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

@@ -130,10 +130,10 @@ theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [IsFiniteMeasure μ
   by_cases hδi : δ = ∞
   · simp only [hδi, imp_true_iff, le_top, exists_const]
   lift δ to ℝ≥0 using hδi
-  rw [gt_iff_lt, ENNReal.coe_pos, ← NNReal.coe_pos] at hδ 
+  rw [gt_iff_lt, ENNReal.coe_pos, ← NNReal.coe_pos] at hδ
   obtain ⟨t, htm, ht, hunif⟩ := tendsto_uniformly_on_of_ae_tendsto' hf hg hfg hδ
-  rw [ENNReal.ofReal_coe_nnreal] at ht 
-  rw [Metric.tendstoUniformlyOn_iff] at hunif 
+  rw [ENNReal.ofReal_coe_nnreal] at ht
+  rw [Metric.tendstoUniformlyOn_iff] at hunif
   obtain ⟨N, hN⟩ := eventually_at_top.1 (hunif ε hε)
   refine' ⟨N, fun n hn => _⟩
   suffices : {x : α | ε ≤ dist (f n x) (g x)} ⊆ t; exact (measure_mono this).trans ht
@@ -169,7 +169,7 @@ theorem exists_nat_measure_lt_two_inv (hfg : TendstoInMeasure μ f atTop g) (n :
     ∃ N, ∀ m ≥ N, μ {x | 2⁻¹ ^ n ≤ dist (f m x) (g x)} ≤ 2⁻¹ ^ n :=
   by
   specialize hfg (2⁻¹ ^ n) (by simp only [zero_lt_bit0, pow_pos, zero_lt_one, inv_pos])
-  rw [ENNReal.tendsto_atTop_zero] at hfg 
+  rw [ENNReal.tendsto_atTop_zero] at hfg
   exact hfg (2⁻¹ ^ n) (pos_iff_ne_zero.mpr fun h_zero => by simpa using pow_eq_zero h_zero)
 #align measure_theory.exists_seq_tendsto_ae.exists_nat_measure_lt_two_inv MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv
 -/
@@ -256,9 +256,9 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae (hfg : TendstoInMeasure μ f atTo
   have h_tendsto : ∀ x ∈ sᶜ, tendsto (fun i => f (ns i) x) at_top (𝓝 (g x)) :=
     by
     refine' fun x hx => metric.tendsto_at_top.mpr fun ε hε => _
-    rw [hs, limsup_eq_infi_supr_of_nat] at hx 
+    rw [hs, limsup_eq_infi_supr_of_nat] at hx
     simp only [Set.iSup_eq_iUnion, Set.iInf_eq_iInter, Set.compl_iInter, Set.compl_iUnion,
-      Set.mem_iUnion, Set.mem_iInter, Set.mem_compl_iff, Set.mem_setOf_eq, not_le] at hx 
+      Set.mem_iUnion, Set.mem_iInter, Set.mem_compl_iff, Set.mem_setOf_eq, not_le] at hx
     obtain ⟨N, hNx⟩ := hx
     obtain ⟨k, hk_lt_ε⟩ := h_lt_ε_real ε hε
     refine' ⟨max N (k - 1), fun n hn_ge => lt_of_le_of_lt _ hk_lt_ε⟩
@@ -340,7 +340,7 @@ theorem tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable (hp_ne_zero : p
     ENNReal.Tendsto.const_mul (tendsto.ennrpow_const p.to_real hfg)
       (Or.inr <| @ENNReal.ofReal_ne_top (1 / ε ^ p.to_real))
   simp only [MulZeroClass.mul_zero,
-    ENNReal.zero_rpow_of_pos (ENNReal.toReal_pos hp_ne_zero hp_ne_top)] at hfg 
+    ENNReal.zero_rpow_of_pos (ENNReal.toReal_pos hp_ne_zero hp_ne_top)] at hfg
   rw [ENNReal.tendsto_nhds_zero] at hfg ⊢
   intro δ hδ
   refine' (hfg δ hδ).mono fun n hn => _
@@ -384,7 +384,7 @@ theorem tendstoInMeasure_of_tendsto_snorm_top {E} [NormedAddCommGroup E] {f : ι
     {l : Filter ι} (hfg : Tendsto (fun n => snorm (f n - g) ∞ μ) l (𝓝 0)) :
     TendstoInMeasure μ f l g := by
   intro δ hδ
-  simp only [snorm_exponent_top, snorm_ess_sup] at hfg 
+  simp only [snorm_exponent_top, snorm_ess_sup] at hfg
   rw [ENNReal.tendsto_nhds_zero] at hfg ⊢
   intro ε hε
   specialize

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

@@ -3,9 +3,9 @@ Copyright (c) 2022 Rémy Degenne, Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne, Kexing Ying
 -/
-import Mathbin.Analysis.SpecialFunctions.Pow.Real
-import Mathbin.MeasureTheory.Function.Egorov
-import Mathbin.MeasureTheory.Function.LpSpace
+import Analysis.SpecialFunctions.Pow.Real
+import MeasureTheory.Function.Egorov
+import MeasureTheory.Function.LpSpace
 
 #align_import measure_theory.function.convergence_in_measure from "leanprover-community/mathlib"@"2ebc1d6c2fed9f54c95bbc3998eaa5570527129a"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

@@ -310,14 +310,14 @@ section AeMeasurableOf
 
 variable [MeasurableSpace E] [NormedAddCommGroup E] [BorelSpace E]
 
-#print MeasureTheory.TendstoInMeasure.aeMeasurable /-
-theorem TendstoInMeasure.aeMeasurable {u : Filter ι} [NeBot u] [IsCountablyGenerated u]
+#print MeasureTheory.TendstoInMeasure.aemeasurable /-
+theorem TendstoInMeasure.aemeasurable {u : Filter ι} [NeBot u] [IsCountablyGenerated u]
     {f : ι → α → E} {g : α → E} (hf : ∀ n, AEMeasurable (f n) μ)
     (h_tendsto : TendstoInMeasure μ f u g) : AEMeasurable g μ :=
   by
   obtain ⟨ns, hns⟩ := h_tendsto.exists_seq_tendsto_ae'
   exact aemeasurable_of_tendsto_metrizable_ae at_top (fun n => hf (ns n)) hns
-#align measure_theory.tendsto_in_measure.ae_measurable MeasureTheory.TendstoInMeasure.aeMeasurable
+#align measure_theory.tendsto_in_measure.ae_measurable MeasureTheory.TendstoInMeasure.aemeasurable
 -/
 
 end AeMeasurableOf

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Rémy Degenne, Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne, Kexing Ying
-
-! This file was ported from Lean 3 source module measure_theory.function.convergence_in_measure
-! leanprover-community/mathlib commit 2ebc1d6c2fed9f54c95bbc3998eaa5570527129a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.SpecialFunctions.Pow.Real
 import Mathbin.MeasureTheory.Function.Egorov
 import Mathbin.MeasureTheory.Function.LpSpace
 
+#align_import measure_theory.function.convergence_in_measure from "leanprover-community/mathlib"@"2ebc1d6c2fed9f54c95bbc3998eaa5570527129a"
+
 /-!
 # Convergence in measure
 

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

@@ -63,17 +63,20 @@ def TendstoInMeasure [Dist E] {m : MeasurableSpace α} (μ : Measure α) (f : ι
 #align measure_theory.tendsto_in_measure MeasureTheory.TendstoInMeasure
 -/
 
