measure_theory.covering.liminf_limsup ⟷ Mathlib.MeasureTheory.Covering.LiminfLimsup

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -92,7 +92,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
       (IsUnifLocDoublingMeasure.ae_tendsto_measure_inter_div μ W 2)
   replace hd : d ∈ blimsup Y₁ at_top p := ((mem_diff _).mp hd).1
   obtain ⟨f : ℕ → ℕ, hf⟩ := exists_forall_mem_of_has_basis_mem_blimsup' at_top_basis hd
-  simp only [forall_and] at hf 
+  simp only [forall_and] at hf
   obtain ⟨hf₀ : ∀ j, d ∈ cthickening (r₁ (f j)) (s (f j)), hf₁, hf₂ : ∀ j, j ≤ f j⟩ := hf
   have hf₃ : tendsto f at_top at_top :=
     tendsto_at_top_at_top.mpr fun j => ⟨f j, fun i hi => (hf₂ j).trans (hi.trans <| hf₂ i)⟩
@@ -101,10 +101,10 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
   replace hf₀ : ∀ j, ∃ w ∈ s (f j), d ∈ closed_ball w (2 * r₁ (f j))
   · intro j
     specialize hrp (f j)
-    rw [Pi.zero_apply] at hrp 
+    rw [Pi.zero_apply] at hrp
     rcases eq_or_lt_of_le hrp with (hr0 | hrp')
     · specialize hf₀ j
-      rw [← hr0, cthickening_zero, (hs (f j)).closure_eq] at hf₀ 
+      rw [← hr0, cthickening_zero, (hs (f j)).closure_eq] at hf₀
       exact ⟨d, hf₀, by simp [← hr0]⟩
     ·
       exact
@@ -166,7 +166,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
     rw [← measure_union' hj₁ measurableSet_closedBall]
     exact measure_mono (union_subset (h₁ j) (h₂ j))
   replace hj₃ := tsub_le_tsub_right hj₃ (↑C⁻¹ * μ (B j))
-  rwa [ENNReal.add_sub_cancel_left hB] at hj₃ 
+  rwa [ENNReal.add_sub_cancel_left hB] at hj₃
 #align blimsup_cthickening_ae_le_of_eventually_mul_le_aux blimsup_cthickening_ae_le_of_eventually_mul_le_aux
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -240,7 +240,7 @@ theorem blimsup_cthickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
     by
     refine'
       tendsto_nhds_within_iff.mpr
-        ⟨tendsto.if' hr tendsto_one_div_add_atTop_nhds_0_nat, eventually_of_forall fun i => _⟩
+        ⟨tendsto.if' hr tendsto_one_div_add_atTop_nhds_zero_nat, eventually_of_forall fun i => _⟩
     by_cases hi : 0 < r i
     · simp [hi, r']
     · simp only [hi, r', one_div, mem_Ioi, if_false, inv_pos]; positivity

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

@@ -325,7 +325,8 @@ theorem blimsup_thickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
       blimsup (fun i => thickening (M * r i) (s i)) at_top q :=
     by
     refine' blimsup_congr' (eventually_of_forall fun i h => _)
-    replace h : 0 < r i; · rw [← zero_lt_mul_left hM]; contrapose! h; apply thickening_of_nonpos h
+    replace h : 0 < r i;
+    · rw [← mul_pos_iff_of_pos_left hM]; contrapose! h; apply thickening_of_nonpos h
     simp only [h, iff_self_and, imp_true_iff]
   rw [h₁, h₂]
   exact blimsup_thickening_mul_ae_eq_aux μ q s hM r hr (eventually_of_forall fun i hi => hi.2)

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

@@ -3,7 +3,7 @@ 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.Covering.DensityTheorem
+import MeasureTheory.Covering.DensityTheorem
 
 #align_import measure_theory.covering.liminf_limsup from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
 

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

@@ -2,14 +2,11 @@
 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.liminf_limsup
-! 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.Covering.DensityTheorem
 
+#align_import measure_theory.covering.liminf_limsup from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-!
 # Liminf, limsup, and uniformly locally doubling measures.
 

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

@@ -40,6 +40,7 @@ variable {α : Type _} [MetricSpace α] [SecondCountableTopology α] [Measurable
 
 variable (μ : Measure α) [IsLocallyFiniteMeasure μ] [IsUnifLocDoublingMeasure μ]
 
+#print blimsup_cthickening_ae_le_of_eventually_mul_le_aux /-
 /-- This is really an auxiliary result en route to `blimsup_cthickening_ae_le_of_eventually_mul_le`
 (which is itself an auxiliary result en route to `blimsup_cthickening_mul_ae_eq`).
 
@@ -170,7 +171,9 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
   replace hj₃ := tsub_le_tsub_right hj₃ (↑C⁻¹ * μ (B j))
   rwa [ENNReal.add_sub_cancel_left hB] at hj₃ 
 #align blimsup_cthickening_ae_le_of_eventually_mul_le_aux blimsup_cthickening_ae_le_of_eventually_mul_le_aux
+-/
 
+#print blimsup_cthickening_ae_le_of_eventually_mul_le /-
 /-- This is really an auxiliary result en route to `blimsup_cthickening_mul_ae_eq`.
 
 NB: The `set : α` type ascription is present because of issue #16932 on GitHub. -/
@@ -199,7 +202,9 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le (p : ℕ → Prop) {s : 
       blimsup_cthickening_ae_le_of_eventually_mul_le_aux μ p hs (tendsto_nhds_max_right hr) hRp hM
         hM' hMr
 #align blimsup_cthickening_ae_le_of_eventually_mul_le blimsup_cthickening_ae_le_of_eventually_mul_le
+-/
 
+#print blimsup_cthickening_mul_ae_eq /-
 /-- Given a sequence of subsets `sᵢ` of a metric space, together with a sequence of radii `rᵢ`
 such that `rᵢ → 0`, the set of points which belong to infinitely many of the closed
 `rᵢ`-thickenings of `sᵢ` is unchanged almost everywhere for a uniformly locally doubling measure if
@@ -258,7 +263,9 @@ theorem blimsup_cthickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
     blimsup_congr (eventually_of_forall h₂)]
   exact ae_eq_set_union (this (fun i => p i ∧ 0 < r i) hr') (ae_eq_refl _)
 #align blimsup_cthickening_mul_ae_eq blimsup_cthickening_mul_ae_eq
+-/
 
