applications
 
-end IsDoublingMeasure
+end IsUnifLocDoublingMeasure

f2ce6086

bump to nightly-2023-02-27-10

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

49ff026a

Diff

@@ -117,7 +117,7 @@ theorem closedBall_mem_vitaliFamily_of_dist_le_mul {K : ℝ} {x y : α} {r : ℝ
       linarith
     apply (measure_mono this).trans _
     refine' le_mul_of_one_le_left (zero_le _) _
-    exact Ennreal.one_le_coe_iff.2 (le_max_right _ _)
+    exact ENNReal.one_le_coe_iff.2 (le_max_right _ _)
 #align is_doubling_measure.closed_ball_mem_vitali_family_of_dist_le_mul IsDoublingMeasure.closedBall_mem_vitaliFamily_of_dist_le_mul
 
 theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type _} {l : Filter ι} (w : ι → α)

f2ce6086

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

5f6e827d

chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

a13e8040

Diff

@@ -123,7 +123,7 @@ theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type*} {l : Filter
       exact (mul_nonneg_iff_left_nonneg_of_pos (mem_Ioi.1 h'j)).1 this
     have δpos := eventually_mem_of_tendsto_nhdsWithin δlim
     replace δlim := tendsto_nhds_of_tendsto_nhdsWithin δlim
-    replace hK : 0 < K + 1; · linarith
+    replace hK : 0 < K + 1 := by linarith
     apply (((Metric.tendsto_nhds.mp δlim _ (div_pos hε hK)).and δpos).and xmem).mono
     rintro j ⟨⟨hjε, hj₀ : 0 < δ j⟩, hx⟩ y hy
     replace hjε : (K + 1) * δ j < ε := by

5f6e827d

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -37,7 +37,7 @@ open scoped NNReal Topology
 
 namespace IsUnifLocDoublingMeasure
 
-variable {α : Type _} [MetricSpace α] [MeasurableSpace α] (μ : Measure α)
+variable {α : Type*} [MetricSpace α] [MeasurableSpace α] (μ : Measure α)
   [IsUnifLocDoublingMeasure μ]
 
 section
@@ -109,7 +109,7 @@ theorem closedBall_mem_vitaliFamily_of_dist_le_mul {K : ℝ} {x y : α} {r : ℝ
     exact ENNReal.one_le_coe_iff.2 (le_max_right _ _)
 #align is_unif_loc_doubling_measure.closed_ball_mem_vitali_family_of_dist_le_mul IsUnifLocDoublingMeasure.closedBall_mem_vitaliFamily_of_dist_le_mul
 
-theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type _} {l : Filter ι} (w : ι → α)
+theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type*} {l : Filter ι} (w : ι → α)
     (δ : ι → ℝ) (δlim : Tendsto δ l (𝓝[>] 0)) (xmem : ∀ᶠ j in l, x ∈ closedBall (w j) (K * δ j)) :
     Tendsto (fun j => closedBall (w j) (δ j)) l ((vitaliFamily μ K).filterAt x) := by
   refine' (vitaliFamily μ K).tendsto_filterAt_iff.mpr ⟨_, fun ε hε => _⟩
@@ -136,7 +136,7 @@ end
 
 section Applications
 
-variable [SecondCountableTopology α] [BorelSpace α] [IsLocallyFiniteMeasure μ] {E : Type _}
+variable [SecondCountableTopology α] [BorelSpace α] [IsLocallyFiniteMeasure μ] {E : Type*}
   [NormedAddCommGroup E]
 
 /-- A version of **Lebesgue's density theorem** for a sequence of closed balls whose centers are
@@ -144,7 +144,7 @@ not required to be fixed.
 
 See also `Besicovitch.ae_tendsto_measure_inter_div`. -/
 theorem ae_tendsto_measure_inter_div (S : Set α) (K : ℝ) : ∀ᵐ x ∂μ.restrict S,
-    ∀ {ι : Type _} {l : Filter ι} (w : ι → α) (δ : ι → ℝ) (δlim : Tendsto δ l (𝓝[>] 0))
+    ∀ {ι : Type*} {l : Filter ι} (w : ι → α) (δ : ι → ℝ) (δlim : Tendsto δ l (𝓝[>] 0))
       (xmem : ∀ᶠ j in l, x ∈ closedBall (w j) (K * δ j)),
       Tendsto (fun j => μ (S ∩ closedBall (w j) (δ j)) / μ (closedBall (w j) (δ j))) l (𝓝 1) := by
   filter_upwards [(vitaliFamily μ K).ae_tendsto_measure_inter_div S] with x hx ι l w δ δlim
@@ -154,7 +154,7 @@ theorem ae_tendsto_measure_inter_div (S : Set α) (K : ℝ) : ∀ᵐ x ∂μ.res
 /-- A version of **Lebesgue differentiation theorem** for a sequence of closed balls whose
 centers are not required to be fixed. -/
 theorem ae_tendsto_average_norm_sub {f : α → E} (hf : LocallyIntegrable f μ) (K : ℝ) : ∀ᵐ x ∂μ,
-    ∀ {ι : Type _} {l : Filter ι} (w : ι → α) (δ : ι → ℝ) (δlim : Tendsto δ l (𝓝[>] 0))
+    ∀ {ι : Type*} {l : Filter ι} (w : ι → α) (δ : ι → ℝ) (δlim : Tendsto δ l (𝓝[>] 0))
       (xmem : ∀ᶠ j in l, x ∈ closedBall (w j) (K * δ j)),
       Tendsto (fun j => ⨍ y in closedBall (w j) (δ j), ‖f y - f x‖ ∂μ) l (𝓝 0) := by
   filter_upwards [(vitaliFamily μ K).ae_tendsto_average_norm_sub hf] with x hx ι l w δ δlim
@@ -165,7 +165,7 @@ theorem ae_tendsto_average_norm_sub {f : α → E} (hf : LocallyIntegrable f μ)
 centers are not required to be fixed. -/
 theorem ae_tendsto_average [NormedSpace ℝ E] [CompleteSpace E]
     {f : α → E} (hf : LocallyIntegrable f μ) (K : ℝ) : ∀ᵐ x ∂μ,
-      ∀ {ι : Type _} {l : Filter ι} (w : ι → α) (δ : ι → ℝ) (δlim : Tendsto δ l (𝓝[>] 0))
+      ∀ {ι : Type*} {l : Filter ι} (w : ι → α) (δ : ι → ℝ) (δlim : Tendsto δ l (𝓝[>] 0))
         (xmem : ∀ᶠ j in l, x ∈ closedBall (w j) (K * δ j)),
         Tendsto (fun j => ⨍ y in closedBall (w j) (δ j), f y ∂μ) l (𝓝 (f x)) := by
   filter_upwards [(vitaliFamily μ K).ae_tendsto_average hf] with x hx ι l w δ δlim xmem using