+#print MeasureTheory.tendstoInMeasure_iff_norm /-
 theorem tendstoInMeasure_iff_norm [SeminormedAddCommGroup E] {l : Filter ι} {f : ι → α → E}
     {g : α → E} :
     TendstoInMeasure μ f l g ↔
       ∀ (ε) (hε : 0 < ε), Tendsto (fun i => μ {x | ε ≤ ‖f i x - g x‖}) l (𝓝 0) :=
   by simp_rw [tendsto_in_measure, dist_eq_norm]
 #align measure_theory.tendsto_in_measure_iff_norm MeasureTheory.tendstoInMeasure_iff_norm
+-/
 
 namespace TendstoInMeasure
 
 variable [Dist E] {l : Filter ι} {f f' : ι → α → E} {g g' : α → E}
 
+#print MeasureTheory.TendstoInMeasure.congr' /-
 protected theorem congr' (h_left : ∀ᶠ i in l, f i =ᵐ[μ] f' i) (h_right : g =ᵐ[μ] g')
     (h_tendsto : TendstoInMeasure μ f l g) : TendstoInMeasure μ f' l g' :=
   by
@@ -89,21 +92,28 @@ protected theorem congr' (h_left : ∀ᶠ i in l, f i =ᵐ[μ] f' i) (h_right :
   change ε ≤ dist (f' i x) (g' x) ↔ ε ≤ dist (f i x) (g x)
   rw [hxg, hxf]
 #align measure_theory.tendsto_in_measure.congr' MeasureTheory.TendstoInMeasure.congr'
+-/
 
+#print MeasureTheory.TendstoInMeasure.congr /-
 protected theorem congr (h_left : ∀ i, f i =ᵐ[μ] f' i) (h_right : g =ᵐ[μ] g')
     (h_tendsto : TendstoInMeasure μ f l g) : TendstoInMeasure μ f' l g' :=
   TendstoInMeasure.congr' (eventually_of_forall h_left) h_right h_tendsto
 #align measure_theory.tendsto_in_measure.congr MeasureTheory.TendstoInMeasure.congr
+-/
 
+#print MeasureTheory.TendstoInMeasure.congr_left /-
 theorem congr_left (h : ∀ i, f i =ᵐ[μ] f' i) (h_tendsto : TendstoInMeasure μ f l g) :
     TendstoInMeasure μ f' l g :=
   h_tendsto.congr h EventuallyEq.rfl
 #align measure_theory.tendsto_in_measure.congr_left MeasureTheory.TendstoInMeasure.congr_left
+-/
 
+#print MeasureTheory.TendstoInMeasure.congr_right /-
 theorem congr_right (h : g =ᵐ[μ] g') (h_tendsto : TendstoInMeasure μ f l g) :
     TendstoInMeasure μ f l g' :=
   h_tendsto.congr (fun i => EventuallyEq.rfl) h
 #align measure_theory.tendsto_in_measure.congr_right MeasureTheory.TendstoInMeasure.congr_right
+-/
 
 end TendstoInMeasure
 
@@ -113,6 +123,7 @@ variable [MetricSpace E]
 
 variable {f : ℕ → α → E} {g : α → E}
 
+#print MeasureTheory.tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable /-
 /-- Auxiliary lemma for `tendsto_in_measure_of_tendsto_ae`. -/
 theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [IsFiniteMeasure μ]
     (hf : ∀ n, StronglyMeasurable (f n)) (hg : StronglyMeasurable g)
@@ -134,7 +145,9 @@ theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [IsFiniteMeasure μ
   rw [Set.mem_compl_iff, Set.nmem_setOf_iff, dist_comm, not_le]
   exact hN n hn x hx
 #align measure_theory.tendsto_in_measure_of_tendsto_ae_of_strongly_measurable MeasureTheory.tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable
+-/
 
+#print MeasureTheory.tendstoInMeasure_of_tendsto_ae /-
 /-- Convergence a.e. implies convergence in measure in a finite measure space. -/
 theorem tendstoInMeasure_of_tendsto_ae [IsFiniteMeasure μ] (hf : ∀ n, AEStronglyMeasurable (f n) μ)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) : TendstoInMeasure μ f atTop g :=
@@ -150,9 +163,11 @@ theorem tendstoInMeasure_of_tendsto_ae [IsFiniteMeasure μ] (hf : ∀ n, AEStron
   rw [← hxg, funext fun n => hxf n]
   exact hxfg
 #align measure_theory.tendsto_in_measure_of_tendsto_ae MeasureTheory.tendstoInMeasure_of_tendsto_ae
+-/
 
 namespace ExistsSeqTendstoAe
 
+#print MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv /-
 theorem exists_nat_measure_lt_two_inv (hfg : TendstoInMeasure μ f atTop g) (n : ℕ) :
     ∃ N, ∀ m ≥ N, μ {x | 2⁻¹ ^ n ≤ dist (f m x) (g x)} ≤ 2⁻¹ ^ n :=
   by
@@ -160,6 +175,7 @@ theorem exists_nat_measure_lt_two_inv (hfg : TendstoInMeasure μ f atTop g) (n :
   rw [ENNReal.tendsto_atTop_zero] at hfg 
   exact hfg (2⁻¹ ^ n) (pos_iff_ne_zero.mpr fun h_zero => by simpa using pow_eq_zero h_zero)
 #align measure_theory.exists_seq_tendsto_ae.exists_nat_measure_lt_two_inv MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv
+-/
 
 #print MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeqAux /-
 /-- Given a sequence of functions `f` which converges in measure to `g`,
@@ -178,12 +194,15 @@ noncomputable def seqTendstoAeSeq (hfg : TendstoInMeasure μ f atTop g) : ℕ 
 #align measure_theory.exists_seq_tendsto_ae.seq_tendsto_ae_seq MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq
 -/
 
+#print MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_succ /-
 theorem seqTendstoAeSeq_succ (hfg : TendstoInMeasure μ f atTop g) {n : ℕ} :
     seqTendstoAeSeq hfg (n + 1) =
       max (seqTendstoAeSeqAux hfg (n + 1)) (seqTendstoAeSeq hfg n + 1) :=
   by rw [seq_tendsto_ae_seq]
 #align measure_theory.exists_seq_tendsto_ae.seq_tendsto_ae_seq_succ MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_succ
+-/
 
+#print MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_spec /-
 theorem seqTendstoAeSeq_spec (hfg : TendstoInMeasure μ f atTop g) (n k : ℕ)
     (hn : seqTendstoAeSeq hfg n ≤ k) : μ {x | 2⁻¹ ^ n ≤ dist (f k x) (g x)} ≤ 2⁻¹ ^ n :=
   by
@@ -193,7 +212,9 @@ theorem seqTendstoAeSeq_spec (hfg : TendstoInMeasure μ f atTop g) (n k : ℕ)
     exact
       Classical.choose_spec (exists_nat_measure_lt_two_inv hfg _) _ (le_trans (le_max_left _ _) hn)
 #align measure_theory.exists_seq_tendsto_ae.seq_tendsto_ae_seq_spec MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_spec
+-/
 
+#print MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_strictMono /-
 theorem seqTendstoAeSeq_strictMono (hfg : TendstoInMeasure μ f atTop g) :
     StrictMono (seqTendstoAeSeq hfg) :=
   by
@@ -201,9 +222,11 @@ theorem seqTendstoAeSeq_strictMono (hfg : TendstoInMeasure μ f atTop g) :
   rw [seq_tendsto_ae_seq_succ]
   exact lt_of_lt_of_le (lt_add_one <| seq_tendsto_ae_seq hfg n) (le_max_right _ _)
 #align measure_theory.exists_seq_tendsto_ae.seq_tendsto_ae_seq_strict_mono MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_strictMono
+-/
 
 end ExistsSeqTendstoAe
 
+#print MeasureTheory.TendstoInMeasure.exists_seq_tendsto_ae /-
 /-- If `f` is a sequence of functions which converges in measure to `g`, then there exists a
 subsequence of `f` which converges a.e. to `g`. -/
 theorem TendstoInMeasure.exists_seq_tendsto_ae (hfg : TendstoInMeasure μ f atTop g) :
@@ -261,7 +284,9 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae (hfg : TendstoInMeasure μ f atTo
   rw [Set.mem_setOf_eq, ← @Classical.not_not (x ∈ s), not_imp_not]
   exact h_tendsto x
 #align measure_theory.tendsto_in_measure.exists_seq_tendsto_ae MeasureTheory.TendstoInMeasure.exists_seq_tendsto_ae
+-/
 