+#print blimsup_cthickening_ae_eq_blimsup_thickening /-
 theorem blimsup_cthickening_ae_eq_blimsup_thickening {p : ℕ → Prop} {s : ℕ → Set α} {r : ℕ → ℝ}
     (hr : Tendsto r atTop (𝓝 0)) (hr' : ∀ᶠ i in atTop, p i → 0 < r i) :
     (blimsup (fun i => cthickening (r i) (s i)) atTop p : Set α) =ᵐ[μ]
@@ -273,7 +280,9 @@ theorem blimsup_cthickening_ae_eq_blimsup_thickening {p : ℕ → Prop} {s : ℕ
     nlinarith [hi pi]
   · exact mono_blimsup fun i pi => thickening_subset_cthickening _ _
 #align blimsup_cthickening_ae_eq_blimsup_thickening blimsup_cthickening_ae_eq_blimsup_thickening
+-/
 
+#print blimsup_thickening_mul_ae_eq_aux /-
 /-- An auxiliary result en route to `blimsup_thickening_mul_ae_eq`. -/
 theorem blimsup_thickening_mul_ae_eq_aux (p : ℕ → Prop) (s : ℕ → Set α) {M : ℝ} (hM : 0 < M)
     (r : ℕ → ℝ) (hr : Tendsto r atTop (𝓝 0)) (hr' : ∀ᶠ i in atTop, p i → 0 < r i) :
@@ -287,7 +296,9 @@ theorem blimsup_thickening_mul_ae_eq_aux (p : ℕ → Prop) (s : ℕ → Set α)
   have h₃ := blimsup_cthickening_ae_eq_blimsup_thickening μ hr hr'
   exact h₃.symm.trans (h₂.trans h₁)
 #align blimsup_thickening_mul_ae_eq_aux blimsup_thickening_mul_ae_eq_aux
+-/
 
+#print blimsup_thickening_mul_ae_eq /-
 /-- Given a sequence of subsets `sᵢ` of a metric space, together with a sequence of radii `rᵢ`
 such that `rᵢ → 0`, the set of points which belong to infinitely many of the
 `rᵢ`-thickenings of `sᵢ` is unchanged almost everywhere for a uniformly locally doubling measure if
@@ -322,4 +333,5 @@ theorem blimsup_thickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
   rw [h₁, h₂]
   exact blimsup_thickening_mul_ae_eq_aux μ q s hM r hr (eventually_of_forall fun i hi => hi.2)
 #align blimsup_thickening_mul_ae_eq blimsup_thickening_mul_ae_eq
+-/
 

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

@@ -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.liminf_limsup
-! 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.
 -/
@@ -13,6 +13,9 @@ import Mathbin.MeasureTheory.Covering.DensityTheorem
 /-!
 # Liminf, limsup, and uniformly locally doubling measures.
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file is a place to collect lemmas about liminf and limsup for subsets of a metric space
 carrying a uniformly locally doubling measure.
 

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

@@ -35,7 +35,7 @@ open scoped NNReal ENNReal Topology
 
 variable {α : Type _} [MetricSpace α] [SecondCountableTopology α] [MeasurableSpace α] [BorelSpace α]
 
-variable (μ : Measure α) [LocallyFiniteMeasure μ] [IsUnifLocDoublingMeasure μ]
+variable (μ : Measure α) [IsLocallyFiniteMeasure μ] [IsUnifLocDoublingMeasure μ]
 
 /-- This is really an auxiliary result en route to `blimsup_cthickening_ae_le_of_eventually_mul_le`
 (which is itself an auxiliary result en route to `blimsup_cthickening_mul_ae_eq`).

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

@@ -91,7 +91,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
       (IsUnifLocDoublingMeasure.ae_tendsto_measure_inter_div μ W 2)
   replace hd : d ∈ blimsup Y₁ at_top p := ((mem_diff _).mp hd).1
   obtain ⟨f : ℕ → ℕ, hf⟩ := exists_forall_mem_of_has_basis_mem_blimsup' at_top_basis hd
-  simp only [forall_and] at hf
+  simp only [forall_and] at hf 
   obtain ⟨hf₀ : ∀ j, d ∈ cthickening (r₁ (f j)) (s (f j)), hf₁, hf₂ : ∀ j, j ≤ f j⟩ := hf
   have hf₃ : tendsto f at_top at_top :=
     tendsto_at_top_at_top.mpr fun j => ⟨f j, fun i hi => (hf₂ j).trans (hi.trans <| hf₂ i)⟩
@@ -100,10 +100,10 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
   replace hf₀ : ∀ j, ∃ w ∈ s (f j), d ∈ closed_ball w (2 * r₁ (f j))
   · intro j
     specialize hrp (f j)
-    rw [Pi.zero_apply] at hrp
+    rw [Pi.zero_apply] at hrp 
     rcases eq_or_lt_of_le hrp with (hr0 | hrp')
     · specialize hf₀ j
-      rw [← hr0, cthickening_zero, (hs (f j)).closure_eq] at hf₀
+      rw [← hr0, cthickening_zero, (hs (f j)).closure_eq] at hf₀ 
       exact ⟨d, hf₀, by simp [← hr0]⟩
     ·
       exact
@@ -165,7 +165,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
     rw [← measure_union' hj₁ measurableSet_closedBall]
     exact measure_mono (union_subset (h₁ j) (h₂ j))
   replace hj₃ := tsub_le_tsub_right hj₃ (↑C⁻¹ * μ (B j))
-  rwa [ENNReal.add_sub_cancel_left hB] at hj₃
+  rwa [ENNReal.add_sub_cancel_left hB] at hj₃ 
 #align blimsup_cthickening_ae_le_of_eventually_mul_le_aux blimsup_cthickening_ae_le_of_eventually_mul_le_aux
 
 /-- This is really an auxiliary result en route to `blimsup_cthickening_mul_ae_eq`.
@@ -240,7 +240,7 @@ theorem blimsup_cthickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
     · simp [hi, r']
     · simp only [hi, r', one_div, mem_Ioi, if_false, inv_pos]; positivity
   have h₀ : ∀ i, p i ∧ 0 < r i → cthickening (r i) (s i) = cthickening (r' i) (s i) := by
-    rintro i ⟨-, hi⟩; congr ; change r i = ite (0 < r i) (r i) _; simp [hi]
+    rintro i ⟨-, hi⟩; congr; change r i = ite (0 < r i) (r i) _; simp [hi]
   have h₁ : ∀ i, p i ∧ 0 < r i → cthickening (M * r i) (s i) = cthickening (M * r' i) (s i) := by
     rintro i ⟨-, hi⟩; simp only [hi, mul_ite, if_true]
   have h₂ : ∀ i, p i ∧ r i ≤ 0 → cthickening (M * r i) (s i) = cthickening (r i) (s i) :=

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

@@ -31,7 +31,7 @@ carrying a uniformly locally doubling measure.
 
 open Set Filter Metric MeasureTheory TopologicalSpace
 
-open NNReal ENNReal Topology
+open scoped NNReal ENNReal Topology
 
 variable {α : Type _} [MetricSpace α] [SecondCountableTopology α] [MeasurableSpace α] [BorelSpace α]
 