5f6e827d

feat: The convolution of a locally integrable function f with a sequence of bump functions converges ae to f (#6102)

33baf7d8

Diff

@@ -153,7 +153,7 @@ theorem ae_tendsto_measure_inter_div (S : Set α) (K : ℝ) : ∀ᵐ x ∂μ.res
 
 /-- A version of **Lebesgue differentiation theorem** for a sequence of closed balls whose
 centers are not required to be fixed. -/
-theorem ae_tendsto_average_norm_sub {f : α → E} (hf : Integrable f μ) (K : ℝ) : ∀ᵐ x ∂μ,
+theorem ae_tendsto_average_norm_sub {f : α → E} (hf : LocallyIntegrable f μ) (K : ℝ) : ∀ᵐ x ∂μ,
     ∀ {ι : Type _} {l : Filter ι} (w : ι → α) (δ : ι → ℝ) (δlim : Tendsto δ l (𝓝[>] 0))
       (xmem : ∀ᶠ j in l, x ∈ closedBall (w j) (K * δ j)),
       Tendsto (fun j => ⨍ y in closedBall (w j) (δ j), ‖f y - f x‖ ∂μ) l (𝓝 0) := by
@@ -163,8 +163,8 @@ theorem ae_tendsto_average_norm_sub {f : α → E} (hf : Integrable f μ) (K : 
 
 /-- A version of **Lebesgue differentiation theorem** for a sequence of closed balls whose
 centers are not required to be fixed. -/
-theorem ae_tendsto_average [NormedSpace ℝ E] [CompleteSpace E] {f : α → E} (hf : Integrable f μ)
-    (K : ℝ) : ∀ᵐ x ∂μ,
+theorem ae_tendsto_average [NormedSpace ℝ E] [CompleteSpace E]
+    {f : α → E} (hf : LocallyIntegrable f μ) (K : ℝ) : ∀ᵐ x ∂μ,
       ∀ {ι : Type _} {l : Filter ι} (w : ι → α) (δ : ι → ℝ) (δlim : Tendsto δ l (𝓝[>] 0))
         (xmem : ∀ᶠ j in l, x ∈ closedBall (w j) (K * δ j)),
         Tendsto (fun j => ⨍ y in closedBall (w j) (δ j), f y ∂μ) l (𝓝 (f x)) := by

5f6e827d

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Oliver Nash. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Oliver Nash
-
-! This file was ported from Lean 3 source module measure_theory.covering.density_theorem
-! leanprover-community/mathlib commit 5f6e827d81dfbeb6151d7016586ceeb0099b9655
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Measure.Doubling
 import Mathlib.MeasureTheory.Covering.Vitali
 import Mathlib.MeasureTheory.Covering.Differentiation
 
+#align_import measure_theory.covering.density_theorem from "leanprover-community/mathlib"@"5f6e827d81dfbeb6151d7016586ceeb0099b9655"
+
 /-!
 # Uniformly locally doubling measures and Lebesgue's density theorem

5f6e827d

feat: add Filter.eq_or_neBot (#5230)

Also add Filter.limsup_bot, Filter.liminf_bot, and golf some proofs using new lemmas.

4574002d

Diff

@@ -118,8 +118,8 @@ theorem tendsto_closedBall_filterAt {K : ℝ} {x : α} {ι : Type _} {l : Filter
   refine' (vitaliFamily μ K).tendsto_filterAt_iff.mpr ⟨_, fun ε hε => _⟩
   · filter_upwards [xmem, δlim self_mem_nhdsWithin] with j hj h'j
     exact closedBall_mem_vitaliFamily_of_dist_le_mul μ hj h'j
-  · by_cases l.NeBot
-    swap; · simp [not_neBot.1 h]
+  · rcases l.eq_or_neBot with rfl | h
+    · simp
     have hK : 0 ≤ K := by
       rcases (xmem.and (δlim self_mem_nhdsWithin)).exists with ⟨j, hj, h'j⟩
       have : 0 ≤ K * δ j := nonempty_closedBall.1 ⟨x, hj⟩

5f6e827d

feat: port MeasureTheory.Covering.DensityTheorem (#4789)

f5cf43d1

`measure_theory.covering.density_theorem` ⟷ `Mathlib.MeasureTheory.Covering.DensityTheorem`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 988

measure_theory.covering.density_theorem ⟷ Mathlib.MeasureTheory.Covering.DensityTheorem

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 988

`measure_theory.covering.density_theorem` ⟷ `Mathlib.MeasureTheory.Covering.DensityTheorem`