+#print MeasureTheory.TendstoInMeasure.exists_seq_tendstoInMeasure_atTop /-
 theorem TendstoInMeasure.exists_seq_tendstoInMeasure_atTop {u : Filter ι} [NeBot u]
     [IsCountablyGenerated u] {f : ι → α → E} {g : α → E} (hfg : TendstoInMeasure μ f u g) :
     ∃ ns : ℕ → ι, TendstoInMeasure μ (fun n => f (ns n)) atTop g :=
@@ -269,7 +294,9 @@ theorem TendstoInMeasure.exists_seq_tendstoInMeasure_atTop {u : Filter ι} [NeBo
   obtain ⟨ns, h_tendsto_ns⟩ : ∃ ns : ℕ → ι, tendsto ns at_top u := exists_seq_tendsto u
   exact ⟨ns, fun ε hε => (hfg ε hε).comp h_tendsto_ns⟩
 #align measure_theory.tendsto_in_measure.exists_seq_tendsto_in_measure_at_top MeasureTheory.TendstoInMeasure.exists_seq_tendstoInMeasure_atTop
+-/
 
+#print MeasureTheory.TendstoInMeasure.exists_seq_tendsto_ae' /-
 theorem TendstoInMeasure.exists_seq_tendsto_ae' {u : Filter ι} [NeBot u] [IsCountablyGenerated u]
     {f : ι → α → E} {g : α → E} (hfg : TendstoInMeasure μ f u g) :
     ∃ ns : ℕ → ι, ∀ᵐ x ∂μ, Tendsto (fun i => f (ns i) x) atTop (𝓝 (g x)) :=
@@ -278,6 +305,7 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae' {u : Filter ι} [NeBot u] [IsCou
   obtain ⟨ns, -, hns⟩ := hms.exists_seq_tendsto_ae
   exact ⟨ms ∘ ns, hns⟩
 #align measure_theory.tendsto_in_measure.exists_seq_tendsto_ae' MeasureTheory.TendstoInMeasure.exists_seq_tendsto_ae'
+-/
 
 end ExistsSeqTendstoAe
 
@@ -285,6 +313,7 @@ section AeMeasurableOf
 
 variable [MeasurableSpace E] [NormedAddCommGroup E] [BorelSpace E]
 
+#print MeasureTheory.TendstoInMeasure.aeMeasurable /-
 theorem TendstoInMeasure.aeMeasurable {u : Filter ι} [NeBot u] [IsCountablyGenerated u]
     {f : ι → α → E} {g : α → E} (hf : ∀ n, AEMeasurable (f n) μ)
     (h_tendsto : TendstoInMeasure μ f u g) : AEMeasurable g μ :=
@@ -292,6 +321,7 @@ theorem TendstoInMeasure.aeMeasurable {u : Filter ι} [NeBot u] [IsCountablyGene
   obtain ⟨ns, hns⟩ := h_tendsto.exists_seq_tendsto_ae'
   exact aemeasurable_of_tendsto_metrizable_ae at_top (fun n => hf (ns n)) hns
 #align measure_theory.tendsto_in_measure.ae_measurable MeasureTheory.TendstoInMeasure.aeMeasurable
+-/
 
 end AeMeasurableOf
 
@@ -301,6 +331,7 @@ variable [NormedAddCommGroup E] {p : ℝ≥0∞}
 
 variable {f : ι → α → E} {g : α → E}
 
+#print MeasureTheory.tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable /-
 /-- This lemma is superceded by `measure_theory.tendsto_in_measure_of_tendsto_snorm` where we
 allow `p = ∞` and only require `ae_strongly_measurable`. -/
 theorem tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable (hp_ne_zero : p ≠ 0)
@@ -329,7 +360,9 @@ theorem tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable (hp_ne_zero : p
   · rw [Ne, ENNReal.ofReal_eq_zero, not_le]
     exact Or.inl (Real.rpow_pos_of_pos hε _)
 #align measure_theory.tendsto_in_measure_of_tendsto_snorm_of_strongly_measurable MeasureTheory.tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable
+-/
 
+#print MeasureTheory.tendstoInMeasure_of_tendsto_snorm_of_ne_top /-
 /-- This lemma is superceded by `measure_theory.tendsto_in_measure_of_tendsto_snorm` where we
 allow `p = ∞`. -/
 theorem tendstoInMeasure_of_tendsto_snorm_of_ne_top (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
@@ -345,7 +378,9 @@ theorem tendstoInMeasure_of_tendsto_snorm_of_ne_top (hp_ne_zero : p ≠ 0) (hp_n
   rw [this]
   exact hfg
 #align measure_theory.tendsto_in_measure_of_tendsto_snorm_of_ne_top MeasureTheory.tendstoInMeasure_of_tendsto_snorm_of_ne_top
+-/
 
+#print MeasureTheory.tendstoInMeasure_of_tendsto_snorm_top /-
 /-- See also `measure_theory.tendsto_in_measure_of_tendsto_snorm` which work for general
 Lp-convergence for all `p ≠ 0`. -/
 theorem tendstoInMeasure_of_tendsto_snorm_top {E} [NormedAddCommGroup E] {f : ι → α → E} {g : α → E}
@@ -371,7 +406,9 @@ theorem tendstoInMeasure_of_tendsto_snorm_top {E} [NormedAddCommGroup E] {f : ι
   rw [← dist_eq_norm (f n x) (g x)]
   rfl
 #align measure_theory.tendsto_in_measure_of_tendsto_snorm_top MeasureTheory.tendstoInMeasure_of_tendsto_snorm_top
+-/
 
+#print MeasureTheory.tendstoInMeasure_of_tendsto_snorm /-
 /-- Convergence in Lp implies convergence in measure. -/
 theorem tendstoInMeasure_of_tendsto_snorm {l : Filter ι} (hp_ne_zero : p ≠ 0)
     (hf : ∀ n, AEStronglyMeasurable (f n) μ) (hg : AEStronglyMeasurable g μ)
@@ -382,7 +419,9 @@ theorem tendstoInMeasure_of_tendsto_snorm {l : Filter ι} (hp_ne_zero : p ≠ 0)
     exact tendsto_in_measure_of_tendsto_snorm_top hfg
   · exact tendsto_in_measure_of_tendsto_snorm_of_ne_top hp_ne_zero hp_ne_top hf hg hfg
 #align measure_theory.tendsto_in_measure_of_tendsto_snorm MeasureTheory.tendstoInMeasure_of_tendsto_snorm
+-/
 
+#print MeasureTheory.tendstoInMeasure_of_tendsto_Lp /-
 /-- Convergence in Lp implies convergence in measure. -/
 theorem tendstoInMeasure_of_tendsto_Lp [hp : Fact (1 ≤ p)] {f : ι → Lp E p μ} {g : Lp E p μ}
     {l : Filter ι} (hfg : Tendsto f l (𝓝 g)) : TendstoInMeasure μ (fun n => f n) l g :=
@@ -390,6 +429,7 @@ theorem tendstoInMeasure_of_tendsto_Lp [hp : Fact (1 ≤ p)] {f : ι → Lp E p
     (fun n => Lp.aestronglyMeasurable _) (Lp.aestronglyMeasurable _)
     ((Lp.tendsto_Lp_iff_tendsto_ℒp' _ _).mp hfg)
 #align measure_theory.tendsto_in_measure_of_tendsto_Lp MeasureTheory.tendstoInMeasure_of_tendsto_Lp
+-/
 
 end TendstoInMeasureOf
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne, Kexing Ying
 