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

@@ -149,8 +149,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
       fun j hj => hj (w j)
   refine' (h₃.and h₄).mono fun j hj₀ => _
   change μ (W ∩ B j) / μ (B j) ≤ ↑(1 - C⁻¹)
-  rcases eq_or_ne (μ (B j)) ∞ with (hB | hB)
-  · simp [hB]
+  rcases eq_or_ne (μ (B j)) ∞ with (hB | hB); · simp [hB]
   apply ENNReal.div_le_of_le_mul
   rw [WithTop.coe_sub, ENNReal.coe_one, ENNReal.sub_mul fun _ _ => hB, one_mul]
   replace hB : ↑C⁻¹ * μ (B j) ≠ ∞
@@ -219,8 +218,7 @@ theorem blimsup_cthickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
       (blimsup (fun i => cthickening (M * r i) (s i)) at_top p : Set α) =ᵐ[μ]
         (blimsup (fun i => cthickening (r i) (s i)) at_top p : Set α) :=
     by
-    clear p hr r
-    intro p r hr
+    clear p hr r; intro p r hr
     have hr' : tendsto (fun i => M * r i) at_top (𝓝[>] 0) := by
       convert tendsto_nhds_within_Ioi.const_mul hM hr <;> simp only [MulZeroClass.mul_zero]
     refine' eventually_le_antisymm_iff.mpr ⟨_, _⟩
@@ -240,26 +238,17 @@ theorem blimsup_cthickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
         ⟨tendsto.if' hr tendsto_one_div_add_atTop_nhds_0_nat, eventually_of_forall fun i => _⟩
     by_cases hi : 0 < r i
     · simp [hi, r']
-    · simp only [hi, r', one_div, mem_Ioi, if_false, inv_pos]
-      positivity
-  have h₀ : ∀ i, p i ∧ 0 < r i → cthickening (r i) (s i) = cthickening (r' i) (s i) :=
-    by
-    rintro i ⟨-, hi⟩
-    congr
-    change r i = ite (0 < r i) (r i) _
-    simp [hi]
-  have h₁ : ∀ i, p i ∧ 0 < r i → cthickening (M * r i) (s i) = cthickening (M * r' i) (s i) :=
-    by
-    rintro i ⟨-, hi⟩
-    simp only [hi, mul_ite, if_true]
+    · simp only [hi, r', one_div, mem_Ioi, if_false, inv_pos]; positivity
+  have h₀ : ∀ i, p i ∧ 0 < r i → cthickening (r i) (s i) = cthickening (r' i) (s i) := by
+    rintro i ⟨-, hi⟩; congr ; change r i = ite (0 < r i) (r i) _; simp [hi]
+  have h₁ : ∀ i, p i ∧ 0 < r i → cthickening (M * r i) (s i) = cthickening (M * r' i) (s i) := by
+    rintro i ⟨-, hi⟩; simp only [hi, mul_ite, if_true]
   have h₂ : ∀ i, p i ∧ r i ≤ 0 → cthickening (M * r i) (s i) = cthickening (r i) (s i) :=
     by
     rintro i ⟨-, hi⟩
     have hi' : M * r i ≤ 0 := mul_nonpos_of_nonneg_of_nonpos hM.le hi
     rw [cthickening_of_nonpos hi, cthickening_of_nonpos hi']
-  have hp : p = fun i => p i ∧ 0 < r i ∨ p i ∧ r i ≤ 0 :=
-    by
-    ext i
+  have hp : p = fun i => p i ∧ 0 < r i ∨ p i ∧ r i ≤ 0 := by ext i;
     simp [← and_or_left, lt_or_le 0 (r i)]
   rw [hp, blimsup_or_eq_sup, blimsup_or_eq_sup, sup_eq_union,
     blimsup_congr (eventually_of_forall h₀), blimsup_congr (eventually_of_forall h₁),
@@ -290,9 +279,7 @@ theorem blimsup_thickening_mul_ae_eq_aux (p : ℕ → Prop) (s : ℕ → Set α)
   by
   have h₁ := blimsup_cthickening_ae_eq_blimsup_thickening μ hr hr'
   have h₂ := blimsup_cthickening_mul_ae_eq μ p s hM r hr
-  replace hr : tendsto (fun i => M * r i) at_top (𝓝 0);
-  · convert hr.const_mul M
-    simp
+  replace hr : tendsto (fun i => M * r i) at_top (𝓝 0); · convert hr.const_mul M; simp
   replace hr' : ∀ᶠ i in at_top, p i → 0 < M * r i := hr'.mono fun i hi hip => mul_pos hM (hi hip)
   have h₃ := blimsup_cthickening_ae_eq_blimsup_thickening μ hr hr'
   exact h₃.symm.trans (h₂.trans h₁)
@@ -320,19 +307,14 @@ theorem blimsup_thickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
       blimsup (fun i => thickening (r i) (s i)) at_top q :=
     by
     refine' blimsup_congr' (eventually_of_forall fun i h => _)
-    replace hi : 0 < r i
-    · contrapose! h
-      apply thickening_of_nonpos h
+    replace hi : 0 < r i; · contrapose! h; apply thickening_of_nonpos h
     simp only [hi, iff_self_and, imp_true_iff]
   have h₂ :
     blimsup (fun i => thickening (M * r i) (s i)) at_top p =
       blimsup (fun i => thickening (M * r i) (s i)) at_top q :=
     by
     refine' blimsup_congr' (eventually_of_forall fun i h => _)
-    replace h : 0 < r i
-    · rw [← zero_lt_mul_left hM]
-      contrapose! h
-      apply thickening_of_nonpos h
+    replace h : 0 < r i; · rw [← zero_lt_mul_left hM]; contrapose! h; apply thickening_of_nonpos h
     simp only [h, iff_self_and, imp_true_iff]
   rw [h₁, h₂]
   exact blimsup_thickening_mul_ae_eq_aux μ q s hM r hr (eventually_of_forall fun i hi => hi.2)

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

@@ -35,7 +35,7 @@ open NNReal ENNReal Topology
 
 variable {α : Type _} [MetricSpace α] [SecondCountableTopology α] [MeasurableSpace α] [BorelSpace α]
 
-variable (μ : Measure α) [IsLocallyFiniteMeasure μ] [IsUnifLocDoublingMeasure μ]
+variable (μ : Measure α) [LocallyFiniteMeasure μ] [IsUnifLocDoublingMeasure μ]
 
 /-- This is really an auxiliary result en route to `blimsup_cthickening_ae_le_of_eventually_mul_le`
 (which is itself an auxiliary result en route to `blimsup_cthickening_mul_ae_eq`).

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

@@ -4,24 +4,24 @@ 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.liminf_limsup
-! leanprover-community/mathlib commit b2ff9a3d7a15fd5b0f060b135421d6a89a999c2f
+! leanprover-community/mathlib commit 5f6e827d81dfbeb6151d7016586ceeb0099b9655
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Covering.DensityTheorem
 
 /-!
-# Liminf, limsup, and doubling measures.
+# Liminf, limsup, and uniformly locally doubling measures.
 
 This file is a place to collect lemmas about liminf and limsup for subsets of a metric space
-carrying a doubling measure.
+carrying a uniformly locally doubling measure.
 
 ## Main results:
 
  * `blimsup_cthickening_mul_ae_eq`: the limsup of the closed thickening of a sequence of subsets
-   of a metric space is unchanged almost everywhere for a doubling measure if the sequence of
-   distances is multiplied by a positive scale factor. This is a generalisation of a result of
-   Cassels, appearing as Lemma 9 on page 217 of
+   of a metric space is unchanged almost everywhere for a uniformly locally doubling measure if the
+   sequence of distances is multiplied by a positive scale factor. This is a generalisation of a
+   result of Cassels, appearing as Lemma 9 on page 217 of
    [J.W.S. Cassels, *Some metrical theorems in Diophantine approximation. I*](cassels1950).
  * `blimsup_thickening_mul_ae_eq`: a variant of `blimsup_cthickening_mul_ae_eq` for thickenings
    rather than closed thickenings.
@@ -35,7 +35,7 @@ open NNReal ENNReal Topology
 
 variable {α : Type _} [MetricSpace α] [SecondCountableTopology α] [MeasurableSpace α] [BorelSpace α]
 
-variable (μ : Measure α) [IsLocallyFiniteMeasure μ] [IsDoublingMeasure μ]
+variable (μ : Measure α) [IsLocallyFiniteMeasure μ] [IsUnifLocDoublingMeasure μ]
 
 /-- This is really an auxiliary result en route to `blimsup_cthickening_ae_le_of_eventually_mul_le`
 (which is itself an auxiliary result en route to `blimsup_cthickening_mul_ae_eq`).
@@ -62,7 +62,8 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
   
     We obtain our contradiction by showing that there exists `η < 1` such that
     `μ (W ∩ (B j)) / μ (B j) ≤ η` for sufficiently large `j`. In fact we claim that `η = 1 - C⁻¹`
-    is such a value where `C` is the scaling constant of `M⁻¹` for the doubling measure `μ`.
+    is such a value where `C` is the scaling constant of `M⁻¹` for the uniformly locally doubling
+    measure `μ`.
   
     To prove the claim, let `b j = closed_ball (w j) (M * r₁ (f j))` and for given `j` consider the
     sets `b j` and `W ∩ (B j)`. These are both subsets of `B j` and are disjoint for large enough `j`
@@ -87,7 +88,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
               tendsto (fun j => μ (W ∩ closed_ball (w j) (δ j)) / μ (closed_ball (w j) (δ j))) l
                 (𝓝 1) :=
     measure.exists_mem_of_measure_ne_zero_of_ae contra
-      (IsDoublingMeasure.ae_tendsto_measure_inter_div μ W 2)
+      (IsUnifLocDoublingMeasure.ae_tendsto_measure_inter_div μ W 2)
   replace hd : d ∈ blimsup Y₁ at_top p := ((mem_diff _).mp hd).1
   obtain ⟨f : ℕ → ℕ, hf⟩ := exists_forall_mem_of_has_basis_mem_blimsup' at_top_basis hd
   simp only [forall_and] at hf
@@ -110,8 +111,9 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
           (cthickening_subset_Union_closed_ball_of_lt (s (f j)) (by positivity)
             (lt_two_mul_self hrp') (hf₀ j))
   choose w hw hw' using hf₀
-  let C := IsDoublingMeasure.scalingConstantOf μ M⁻¹
-  have hC : 0 < C := lt_of_lt_of_le zero_lt_one (IsDoublingMeasure.one_le_scalingConstantOf μ M⁻¹)
+  let C := IsUnifLocDoublingMeasure.scalingConstantOf μ M⁻¹
+  have hC : 0 < C :=
+    lt_of_lt_of_le zero_lt_one (IsUnifLocDoublingMeasure.one_le_scalingConstantOf μ M⁻¹)
   suffices
     ∃ η < (1 : ℝ≥0),
       ∀ᶠ j in at_top, μ (W ∩ closed_ball (w j) (r₁ (f j))) / μ (closed_ball (w j) (r₁ (f j))) ≤ η
@@ -142,7 +144,8 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
     simp only [mem_Union, exists_prop]
     exact ⟨f j, ⟨hf₁ j, hj.le.trans (hf₂ j)⟩, ha⟩
   have h₄ : ∀ᶠ j in at_top, μ (B j) ≤ C * μ (b j) :=
-    (hr.eventually (IsDoublingMeasure.eventually_measure_le_scaling_constant_mul' μ M hM)).mono
+    (hr.eventually
+          (IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul' μ M hM)).mono
       fun j hj => hj (w j)
   refine' (h₃.and h₄).mono fun j hj₀ => _
   change μ (W ∩ B j) / μ (B j) ≤ ↑(1 - C⁻¹)
@@ -197,8 +200,8 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le (p : ℕ → Prop) {s : 
 
 /-- Given a sequence of subsets `sᵢ` of a metric space, together with a sequence of radii `rᵢ`
 such that `rᵢ → 0`, the set of points which belong to infinitely many of the closed
-`rᵢ`-thickenings of `sᵢ` is unchanged almost everywhere for a doubling measure if the `rᵢ` are all
-scaled by a positive constant.
+`rᵢ`-thickenings of `sᵢ` is unchanged almost everywhere for a uniformly locally doubling measure if
+the `rᵢ` are all scaled by a positive constant.
 
 This lemma is a generalisation of Lemma 9 appearing on page 217 of
 [J.W.S. Cassels, *Some metrical theorems in Diophantine approximation. I*](cassels1950).
@@ -297,8 +300,8 @@ theorem blimsup_thickening_mul_ae_eq_aux (p : ℕ → Prop) (s : ℕ → Set α)
 
 /-- Given a sequence of subsets `sᵢ` of a metric space, together with a sequence of radii `rᵢ`
 such that `rᵢ → 0`, the set of points which belong to infinitely many of the
-`rᵢ`-thickenings of `sᵢ` is unchanged almost everywhere for a doubling measure if the `rᵢ` are all
-scaled by a positive constant.
+`rᵢ`-thickenings of `sᵢ` is unchanged almost everywhere for a uniformly locally doubling measure if
+the `rᵢ` are all scaled by a positive constant.
 
 This lemma is a generalisation of Lemma 9 appearing on page 217 of
 [J.W.S. Cassels, *Some metrical theorems in Diophantine approximation. I*](cassels1950).