 ! This file was ported from Lean 3 source module measure_theory.function.convergence_in_measure
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
+! leanprover-community/mathlib commit 2ebc1d6c2fed9f54c95bbc3998eaa5570527129a
 ! 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.Function.LpSpace
 /-!
 # Convergence in measure
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We define convergence in measure which is one of the many notions of convergence in probability.
 A sequence of functions `f` is said to converge in measure to some function `g`
 if for all `ε > 0`, the measure of the set `{x | ε ≤ dist (f i x) (g x)}` tends to 0 as `i`
@@ -56,14 +59,14 @@ variable {α ι E : Type _} {m : MeasurableSpace α} {μ : Measure α}
 some given filter `l`. -/
 def TendstoInMeasure [Dist E] {m : MeasurableSpace α} (μ : Measure α) (f : ι → α → E) (l : Filter ι)
     (g : α → E) : Prop :=
-  ∀ (ε) (hε : 0 < ε), Tendsto (fun i => μ { x | ε ≤ dist (f i x) (g x) }) l (𝓝 0)
+  ∀ (ε) (hε : 0 < ε), Tendsto (fun i => μ {x | ε ≤ dist (f i x) (g x)}) l (𝓝 0)
 #align measure_theory.tendsto_in_measure MeasureTheory.TendstoInMeasure
 -/
 
 theorem tendstoInMeasure_iff_norm [SeminormedAddCommGroup E] {l : Filter ι} {f : ι → α → E}
     {g : α → E} :
     TendstoInMeasure μ f l g ↔
-      ∀ (ε) (hε : 0 < ε), Tendsto (fun i => μ { x | ε ≤ ‖f i x - g x‖ }) l (𝓝 0) :=
+      ∀ (ε) (hε : 0 < ε), Tendsto (fun i => μ {x | ε ≤ ‖f i x - g x‖}) l (𝓝 0) :=
   by simp_rw [tendsto_in_measure, dist_eq_norm]
 #align measure_theory.tendsto_in_measure_iff_norm MeasureTheory.tendstoInMeasure_iff_norm
 
@@ -75,14 +78,13 @@ protected theorem congr' (h_left : ∀ᶠ i in l, f i =ᵐ[μ] f' i) (h_right :
     (h_tendsto : TendstoInMeasure μ f l g) : TendstoInMeasure μ f' l g' :=
   by
   intro ε hε
-  suffices
-    (fun i => μ { x | ε ≤ dist (f' i x) (g' x) }) =ᶠ[l] fun i => μ { x | ε ≤ dist (f i x) (g x) }
+  suffices (fun i => μ {x | ε ≤ dist (f' i x) (g' x)}) =ᶠ[l] fun i => μ {x | ε ≤ dist (f i x) (g x)}
     by
     rw [tendsto_congr' this]
     exact h_tendsto ε hε
-  filter_upwards [h_left]with i h_ae_eq
+  filter_upwards [h_left] with i h_ae_eq
   refine' measure_congr _
-  filter_upwards [h_ae_eq, h_right]with x hxf hxg
+  filter_upwards [h_ae_eq, h_right] with x hxf hxg
   rw [eq_iff_iff]
   change ε ≤ dist (f' i x) (g' x) ↔ ε ≤ dist (f i x) (g x)
   rw [hxg, hxf]
@@ -112,7 +114,7 @@ variable [MetricSpace E]
 variable {f : ℕ → α → E} {g : α → E}
 
 /-- Auxiliary lemma for `tendsto_in_measure_of_tendsto_ae`. -/
-theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [FiniteMeasure μ]
+theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [IsFiniteMeasure μ]
     (hf : ∀ n, StronglyMeasurable (f n)) (hg : StronglyMeasurable g)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) : TendstoInMeasure μ f atTop g :=
   by
@@ -126,7 +128,7 @@ theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [FiniteMeasure μ]
   rw [Metric.tendstoUniformlyOn_iff] at hunif 
   obtain ⟨N, hN⟩ := eventually_at_top.1 (hunif ε hε)
   refine' ⟨N, fun n hn => _⟩
-  suffices : { x : α | ε ≤ dist (f n x) (g x) } ⊆ t; exact (measure_mono this).trans ht
+  suffices : {x : α | ε ≤ dist (f n x) (g x)} ⊆ t; exact (measure_mono this).trans ht
   rw [← Set.compl_subset_compl]
   intro x hx
   rw [Set.mem_compl_iff, Set.nmem_setOf_iff, dist_comm, not_le]
@@ -134,7 +136,7 @@ theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [FiniteMeasure μ]
 #align measure_theory.tendsto_in_measure_of_tendsto_ae_of_strongly_measurable MeasureTheory.tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable
 
 /-- Convergence a.e. implies convergence in measure in a finite measure space. -/
-theorem tendstoInMeasure_of_tendsto_ae [FiniteMeasure μ] (hf : ∀ n, AEStronglyMeasurable (f n) μ)
+theorem tendstoInMeasure_of_tendsto_ae [IsFiniteMeasure μ] (hf : ∀ n, AEStronglyMeasurable (f n) μ)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) : TendstoInMeasure μ f atTop g :=
   by
   have hg : ae_strongly_measurable g μ := aestronglyMeasurable_of_tendsto_ae _ hf hfg
@@ -144,7 +146,7 @@ theorem tendstoInMeasure_of_tendsto_ae [FiniteMeasure μ] (hf : ∀ n, AEStrongl
       hg.strongly_measurable_mk _
   have hf_eq_ae : ∀ᵐ x ∂μ, ∀ n, (hf n).mk (f n) x = f n x :=
     ae_all_iff.mpr fun n => (hf n).ae_eq_mk.symm
-  filter_upwards [hf_eq_ae, hg.ae_eq_mk, hfg]with x hxf hxg hxfg
+  filter_upwards [hf_eq_ae, hg.ae_eq_mk, hfg] with x hxf hxg hxfg
   rw [← hxg, funext fun n => hxf n]
   exact hxfg
 #align measure_theory.tendsto_in_measure_of_tendsto_ae MeasureTheory.tendstoInMeasure_of_tendsto_ae
@@ -152,7 +154,7 @@ theorem tendstoInMeasure_of_tendsto_ae [FiniteMeasure μ] (hf : ∀ n, AEStrongl
 namespace ExistsSeqTendstoAe
 
 theorem exists_nat_measure_lt_two_inv (hfg : TendstoInMeasure μ f atTop g) (n : ℕ) :
-    ∃ N, ∀ m ≥ N, μ { x | 2⁻¹ ^ n ≤ dist (f m x) (g x) } ≤ 2⁻¹ ^ n :=
+    ∃ N, ∀ m ≥ N, μ {x | 2⁻¹ ^ n ≤ dist (f m x) (g x)} ≤ 2⁻¹ ^ n :=
   by
   specialize hfg (2⁻¹ ^ n) (by simp only [zero_lt_bit0, pow_pos, zero_lt_one, inv_pos])
   rw [ENNReal.tendsto_atTop_zero] at hfg 
@@ -183,7 +185,7 @@ theorem seqTendstoAeSeq_succ (hfg : TendstoInMeasure μ f atTop g) {n : ℕ} :
 #align measure_theory.exists_seq_tendsto_ae.seq_tendsto_ae_seq_succ MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq_succ
 
 theorem seqTendstoAeSeq_spec (hfg : TendstoInMeasure μ f atTop g) (n k : ℕ)
-    (hn : seqTendstoAeSeq hfg n ≤ k) : μ { x | 2⁻¹ ^ n ≤ dist (f k x) (g x) } ≤ 2⁻¹ ^ n :=
+    (hn : seqTendstoAeSeq hfg n ≤ k) : μ {x | 2⁻¹ ^ n ≤ dist (f k x) (g x)} ≤ 2⁻¹ ^ n :=
   by
   cases n
   · exact Classical.choose_spec (exists_nat_measure_lt_two_inv hfg 0) k hn
@@ -222,7 +224,7 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae (hfg : TendstoInMeasure μ f atTo
     rw [pow_add]; ring
   set ns := exists_seq_tendsto_ae.seq_tendsto_ae_seq hfg
   use ns
-  let S k := { x | 2⁻¹ ^ k ≤ dist (f (ns k) x) (g x) }
+  let S k := {x | 2⁻¹ ^ k ≤ dist (f (ns k) x) (g x)}
   have hμS_le : ∀ k, μ (S k) ≤ 2⁻¹ ^ k := fun k =>
     exists_seq_tendsto_ae.seq_tendsto_ae_seq_spec hfg k (ns k) le_rfl
   set s := filter.at_top.limsup S with hs
@@ -317,7 +319,8 @@ theorem tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable (hp_ne_zero : p
   refine' le_trans _ hn
   rw [ENNReal.ofReal_div_of_pos (Real.rpow_pos_of_pos hε _), ENNReal.ofReal_one, mul_comm,
     mul_one_div, ENNReal.le_div_iff_mul_le _ (Or.inl ENNReal.ofReal_ne_top), mul_comm]
-  · convert mul_meas_ge_le_pow_snorm' μ hp_ne_zero hp_ne_top ((hf n).sub hg).AEStronglyMeasurable
+  · convert
+      mul_meas_ge_le_pow_snorm' μ hp_ne_zero hp_ne_top ((hf n).sub hg).AEStronglyMeasurable
         (ENNReal.ofReal ε)
     · exact (ENNReal.ofReal_rpow_of_pos hε).symm
     · ext x