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -180,7 +180,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le (p : ℕ → Prop) {s : 
   have hRp : 0 ≤ R₁ := fun i => le_max_left 0 (r₁ i)
   replace hMr : ∀ᶠ i in at_top, M * R₁ i ≤ R₂ i
   · refine' hMr.mono fun i hi => _
-    rw [mul_max_of_nonneg _ _ hM.le, mul_zero]
+    rw [mul_max_of_nonneg _ _ hM.le, MulZeroClass.mul_zero]
     exact max_le_max (le_refl 0) hi
   simp_rw [← cthickening_max_zero (r₁ _), ← cthickening_max_zero (r₂ _)]
   cases' le_or_lt 1 M with hM' hM'
@@ -219,7 +219,7 @@ theorem blimsup_cthickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
     clear p hr r
     intro p r hr
     have hr' : tendsto (fun i => M * r i) at_top (𝓝[>] 0) := by
-      convert tendsto_nhds_within_Ioi.const_mul hM hr <;> simp only [mul_zero]
+      convert tendsto_nhds_within_Ioi.const_mul hM hr <;> simp only [MulZeroClass.mul_zero]
     refine' eventually_le_antisymm_iff.mpr ⟨_, _⟩
     ·
       exact

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -184,7 +184,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le (p : ℕ → Prop) {s : 
     exact max_le_max (le_refl 0) hi
   simp_rw [← cthickening_max_zero (r₁ _), ← cthickening_max_zero (r₂ _)]
   cases' le_or_lt 1 M with hM' hM'
-  · apply HasSubset.Subset.eventuallyLe
+  · apply HasSubset.Subset.eventuallyLE
     change _ ≤ _
     refine' mono_blimsup' (hMr.mono fun i hi hp => cthickening_mono _ (s i))
     exact (le_mul_of_one_le_left (hRp i) hM').trans hi
@@ -269,10 +269,10 @@ theorem blimsup_cthickening_ae_eq_blimsup_thickening {p : ℕ → Prop} {s : ℕ
     (blimsup (fun i => cthickening (r i) (s i)) atTop p : Set α) =ᵐ[μ]
       (blimsup (fun i => thickening (r i) (s i)) atTop p : Set α) :=
   by
-  refine' eventually_le_antisymm_iff.mpr ⟨_, HasSubset.Subset.eventuallyLe (_ : _ ≤ _)⟩
+  refine' eventually_le_antisymm_iff.mpr ⟨_, HasSubset.Subset.eventuallyLE (_ : _ ≤ _)⟩
   · rw [eventually_le_congr (blimsup_cthickening_mul_ae_eq μ p s (@one_half_pos ℝ _) r hr).symm
         eventually_eq.rfl]
-    apply HasSubset.Subset.eventuallyLe
+    apply HasSubset.Subset.eventuallyLE
     change _ ≤ _
     refine' mono_blimsup' (hr'.mono fun i hi pi => cthickening_subset_thickening' (hi pi) _ (s i))
     nlinarith [hi pi]

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

@@ -31,7 +31,7 @@ carrying a doubling measure.
 
 open Set Filter Metric MeasureTheory TopologicalSpace
 
-open NNReal Ennreal Topology
+open NNReal ENNReal Topology
 
 variable {α : Type _} [MetricSpace α] [SecondCountableTopology α] [MeasurableSpace α] [BorelSpace α]
 
@@ -118,7 +118,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
     by
     obtain ⟨η, hη, hη'⟩ := this
     replace hη' : 1 ≤ η := by
-      simpa only [Ennreal.one_le_coe_iff] using
+      simpa only [ENNReal.one_le_coe_iff] using
         le_of_tendsto (hd' w (fun j => r₁ (f j)) hr <| eventually_of_forall hw') hη'
     exact (lt_self_iff_false _).mp (lt_of_lt_of_le hη hη')
   refine' ⟨1 - C⁻¹, tsub_lt_self zero_lt_one (inv_pos.mpr hC), _⟩
@@ -148,22 +148,22 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
   change μ (W ∩ B j) / μ (B j) ≤ ↑(1 - C⁻¹)
   rcases eq_or_ne (μ (B j)) ∞ with (hB | hB)
   · simp [hB]
-  apply Ennreal.div_le_of_le_mul
-  rw [WithTop.coe_sub, Ennreal.coe_one, Ennreal.sub_mul fun _ _ => hB, one_mul]
+  apply ENNReal.div_le_of_le_mul
+  rw [WithTop.coe_sub, ENNReal.coe_one, ENNReal.sub_mul fun _ _ => hB, one_mul]
   replace hB : ↑C⁻¹ * μ (B j) ≠ ∞
-  · refine' Ennreal.mul_ne_top _ hB
-    rwa [Ennreal.coe_inv hC, Ne.def, Ennreal.inv_eq_top, Ennreal.coe_eq_zero]
+  · refine' ENNReal.mul_ne_top _ hB
+    rwa [ENNReal.coe_inv hC, Ne.def, ENNReal.inv_eq_top, ENNReal.coe_eq_zero]
   obtain ⟨hj₁ : Disjoint (b j) (W ∩ B j), hj₂ : μ (B j) ≤ C * μ (b j)⟩ := hj₀
   replace hj₂ : ↑C⁻¹ * μ (B j) ≤ μ (b j)
-  · rw [Ennreal.coe_inv hC, ← Ennreal.div_eq_inv_mul]
-    exact Ennreal.div_le_of_le_mul' hj₂
+  · rw [ENNReal.coe_inv hC, ← ENNReal.div_eq_inv_mul]
+    exact ENNReal.div_le_of_le_mul' hj₂
   have hj₃ : ↑C⁻¹ * μ (B j) + μ (W ∩ B j) ≤ μ (B j) :=
     by
     refine' le_trans (add_le_add_right hj₂ _) _
     rw [← measure_union' hj₁ measurableSet_closedBall]
     exact measure_mono (union_subset (h₁ j) (h₂ j))
   replace hj₃ := tsub_le_tsub_right hj₃ (↑C⁻¹ * μ (B j))
-  rwa [Ennreal.add_sub_cancel_left hB] at hj₃
+  rwa [ENNReal.add_sub_cancel_left hB] at hj₃
 #align blimsup_cthickening_ae_le_of_eventually_mul_le_aux blimsup_cthickening_ae_le_of_eventually_mul_le_aux
 
 /-- This is really an auxiliary result en route to `blimsup_cthickening_mul_ae_eq`.

mathlib commit https://github.com/leanprover-community/mathlib/commit/271bf175e6c51b8d31d6c0107b7bb4a967c7277e

@@ -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.liminf_limsup
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit b2ff9a3d7a15fd5b0f060b135421d6a89a999c2f
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -121,7 +121,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
       simpa only [Ennreal.one_le_coe_iff] using
         le_of_tendsto (hd' w (fun j => r₁ (f j)) hr <| eventually_of_forall hw') hη'
     exact (lt_self_iff_false _).mp (lt_of_lt_of_le hη hη')
-  refine' ⟨1 - C⁻¹, tsub_lt_self zero_lt_one (nnreal.inv_pos.mpr hC), _⟩
+  refine' ⟨1 - C⁻¹, tsub_lt_self zero_lt_one (inv_pos.mpr hC), _⟩
   replace hC : C ≠ 0 := ne_of_gt hC
   let b : ℕ → Set α := fun j => closed_ball (w j) (M * r₁ (f j))
   let B : ℕ → Set α := fun j => closed_ball (w j) (r₁ (f j))

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

@@ -137,7 +137,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
   rw [ENNReal.coe_sub, ENNReal.coe_one, ENNReal.sub_mul fun _ _ => hB, one_mul]
   replace hB : ↑C⁻¹ * μ (B j) ≠ ∞ := by
     refine ENNReal.mul_ne_top ?_ hB
-    rwa [ENNReal.coe_inv hC, Ne.def, ENNReal.inv_eq_top, ENNReal.coe_eq_zero]
+    rwa [ENNReal.coe_inv hC, Ne, ENNReal.inv_eq_top, ENNReal.coe_eq_zero]
   obtain ⟨hj₁ : Disjoint (b j) (W ∩ B j), hj₂ : μ (B j) ≤ C * μ (b j)⟩ := hj₀
   replace hj₂ : ↑C⁻¹ * μ (B j) ≤ μ (b j) := by
     rw [ENNReal.coe_inv hC, ← ENNReal.div_eq_inv_mul]

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -31,7 +31,6 @@ open Set Filter Metric MeasureTheory TopologicalSpace
 open scoped NNReal ENNReal Topology
 
 variable {α : Type*} [MetricSpace α] [SecondCountableTopology α] [MeasurableSpace α] [BorelSpace α]
-
 variable (μ : Measure α) [IsLocallyFiniteMeasure μ] [IsUnifLocDoublingMeasure μ]
 
 /-- This is really an auxiliary result en route to `blimsup_cthickening_ae_le_of_eventually_mul_le`

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -126,7 +126,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
     rw [disjoint_compl_right_iff_subset]
     refine' (closedBall_subset_cthickening (hw j) (M * r₁ (f j))).trans
       ((cthickening_mono hj' _).trans fun a ha => _)
-    simp only [mem_iUnion, exists_prop]
+    simp only [Z, mem_iUnion, exists_prop]
     exact ⟨f j, ⟨hf₁ j, hj.le.trans (hf₂ j)⟩, ha⟩
   have h₄ : ∀ᶠ j in atTop, μ (B j) ≤ C * μ (b j) :=
     (hr.eventually (IsUnifLocDoublingMeasure.eventually_measure_le_scaling_constant_mul'
@@ -211,12 +211,12 @@ theorem blimsup_cthickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
     refine' tendsto_nhdsWithin_iff.mpr
       ⟨Tendsto.if' hr tendsto_one_div_add_atTop_nhds_zero_nat, eventually_of_forall fun i => _⟩
     by_cases hi : 0 < r i
-    · simp [hi]
-    · simp only [hi, one_div, mem_Ioi, if_false, inv_pos]; positivity
+    · simp [r', hi]
+    · simp only [r', hi, one_div, mem_Ioi, if_false, inv_pos]; positivity
   have h₀ : ∀ i, p i ∧ 0 < r i → cthickening (r i) (s i) = cthickening (r' i) (s i) := by
     rintro i ⟨-, hi⟩; congr! 1; change r i = ite (0 < r i) (r i) _; simp [hi]
   have h₁ : ∀ i, p i ∧ 0 < r i → cthickening (M * r i) (s i) = cthickening (M * r' i) (s i) := by
-    rintro i ⟨-, hi⟩; simp only [hi, mul_ite, if_true]
+    rintro i ⟨-, hi⟩; simp only [r', hi, mul_ite, if_true]
   have h₂ : ∀ i, p i ∧ r i ≤ 0 → cthickening (M * r i) (s i) = cthickening (r i) (s i) := by
     rintro i ⟨-, hi⟩
     have hi' : M * r i ≤ 0 := mul_nonpos_of_nonneg_of_nonpos hM.le hi
@@ -278,13 +278,13 @@ theorem blimsup_thickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
       blimsup (fun i => thickening (r i) (s i)) atTop q := by
     refine' blimsup_congr' (eventually_of_forall fun i h => _)
     replace hi : 0 < r i := by contrapose! h; apply thickening_of_nonpos h
-    simp only [hi, iff_self_and, imp_true_iff]
+    simp only [q, hi, iff_self_and, imp_true_iff]
   have h₂ : blimsup (fun i => thickening (M * r i) (s i)) atTop p =
       blimsup (fun i => thickening (M * r i) (s i)) atTop q := by
     refine blimsup_congr' (eventually_of_forall fun i h ↦ ?_)
     replace h : 0 < r i := by
       rw [← mul_pos_iff_of_pos_left hM]; contrapose! h; apply thickening_of_nonpos h
-    simp only [h, iff_self_and, imp_true_iff]
+    simp only [q, h, iff_self_and, imp_true_iff]
   rw [h₁, h₂]
   exact blimsup_thickening_mul_ae_eq_aux μ q s hM r hr (eventually_of_forall fun i hi => hi.2)
 #align blimsup_thickening_mul_ae_eq blimsup_thickening_mul_ae_eq