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

@@ -120,10 +120,10 @@ theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [FiniteMeasure μ]
   by_cases hδi : δ = ∞
   · simp only [hδi, imp_true_iff, le_top, exists_const]
   lift δ to ℝ≥0 using hδi
-  rw [gt_iff_lt, ENNReal.coe_pos, ← NNReal.coe_pos] at hδ
+  rw [gt_iff_lt, ENNReal.coe_pos, ← NNReal.coe_pos] at hδ 
   obtain ⟨t, htm, ht, hunif⟩ := tendsto_uniformly_on_of_ae_tendsto' hf hg hfg hδ
-  rw [ENNReal.ofReal_coe_nnreal] at ht
-  rw [Metric.tendstoUniformlyOn_iff] at hunif
+  rw [ENNReal.ofReal_coe_nnreal] at ht 
+  rw [Metric.tendstoUniformlyOn_iff] at hunif 
   obtain ⟨N, hN⟩ := eventually_at_top.1 (hunif ε hε)
   refine' ⟨N, fun n hn => _⟩
   suffices : { x : α | ε ≤ dist (f n x) (g x) } ⊆ t; exact (measure_mono this).trans ht
@@ -155,7 +155,7 @@ theorem exists_nat_measure_lt_two_inv (hfg : TendstoInMeasure μ f atTop g) (n :
     ∃ N, ∀ m ≥ N, μ { x | 2⁻¹ ^ n ≤ dist (f m x) (g x) } ≤ 2⁻¹ ^ n :=
   by
   specialize hfg (2⁻¹ ^ n) (by simp only [zero_lt_bit0, pow_pos, zero_lt_one, inv_pos])
-  rw [ENNReal.tendsto_atTop_zero] at hfg
+  rw [ENNReal.tendsto_atTop_zero] at hfg 
   exact hfg (2⁻¹ ^ n) (pos_iff_ne_zero.mpr fun h_zero => by simpa using pow_eq_zero h_zero)
 #align measure_theory.exists_seq_tendsto_ae.exists_nat_measure_lt_two_inv MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv
 
@@ -234,9 +234,9 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae (hfg : TendstoInMeasure μ f atTo
   have h_tendsto : ∀ x ∈ sᶜ, tendsto (fun i => f (ns i) x) at_top (𝓝 (g x)) :=
     by
     refine' fun x hx => metric.tendsto_at_top.mpr fun ε hε => _
-    rw [hs, limsup_eq_infi_supr_of_nat] at hx
+    rw [hs, limsup_eq_infi_supr_of_nat] at hx 
     simp only [Set.iSup_eq_iUnion, Set.iInf_eq_iInter, Set.compl_iInter, Set.compl_iUnion,
-      Set.mem_iUnion, Set.mem_iInter, Set.mem_compl_iff, Set.mem_setOf_eq, not_le] at hx
+      Set.mem_iUnion, Set.mem_iInter, Set.mem_compl_iff, Set.mem_setOf_eq, not_le] at hx 
     obtain ⟨N, hNx⟩ := hx
     obtain ⟨k, hk_lt_ε⟩ := h_lt_ε_real ε hε
     refine' ⟨max N (k - 1), fun n hn_ge => lt_of_le_of_lt _ hk_lt_ε⟩
@@ -310,8 +310,8 @@ theorem tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable (hp_ne_zero : p
     ENNReal.Tendsto.const_mul (tendsto.ennrpow_const p.to_real hfg)
       (Or.inr <| @ENNReal.ofReal_ne_top (1 / ε ^ p.to_real))
   simp only [MulZeroClass.mul_zero,
-    ENNReal.zero_rpow_of_pos (ENNReal.toReal_pos hp_ne_zero hp_ne_top)] at hfg
-  rw [ENNReal.tendsto_nhds_zero] at hfg⊢
+    ENNReal.zero_rpow_of_pos (ENNReal.toReal_pos hp_ne_zero hp_ne_top)] at hfg 
+  rw [ENNReal.tendsto_nhds_zero] at hfg ⊢
   intro δ hδ
   refine' (hfg δ hδ).mono fun n hn => _
   refine' le_trans _ hn
@@ -349,8 +349,8 @@ theorem tendstoInMeasure_of_tendsto_snorm_top {E} [NormedAddCommGroup E] {f : ι
     {l : Filter ι} (hfg : Tendsto (fun n => snorm (f n - g) ∞ μ) l (𝓝 0)) :
     TendstoInMeasure μ f l g := by
   intro δ hδ
-  simp only [snorm_exponent_top, snorm_ess_sup] at hfg
-  rw [ENNReal.tendsto_nhds_zero] at hfg⊢
+  simp only [snorm_exponent_top, snorm_ess_sup] at hfg 
+  rw [ENNReal.tendsto_nhds_zero] at hfg ⊢
   intro ε hε
   specialize
     hfg (ENNReal.ofReal δ / 2)

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

@@ -50,6 +50,7 @@ namespace MeasureTheory
 
 variable {α ι E : Type _} {m : MeasurableSpace α} {μ : Measure α}
 
+#print MeasureTheory.TendstoInMeasure /-
 /-- A sequence of functions `f` is said to converge in measure to some function `g` if for all
 `ε > 0`, the measure of the set `{x | ε ≤ dist (f i x) (g x)}` tends to 0 as `i` converges along
 some given filter `l`. -/
@@ -57,6 +58,7 @@ def TendstoInMeasure [Dist E] {m : MeasurableSpace α} (μ : Measure α) (f : ι
     (g : α → E) : Prop :=
   ∀ (ε) (hε : 0 < ε), Tendsto (fun i => μ { x | ε ≤ dist (f i x) (g x) }) l (𝓝 0)
 #align measure_theory.tendsto_in_measure MeasureTheory.TendstoInMeasure
+-/
 
 theorem tendstoInMeasure_iff_norm [SeminormedAddCommGroup E] {l : Filter ι} {f : ι → α → E}
     {g : α → E} :
@@ -157,18 +159,22 @@ theorem exists_nat_measure_lt_two_inv (hfg : TendstoInMeasure μ f atTop g) (n :
   exact hfg (2⁻¹ ^ n) (pos_iff_ne_zero.mpr fun h_zero => by simpa using pow_eq_zero h_zero)
 #align measure_theory.exists_seq_tendsto_ae.exists_nat_measure_lt_two_inv MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv
 
+#print MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeqAux /-
 /-- Given a sequence of functions `f` which converges in measure to `g`,
 `seq_tendsto_ae_seq_aux` is a sequence such that
 `∀ m ≥ seq_tendsto_ae_seq_aux n, μ {x | 2⁻¹ ^ n ≤ dist (f m x) (g x)} ≤ 2⁻¹ ^ n`. -/
 noncomputable def seqTendstoAeSeqAux (hfg : TendstoInMeasure μ f atTop g) (n : ℕ) :=
   Classical.choose (exists_nat_measure_lt_two_inv hfg n)
 #align measure_theory.exists_seq_tendsto_ae.seq_tendsto_ae_seq_aux MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeqAux
+-/
 
+#print MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq /-
 /-- Transformation of `seq_tendsto_ae_seq_aux` to makes sure it is strictly monotone. -/
 noncomputable def seqTendstoAeSeq (hfg : TendstoInMeasure μ f atTop g) : ℕ → ℕ
   | 0 => seqTendstoAeSeqAux hfg 0
   | n + 1 => max (seqTendstoAeSeqAux hfg (n + 1)) (seq_tendsto_ae_seq n + 1)
 #align measure_theory.exists_seq_tendsto_ae.seq_tendsto_ae_seq MeasureTheory.ExistsSeqTendstoAe.seqTendstoAeSeq
+-/
 
 theorem seqTendstoAeSeq_succ (hfg : TendstoInMeasure μ f atTop g) {n : ℕ} :
     seqTendstoAeSeq hfg (n + 1) =
@@ -277,13 +283,13 @@ section AeMeasurableOf
 
 variable [MeasurableSpace E] [NormedAddCommGroup E] [BorelSpace E]
 