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>

@@ -89,8 +89,8 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
     tendsto_atTop_atTop.mpr fun j => ⟨f j, fun i hi => (hf₂ j).trans (hi.trans <| hf₂ i)⟩
   replace hr : Tendsto (r₁ ∘ f) atTop (𝓝[>] 0) := hr.comp hf₃
   replace hMr : ∀ᶠ j in atTop, M * r₁ (f j) ≤ r₂ (f j) := hf₃.eventually hMr
-  replace hf₀ : ∀ j, ∃ w ∈ s (f j), d ∈ closedBall w (2 * r₁ (f j))
-  · intro j
+  replace hf₀ : ∀ j, ∃ w ∈ s (f j), d ∈ closedBall w (2 * r₁ (f j)) := by
+    intro j
     specialize hrp (f j)
     rw [Pi.zero_apply] at hrp
     rcases eq_or_lt_of_le hrp with (hr0 | hrp')
@@ -136,12 +136,12 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
   rcases eq_or_ne (μ (B j)) ∞ with (hB | hB); · simp [hB]
   apply ENNReal.div_le_of_le_mul
   rw [ENNReal.coe_sub, ENNReal.coe_one, ENNReal.sub_mul fun _ _ => hB, one_mul]
-  replace hB : ↑C⁻¹ * μ (B j) ≠ ∞
-  · refine' ENNReal.mul_ne_top _ hB
+  replace hB : ↑C⁻¹ * μ (B j) ≠ ∞ := by
+    refine ENNReal.mul_ne_top ?_ hB
     rwa [ENNReal.coe_inv hC, Ne.def, ENNReal.inv_eq_top, ENNReal.coe_eq_zero]
   obtain ⟨hj₁ : Disjoint (b j) (W ∩ B j), hj₂ : μ (B j) ≤ C * μ (b j)⟩ := hj₀
-  replace hj₂ : ↑C⁻¹ * μ (B j) ≤ μ (b j)
-  · rw [ENNReal.coe_inv hC, ← ENNReal.div_eq_inv_mul]
+  replace hj₂ : ↑C⁻¹ * μ (B j) ≤ μ (b j) := by
+    rw [ENNReal.coe_inv hC, ← ENNReal.div_eq_inv_mul]
     exact ENNReal.div_le_of_le_mul' hj₂
   have hj₃ : ↑C⁻¹ * μ (B j) + μ (W ∩ B j) ≤ μ (B j) := by
     refine' le_trans (add_le_add_right hj₂ _) _
@@ -163,8 +163,8 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le (p : ℕ → Prop) {s : 
   let R₁ i := max 0 (r₁ i)
   let R₂ i := max 0 (r₂ i)
   have hRp : 0 ≤ R₁ := fun i => le_max_left 0 (r₁ i)
-  replace hMr : ∀ᶠ i in atTop, M * R₁ i ≤ R₂ i
-  · refine' hMr.mono fun i hi => _
+  replace hMr : ∀ᶠ i in atTop, M * R₁ i ≤ R₂ i := by
+    refine hMr.mono fun i hi ↦ ?_
     rw [mul_max_of_nonneg _ _ hM.le, mul_zero]
     exact max_le_max (le_refl 0) hi
   simp_rw [← cthickening_max_zero (r₁ _), ← cthickening_max_zero (r₂ _)]
@@ -251,8 +251,8 @@ theorem blimsup_thickening_mul_ae_eq_aux (p : ℕ → Prop) (s : ℕ → Set α)
       (blimsup (fun i => thickening (r i) (s i)) atTop p : Set α) := by
   have h₁ := blimsup_cthickening_ae_eq_blimsup_thickening (s := s) μ hr hr'
   have h₂ := blimsup_cthickening_mul_ae_eq μ p s hM r hr
-  replace hr : Tendsto (fun i => M * r i) atTop (𝓝 0); · convert hr.const_mul M; simp
-  replace hr' : ∀ᶠ i in atTop, p i → 0 < M * r i := hr'.mono fun i hi hip => mul_pos hM (hi hip)
+  replace hr : Tendsto (fun i => M * r i) atTop (𝓝 0) := by convert hr.const_mul M; simp
+  replace hr' : ∀ᶠ i in atTop, p i → 0 < M * r i := hr'.mono fun i hi hip ↦ mul_pos hM (hi hip)
   have h₃ := blimsup_cthickening_ae_eq_blimsup_thickening (s := s) μ hr hr'
   exact h₃.symm.trans (h₂.trans h₁)
 #align blimsup_thickening_mul_ae_eq_aux blimsup_thickening_mul_ae_eq_aux
@@ -277,13 +277,13 @@ theorem blimsup_thickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
   have h₁ : blimsup (fun i => thickening (r i) (s i)) atTop p =
       blimsup (fun i => thickening (r i) (s i)) atTop q := by
     refine' blimsup_congr' (eventually_of_forall fun i h => _)
-    replace hi : 0 < r i; · contrapose! h; apply thickening_of_nonpos h
+    replace hi : 0 < r i := by contrapose! h; apply thickening_of_nonpos h
     simp only [hi, iff_self_and, imp_true_iff]
   have h₂ : blimsup (fun i => thickening (M * r i) (s i)) atTop p =
       blimsup (fun i => thickening (M * r i) (s i)) atTop q := by
-    refine' blimsup_congr' (eventually_of_forall fun i h => _)
-    replace h : 0 < r i
-    · rw [← mul_pos_iff_of_pos_left hM]; contrapose! h; apply thickening_of_nonpos h
+    refine blimsup_congr' (eventually_of_forall fun i h ↦ ?_)
+    replace h : 0 < r i := by
+      rw [← mul_pos_iff_of_pos_left hM]; contrapose! h; apply thickening_of_nonpos h
     simp only [h, iff_self_and, imp_true_iff]
   rw [h₁, h₂]
   exact blimsup_thickening_mul_ae_eq_aux μ q s hM r hr (eventually_of_forall fun i hi => hi.2)

See here on Zulip.

This PR changes a bunch of names containing nhds_0 or/and lt_1 to nhds_zero or/and lt_one.

@@ -209,7 +209,7 @@ theorem blimsup_cthickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
   let r' : ℕ → ℝ := fun i => if 0 < r i then r i else 1 / ((i : ℝ) + 1)
   have hr' : Tendsto r' atTop (𝓝[>] 0) := by
     refine' tendsto_nhdsWithin_iff.mpr
-      ⟨Tendsto.if' hr tendsto_one_div_add_atTop_nhds_0_nat, eventually_of_forall fun i => _⟩
+      ⟨Tendsto.if' hr tendsto_one_div_add_atTop_nhds_zero_nat, eventually_of_forall fun i => _⟩
     by_cases hi : 0 < r i
     · simp [hi]
     · simp only [hi, one_div, mem_Ioi, if_false, inv_pos]; positivity

I had a slightly logic-heavy argument that was nicely simplified by stating this lemma. Also fix a few lemma names.

From LeanAPAP and LeanCamCombi

@@ -282,7 +282,8 @@ theorem blimsup_thickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
   have h₂ : blimsup (fun i => thickening (M * r i) (s i)) atTop p =
       blimsup (fun i => thickening (M * r i) (s i)) atTop q := by
     refine' blimsup_congr' (eventually_of_forall fun i h => _)
-    replace h : 0 < r i; · rw [← zero_lt_mul_left hM]; contrapose! h; apply thickening_of_nonpos h
+    replace h : 0 < r i
+    · rw [← mul_pos_iff_of_pos_left hM]; contrapose! h; apply thickening_of_nonpos h
     simp only [h, iff_self_and, imp_true_iff]
   rw [h₁, h₂]
   exact blimsup_thickening_mul_ae_eq_aux μ q s hM r hr (eventually_of_forall fun i hi => hi.2)