-theorem TendstoInMeasure.aEMeasurable {u : Filter ι} [NeBot u] [IsCountablyGenerated u]
+theorem TendstoInMeasure.aeMeasurable {u : Filter ι} [NeBot u] [IsCountablyGenerated u]
     {f : ι → α → E} {g : α → E} (hf : ∀ n, AEMeasurable (f n) μ)
     (h_tendsto : TendstoInMeasure μ f u g) : AEMeasurable g μ :=
   by
   obtain ⟨ns, hns⟩ := h_tendsto.exists_seq_tendsto_ae'
   exact aemeasurable_of_tendsto_metrizable_ae at_top (fun n => hf (ns n)) hns
-#align measure_theory.tendsto_in_measure.ae_measurable MeasureTheory.TendstoInMeasure.aEMeasurable
+#align measure_theory.tendsto_in_measure.ae_measurable MeasureTheory.TendstoInMeasure.aeMeasurable
 
 end AeMeasurableOf
 
@@ -375,12 +381,12 @@ theorem tendstoInMeasure_of_tendsto_snorm {l : Filter ι} (hp_ne_zero : p ≠ 0)
 #align measure_theory.tendsto_in_measure_of_tendsto_snorm MeasureTheory.tendstoInMeasure_of_tendsto_snorm
 
 /-- Convergence in Lp implies convergence in measure. -/
-theorem tendstoInMeasure_of_tendsto_lp [hp : Fact (1 ≤ p)] {f : ι → Lp E p μ} {g : Lp E p μ}
+theorem tendstoInMeasure_of_tendsto_Lp [hp : Fact (1 ≤ p)] {f : ι → Lp E p μ} {g : Lp E p μ}
     {l : Filter ι} (hfg : Tendsto f l (𝓝 g)) : TendstoInMeasure μ (fun n => f n) l g :=
   tendstoInMeasure_of_tendsto_snorm (zero_lt_one.trans_le hp.elim).Ne.symm
     (fun n => Lp.aestronglyMeasurable _) (Lp.aestronglyMeasurable _)
     ((Lp.tendsto_Lp_iff_tendsto_ℒp' _ _).mp hfg)
-#align measure_theory.tendsto_in_measure_of_tendsto_Lp MeasureTheory.tendstoInMeasure_of_tendsto_lp
+#align measure_theory.tendsto_in_measure_of_tendsto_Lp MeasureTheory.tendstoInMeasure_of_tendsto_Lp
 
 end TendstoInMeasureOf
 

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

@@ -375,11 +375,11 @@ theorem tendstoInMeasure_of_tendsto_snorm {l : Filter ι} (hp_ne_zero : p ≠ 0)
 #align measure_theory.tendsto_in_measure_of_tendsto_snorm MeasureTheory.tendstoInMeasure_of_tendsto_snorm
 
 /-- Convergence in Lp implies convergence in measure. -/
-theorem tendstoInMeasure_of_tendsto_lp [hp : Fact (1 ≤ p)] {f : ι → lp E p μ} {g : lp E p μ}
+theorem tendstoInMeasure_of_tendsto_lp [hp : Fact (1 ≤ p)] {f : ι → Lp E p μ} {g : Lp E p μ}
     {l : Filter ι} (hfg : Tendsto f l (𝓝 g)) : TendstoInMeasure μ (fun n => f n) l g :=
   tendstoInMeasure_of_tendsto_snorm (zero_lt_one.trans_le hp.elim).Ne.symm
-    (fun n => lp.aEStronglyMeasurable _) (lp.aEStronglyMeasurable _)
-    ((lp.tendsto_lp_iff_tendsto_ℒp' _ _).mp hfg)
+    (fun n => Lp.aestronglyMeasurable _) (Lp.aestronglyMeasurable _)
+    ((Lp.tendsto_Lp_iff_tendsto_ℒp' _ _).mp hfg)
 #align measure_theory.tendsto_in_measure_of_tendsto_Lp MeasureTheory.tendstoInMeasure_of_tendsto_lp
 
 end TendstoInMeasureOf

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

@@ -44,7 +44,7 @@ convergence in measure and other notions of convergence.
 
 open TopologicalSpace Filter
 
-open NNReal ENNReal MeasureTheory Topology
+open scoped NNReal ENNReal MeasureTheory Topology
 
 namespace MeasureTheory
 

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

@@ -213,8 +213,7 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae (hfg : TendstoInMeasure μ f atTo
     intro ε hε
     obtain ⟨k, h_k⟩ : ∃ k : ℕ, 2⁻¹ ^ k < ε := exists_pow_lt_of_lt_one hε (by norm_num)
     refine' ⟨k + 1, (le_of_eq _).trans_lt h_k⟩
-    rw [pow_add]
-    ring
+    rw [pow_add]; ring
   set ns := exists_seq_tendsto_ae.seq_tendsto_ae_seq hfg
   use ns
   let S k := { x | 2⁻¹ ^ k ≤ dist (f (ns k) x) (g x) }
@@ -332,10 +331,8 @@ theorem tendstoInMeasure_of_tendsto_snorm_of_ne_top (hp_ne_zero : p ≠ 0) (hp_n
   refine'
     tendsto_in_measure_of_tendsto_snorm_of_strongly_measurable hp_ne_zero hp_ne_top
       (fun i => (hf i).stronglyMeasurable_mk) hg.strongly_measurable_mk _
-  have : (fun n => snorm ((hf n).mk (f n) - hg.mk g) p μ) = fun n => snorm (f n - g) p μ :=
-    by
-    ext1 n
-    refine' snorm_congr_ae (eventually_eq.sub (hf n).ae_eq_mk.symm hg.ae_eq_mk.symm)
+  have : (fun n => snorm ((hf n).mk (f n) - hg.mk g) p μ) = fun n => snorm (f n - g) p μ := by
+    ext1 n; refine' snorm_congr_ae (eventually_eq.sub (hf n).ae_eq_mk.symm hg.ae_eq_mk.symm)
   rw [this]
   exact hfg
 #align measure_theory.tendsto_in_measure_of_tendsto_snorm_of_ne_top MeasureTheory.tendstoInMeasure_of_tendsto_snorm_of_ne_top

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -132,10 +132,10 @@ theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [FiniteMeasure μ]
 #align measure_theory.tendsto_in_measure_of_tendsto_ae_of_strongly_measurable MeasureTheory.tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable
 
 /-- Convergence a.e. implies convergence in measure in a finite measure space. -/
-theorem tendstoInMeasure_of_tendsto_ae [FiniteMeasure μ] (hf : ∀ n, AeStronglyMeasurable (f n) μ)
+theorem tendstoInMeasure_of_tendsto_ae [FiniteMeasure μ] (hf : ∀ n, AEStronglyMeasurable (f n) μ)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) : TendstoInMeasure μ f atTop g :=
   by
-  have hg : ae_strongly_measurable g μ := aeStronglyMeasurable_of_tendsto_ae _ hf hfg
+  have hg : ae_strongly_measurable g μ := aestronglyMeasurable_of_tendsto_ae _ hf hfg
   refine' tendsto_in_measure.congr (fun i => (hf i).ae_eq_mk.symm) hg.ae_eq_mk.symm _
   refine'
     tendsto_in_measure_of_tendsto_ae_of_strongly_measurable (fun i => (hf i).stronglyMeasurable_mk)
@@ -312,7 +312,7 @@ theorem tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable (hp_ne_zero : p
   refine' le_trans _ hn
   rw [ENNReal.ofReal_div_of_pos (Real.rpow_pos_of_pos hε _), ENNReal.ofReal_one, mul_comm,
     mul_one_div, ENNReal.le_div_iff_mul_le _ (Or.inl ENNReal.ofReal_ne_top), mul_comm]
-  · convert mul_meas_ge_le_pow_snorm' μ hp_ne_zero hp_ne_top ((hf n).sub hg).AeStronglyMeasurable
+  · convert mul_meas_ge_le_pow_snorm' μ hp_ne_zero hp_ne_top ((hf n).sub hg).AEStronglyMeasurable
         (ENNReal.ofReal ε)
     · exact (ENNReal.ofReal_rpow_of_pos hε).symm
     · ext x
@@ -325,7 +325,7 @@ theorem tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable (hp_ne_zero : p
 /-- This lemma is superceded by `measure_theory.tendsto_in_measure_of_tendsto_snorm` where we
 allow `p = ∞`. -/
 theorem tendstoInMeasure_of_tendsto_snorm_of_ne_top (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
-    (hf : ∀ n, AeStronglyMeasurable (f n) μ) (hg : AeStronglyMeasurable g μ) {l : Filter ι}
+    (hf : ∀ n, AEStronglyMeasurable (f n) μ) (hg : AEStronglyMeasurable g μ) {l : Filter ι}
     (hfg : Tendsto (fun n => snorm (f n - g) p μ) l (𝓝 0)) : TendstoInMeasure μ f l g :=
   by
   refine' tendsto_in_measure.congr (fun i => (hf i).ae_eq_mk.symm) hg.ae_eq_mk.symm _
@@ -368,7 +368,7 @@ theorem tendstoInMeasure_of_tendsto_snorm_top {E} [NormedAddCommGroup E] {f : ι
 