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -168,7 +168,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le (p : ℕ → Prop) {s : 
     rw [mul_max_of_nonneg _ _ hM.le, mul_zero]
     exact max_le_max (le_refl 0) hi
   simp_rw [← cthickening_max_zero (r₁ _), ← cthickening_max_zero (r₂ _)]
-  cases' le_or_lt 1 M with hM' hM'
+  rcases le_or_lt 1 M with hM' | hM'
   · apply HasSubset.Subset.eventuallyLE
     change _ ≤ _
     refine' mono_blimsup' (hMr.mono fun i hi _ => cthickening_mono _ (s i))

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -165,7 +165,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le (p : ℕ → Prop) {s : 
   have hRp : 0 ≤ R₁ := fun i => le_max_left 0 (r₁ i)
   replace hMr : ∀ᶠ i in atTop, M * R₁ i ≤ R₂ i
   · refine' hMr.mono fun i hi => _
-    rw [mul_max_of_nonneg _ _ hM.le, MulZeroClass.mul_zero]
+    rw [mul_max_of_nonneg _ _ hM.le, mul_zero]
     exact max_le_max (le_refl 0) hi
   simp_rw [← cthickening_max_zero (r₁ _), ← cthickening_max_zero (r₂ _)]
   cases' le_or_lt 1 M with hM' hM'
@@ -200,7 +200,7 @@ theorem blimsup_cthickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M
         (blimsup (fun i => cthickening (r i) (s i)) atTop p : Set α) := by
     clear p hr r; intro p r hr
     have hr' : Tendsto (fun i => M * r i) atTop (𝓝[>] 0) := by
-      convert TendstoNhdsWithinIoi.const_mul hM hr <;> simp only [MulZeroClass.mul_zero]
+      convert TendstoNhdsWithinIoi.const_mul hM hr <;> simp only [mul_zero]
     refine' eventuallyLE_antisymm_iff.mpr ⟨_, _⟩
     · exact blimsup_cthickening_ae_le_of_eventually_mul_le μ p (inv_pos.mpr hM) hr'
         (eventually_of_forall fun i => by rw [inv_mul_cancel_left₀ hM.ne' (r i)])

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

This has nice performance benefits.

@@ -30,7 +30,7 @@ open Set Filter Metric MeasureTheory TopologicalSpace
 
 open scoped NNReal ENNReal Topology
 
-variable {α : Type _} [MetricSpace α] [SecondCountableTopology α] [MeasurableSpace α] [BorelSpace α]
+variable {α : Type*} [MetricSpace α] [SecondCountableTopology α] [MeasurableSpace α] [BorelSpace α]
 
 variable (μ : Measure α) [IsLocallyFiniteMeasure μ] [IsUnifLocDoublingMeasure μ]
 

• depends on: #5966

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

@@ -2,14 +2,11 @@
 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.liminf_limsup
-! 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.Covering.DensityTheorem
 
+#align_import measure_theory.covering.liminf_limsup from "leanprover-community/mathlib"@"5f6e827d81dfbeb6151d7016586ceeb0099b9655"
+
 /-!
 # Liminf, limsup, and uniformly locally doubling measures.
 

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -125,7 +125,7 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
     rw [eventually_atTop]
     refine'
       ⟨i, fun j hj hj' => Disjoint.inf_right (B j) <| Disjoint.inf_right' (blimsup Y₁ atTop p) _⟩
-    change Disjoint (b j) (Z iᶜ)
+    change Disjoint (b j) (Z i)ᶜ
     rw [disjoint_compl_right_iff_subset]
     refine' (closedBall_subset_cthickening (hw j) (M * r₁ (f j))).trans
       ((cthickening_mono hj' _).trans fun a ha => _)

Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -40,7 +40,8 @@ variable (μ : Measure α) [IsLocallyFiniteMeasure μ] [IsUnifLocDoublingMeasure
 /-- This is really an auxiliary result en route to `blimsup_cthickening_ae_le_of_eventually_mul_le`
 (which is itself an auxiliary result en route to `blimsup_cthickening_mul_ae_eq`).
 
-NB: The `set : α` type ascription is present because of issue #16932 on GitHub. -/
+NB: The `: Set α` type ascription is present because of
+https://github.com/leanprover-community/mathlib/issues/16932. -/
 theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s : ℕ → Set α}
     (hs : ∀ i, IsClosed (s i)) {r₁ r₂ : ℕ → ℝ} (hr : Tendsto r₁ atTop (𝓝[>] 0)) (hrp : 0 ≤ r₁)
     {M : ℝ} (hM : 0 < M) (hM' : M < 1) (hMr : ∀ᶠ i in atTop, M * r₁ i ≤ r₂ i) :
@@ -155,7 +156,8 @@ theorem blimsup_cthickening_ae_le_of_eventually_mul_le_aux (p : ℕ → Prop) {s
 
 /-- This is really an auxiliary result en route to `blimsup_cthickening_mul_ae_eq`.
 
-NB: The `Set α` type ascription is present because of issue #16932 on GitHub. -/
+NB: The `: Set α` type ascription is present because of
+https://github.com/leanprover-community/mathlib/issues/16932. -/
 theorem blimsup_cthickening_ae_le_of_eventually_mul_le (p : ℕ → Prop) {s : ℕ → Set α} {M : ℝ}
     (hM : 0 < M) {r₁ r₂ : ℕ → ℝ} (hr : Tendsto r₁ atTop (𝓝[>] 0))
     (hMr : ∀ᶠ i in atTop, M * r₁ i ≤ r₂ i) :
@@ -190,7 +192,8 @@ This lemma is a generalisation of Lemma 9 appearing on page 217 of
 
 See also `blimsup_thickening_mul_ae_eq`.
 
-NB: The `Set α` type ascription is present because of issue #16932 on GitHub. -/
+NB: The `: Set α` type ascription is present because of
+https://github.com/leanprover-community/mathlib/issues/16932. -/
 theorem blimsup_cthickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M : ℝ} (hM : 0 < M)
     (r : ℕ → ℝ) (hr : Tendsto r atTop (𝓝 0)) :
     (blimsup (fun i => cthickening (M * r i) (s i)) atTop p : Set α) =ᵐ[μ]
@@ -267,7 +270,8 @@ This lemma is a generalisation of Lemma 9 appearing on page 217 of
 
 See also `blimsup_cthickening_mul_ae_eq`.
 
-NB: The `Set α` type ascription is present because of issue #16932 on GitHub. -/
+NB: The `: Set α` type ascription is present because of
+https://github.com/leanprover-community/mathlib/issues/16932. -/
 theorem blimsup_thickening_mul_ae_eq (p : ℕ → Prop) (s : ℕ → Set α) {M : ℝ} (hM : 0 < M) (r : ℕ → ℝ)
     (hr : Tendsto r atTop (𝓝 0)) :
     (blimsup (fun i => thickening (M * r i) (s i)) atTop p : Set α) =ᵐ[μ]