 /-- Convergence in Lp implies convergence in measure. -/
 theorem tendstoInMeasure_of_tendsto_snorm {l : Filter ι} (hp_ne_zero : p ≠ 0)
-    (hf : ∀ n, AeStronglyMeasurable (f n) μ) (hg : AeStronglyMeasurable g μ)
+    (hf : ∀ n, AEStronglyMeasurable (f n) μ) (hg : AEStronglyMeasurable g μ)
     (hfg : Tendsto (fun n => snorm (f n - g) p μ) l (𝓝 0)) : TendstoInMeasure μ f l g :=
   by
   by_cases hp_ne_top : p = ∞
@@ -381,7 +381,7 @@ theorem tendstoInMeasure_of_tendsto_snorm {l : Filter ι} (hp_ne_zero : p ≠ 0)
 theorem tendstoInMeasure_of_tendsto_lp [hp : Fact (1 ≤ p)] {f : ι → lp E p μ} {g : lp E p μ}
     {l : Filter ι} (hfg : Tendsto f l (𝓝 g)) : TendstoInMeasure μ (fun n => f n) l g :=
   tendstoInMeasure_of_tendsto_snorm (zero_lt_one.trans_le hp.elim).Ne.symm
-    (fun n => lp.aeStronglyMeasurable _) (lp.aeStronglyMeasurable _)
+    (fun n => lp.aEStronglyMeasurable _) (lp.aEStronglyMeasurable _)
     ((lp.tendsto_lp_iff_tendsto_ℒp' _ _).mp hfg)
 #align measure_theory.tendsto_in_measure_of_tendsto_Lp MeasureTheory.tendstoInMeasure_of_tendsto_lp
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -283,7 +283,7 @@ theorem TendstoInMeasure.aEMeasurable {u : Filter ι} [NeBot u] [IsCountablyGene
     (h_tendsto : TendstoInMeasure μ f u g) : AEMeasurable g μ :=
   by
   obtain ⟨ns, hns⟩ := h_tendsto.exists_seq_tendsto_ae'
-  exact aEMeasurable_of_tendsto_metrizable_ae at_top (fun n => hf (ns n)) hns
+  exact aemeasurable_of_tendsto_metrizable_ae at_top (fun n => hf (ns n)) hns
 #align measure_theory.tendsto_in_measure.ae_measurable MeasureTheory.TendstoInMeasure.aEMeasurable
 
 end AeMeasurableOf

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne, Kexing Ying
 
 ! This file was ported from Lean 3 source module measure_theory.function.convergence_in_measure
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
+! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.SpecialFunctions.Pow
+import Mathbin.Analysis.SpecialFunctions.Pow.Real
 import Mathbin.MeasureTheory.Function.Egorov
 import Mathbin.MeasureTheory.Function.LpSpace
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -230,8 +230,8 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae (hfg : TendstoInMeasure μ f atTo
     by
     refine' fun x hx => metric.tendsto_at_top.mpr fun ε hε => _
     rw [hs, limsup_eq_infi_supr_of_nat] at hx
-    simp only [Set.supᵢ_eq_unionᵢ, Set.infᵢ_eq_interᵢ, Set.compl_interᵢ, Set.compl_unionᵢ,
-      Set.mem_unionᵢ, Set.mem_interᵢ, Set.mem_compl_iff, Set.mem_setOf_eq, not_le] at hx
+    simp only [Set.iSup_eq_iUnion, Set.iInf_eq_iInter, Set.compl_iInter, Set.compl_iUnion,
+      Set.mem_iUnion, Set.mem_iInter, Set.mem_compl_iff, Set.mem_setOf_eq, not_le] at hx
     obtain ⟨N, hNx⟩ := hx
     obtain ⟨k, hk_lt_ε⟩ := h_lt_ε_real ε hε
     refine' ⟨max N (k - 1), fun n hn_ge => lt_of_le_of_lt _ hk_lt_ε⟩

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

@@ -110,7 +110,7 @@ variable [MetricSpace E]
 variable {f : ℕ → α → E} {g : α → E}
 
 /-- Auxiliary lemma for `tendsto_in_measure_of_tendsto_ae`. -/
-theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [IsFiniteMeasure μ]
+theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [FiniteMeasure μ]
     (hf : ∀ n, StronglyMeasurable (f n)) (hg : StronglyMeasurable g)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) : TendstoInMeasure μ f atTop g :=
   by
@@ -132,7 +132,7 @@ theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [IsFiniteMeasure μ
 #align measure_theory.tendsto_in_measure_of_tendsto_ae_of_strongly_measurable MeasureTheory.tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable
 
 /-- Convergence a.e. implies convergence in measure in a finite measure space. -/
-theorem tendstoInMeasure_of_tendsto_ae [IsFiniteMeasure μ] (hf : ∀ n, AeStronglyMeasurable (f n) μ)
+theorem tendstoInMeasure_of_tendsto_ae [FiniteMeasure μ] (hf : ∀ n, AeStronglyMeasurable (f n) μ)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) : TendstoInMeasure μ f atTop g :=
   by
   have hg : ae_strongly_measurable g μ := aeStronglyMeasurable_of_tendsto_ae _ hf hfg

mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa

@@ -91,15 +91,15 @@ protected theorem congr (h_left : ∀ i, f i =ᵐ[μ] f' i) (h_right : g =ᵐ[μ
   TendstoInMeasure.congr' (eventually_of_forall h_left) h_right h_tendsto
 #align measure_theory.tendsto_in_measure.congr MeasureTheory.TendstoInMeasure.congr
 
-theorem congrLeft (h : ∀ i, f i =ᵐ[μ] f' i) (h_tendsto : TendstoInMeasure μ f l g) :
+theorem congr_left (h : ∀ i, f i =ᵐ[μ] f' i) (h_tendsto : TendstoInMeasure μ f l g) :
     TendstoInMeasure μ f' l g :=
   h_tendsto.congr h EventuallyEq.rfl
-#align measure_theory.tendsto_in_measure.congr_left MeasureTheory.TendstoInMeasure.congrLeft
+#align measure_theory.tendsto_in_measure.congr_left MeasureTheory.TendstoInMeasure.congr_left
 
-theorem congrRight (h : g =ᵐ[μ] g') (h_tendsto : TendstoInMeasure μ f l g) :
+theorem congr_right (h : g =ᵐ[μ] g') (h_tendsto : TendstoInMeasure μ f l g) :
     TendstoInMeasure μ f l g' :=
   h_tendsto.congr (fun i => EventuallyEq.rfl) h
-#align measure_theory.tendsto_in_measure.congr_right MeasureTheory.TendstoInMeasure.congrRight
+#align measure_theory.tendsto_in_measure.congr_right MeasureTheory.TendstoInMeasure.congr_right
 
 end TendstoInMeasure
 
@@ -110,7 +110,7 @@ variable [MetricSpace E]
 variable {f : ℕ → α → E} {g : α → E}
 
 /-- Auxiliary lemma for `tendsto_in_measure_of_tendsto_ae`. -/
-theorem tendstoInMeasureOfTendstoAeOfStronglyMeasurable [IsFiniteMeasure μ]
+theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [IsFiniteMeasure μ]
     (hf : ∀ n, StronglyMeasurable (f n)) (hg : StronglyMeasurable g)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) : TendstoInMeasure μ f atTop g :=
   by
@@ -129,13 +129,13 @@ theorem tendstoInMeasureOfTendstoAeOfStronglyMeasurable [IsFiniteMeasure μ]
   intro x hx
   rw [Set.mem_compl_iff, Set.nmem_setOf_iff, dist_comm, not_le]
   exact hN n hn x hx
-#align measure_theory.tendsto_in_measure_of_tendsto_ae_of_strongly_measurable MeasureTheory.tendstoInMeasureOfTendstoAeOfStronglyMeasurable
+#align measure_theory.tendsto_in_measure_of_tendsto_ae_of_strongly_measurable MeasureTheory.tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable
 
 /-- Convergence a.e. implies convergence in measure in a finite measure space. -/
-theorem tendstoInMeasureOfTendstoAe [IsFiniteMeasure μ] (hf : ∀ n, AeStronglyMeasurable (f n) μ)
+theorem tendstoInMeasure_of_tendsto_ae [IsFiniteMeasure μ] (hf : ∀ n, AeStronglyMeasurable (f n) μ)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) : TendstoInMeasure μ f atTop g :=
   by
-  have hg : ae_strongly_measurable g μ := aeStronglyMeasurableOfTendstoAe _ hf hfg
+  have hg : ae_strongly_measurable g μ := aeStronglyMeasurable_of_tendsto_ae _ hf hfg
   refine' tendsto_in_measure.congr (fun i => (hf i).ae_eq_mk.symm) hg.ae_eq_mk.symm _
   refine'
     tendsto_in_measure_of_tendsto_ae_of_strongly_measurable (fun i => (hf i).stronglyMeasurable_mk)
@@ -145,7 +145,7 @@ theorem tendstoInMeasureOfTendstoAe [IsFiniteMeasure μ] (hf : ∀ n, AeStrongly
   filter_upwards [hf_eq_ae, hg.ae_eq_mk, hfg]with x hxf hxg hxfg
   rw [← hxg, funext fun n => hxf n]
   exact hxfg
-#align measure_theory.tendsto_in_measure_of_tendsto_ae MeasureTheory.tendstoInMeasureOfTendstoAe
+#align measure_theory.tendsto_in_measure_of_tendsto_ae MeasureTheory.tendstoInMeasure_of_tendsto_ae
 
 namespace ExistsSeqTendstoAe
 
@@ -278,13 +278,13 @@ section AeMeasurableOf
 
 variable [MeasurableSpace E] [NormedAddCommGroup E] [BorelSpace E]
 
-theorem TendstoInMeasure.aeMeasurable {u : Filter ι} [NeBot u] [IsCountablyGenerated u]
-    {f : ι → α → E} {g : α → E} (hf : ∀ n, AeMeasurable (f n) μ)
-    (h_tendsto : TendstoInMeasure μ f u g) : AeMeasurable g μ :=
+theorem TendstoInMeasure.aEMeasurable {u : Filter ι} [NeBot u] [IsCountablyGenerated u]
+    {f : ι → α → E} {g : α → E} (hf : ∀ n, AEMeasurable (f n) μ)
+    (h_tendsto : TendstoInMeasure μ f u g) : AEMeasurable g μ :=
   by
   obtain ⟨ns, hns⟩ := h_tendsto.exists_seq_tendsto_ae'
-  exact aeMeasurableOfTendstoMetrizableAe at_top (fun n => hf (ns n)) hns
-#align measure_theory.tendsto_in_measure.ae_measurable MeasureTheory.TendstoInMeasure.aeMeasurable
+  exact aEMeasurable_of_tendsto_metrizable_ae at_top (fun n => hf (ns n)) hns
+#align measure_theory.tendsto_in_measure.ae_measurable MeasureTheory.TendstoInMeasure.aEMeasurable
 
 end AeMeasurableOf
 
@@ -296,10 +296,10 @@ variable {f : ι → α → E} {g : α → E}
 
 /-- This lemma is superceded by `measure_theory.tendsto_in_measure_of_tendsto_snorm` where we
 allow `p = ∞` and only require `ae_strongly_measurable`. -/
-theorem tendstoInMeasureOfTendstoSnormOfStronglyMeasurable (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
-    (hf : ∀ n, StronglyMeasurable (f n)) (hg : StronglyMeasurable g) {l : Filter ι}
-    (hfg : Tendsto (fun n => snorm (f n - g) p μ) l (𝓝 0)) : TendstoInMeasure μ f l g :=
-  by
+theorem tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable (hp_ne_zero : p ≠ 0)
+    (hp_ne_top : p ≠ ∞) (hf : ∀ n, StronglyMeasurable (f n)) (hg : StronglyMeasurable g)
+    {l : Filter ι} (hfg : Tendsto (fun n => snorm (f n - g) p μ) l (𝓝 0)) :
+    TendstoInMeasure μ f l g := by
   intro ε hε
   replace hfg :=
     ENNReal.Tendsto.const_mul (tendsto.ennrpow_const p.to_real hfg)
@@ -320,11 +320,11 @@ theorem tendstoInMeasureOfTendstoSnormOfStronglyMeasurable (hp_ne_zero : p ≠ 0
       exact Iff.rfl
   · rw [Ne, ENNReal.ofReal_eq_zero, not_le]
     exact Or.inl (Real.rpow_pos_of_pos hε _)
-#align measure_theory.tendsto_in_measure_of_tendsto_snorm_of_strongly_measurable MeasureTheory.tendstoInMeasureOfTendstoSnormOfStronglyMeasurable
+#align measure_theory.tendsto_in_measure_of_tendsto_snorm_of_strongly_measurable MeasureTheory.tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable
 
 /-- This lemma is superceded by `measure_theory.tendsto_in_measure_of_tendsto_snorm` where we
 allow `p = ∞`. -/
-theorem tendstoInMeasureOfTendstoSnormOfNeTop (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
+theorem tendstoInMeasure_of_tendsto_snorm_of_ne_top (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
     (hf : ∀ n, AeStronglyMeasurable (f n) μ) (hg : AeStronglyMeasurable g μ) {l : Filter ι}
     (hfg : Tendsto (fun n => snorm (f n - g) p μ) l (𝓝 0)) : TendstoInMeasure μ f l g :=
   by
@@ -338,11 +338,11 @@ theorem tendstoInMeasureOfTendstoSnormOfNeTop (hp_ne_zero : p ≠ 0) (hp_ne_top
     refine' snorm_congr_ae (eventually_eq.sub (hf n).ae_eq_mk.symm hg.ae_eq_mk.symm)
   rw [this]
   exact hfg
-#align measure_theory.tendsto_in_measure_of_tendsto_snorm_of_ne_top MeasureTheory.tendstoInMeasureOfTendstoSnormOfNeTop
+#align measure_theory.tendsto_in_measure_of_tendsto_snorm_of_ne_top MeasureTheory.tendstoInMeasure_of_tendsto_snorm_of_ne_top
 
 /-- See also `measure_theory.tendsto_in_measure_of_tendsto_snorm` which work for general
 Lp-convergence for all `p ≠ 0`. -/
-theorem tendstoInMeasureOfTendstoSnormTop {E} [NormedAddCommGroup E] {f : ι → α → E} {g : α → E}
+theorem tendstoInMeasure_of_tendsto_snorm_top {E} [NormedAddCommGroup E] {f : ι → α → E} {g : α → E}
     {l : Filter ι} (hfg : Tendsto (fun n => snorm (f n - g) ∞ μ) l (𝓝 0)) :
     TendstoInMeasure μ f l g := by
   intro δ hδ
@@ -364,10 +364,10 @@ theorem tendstoInMeasureOfTendstoSnormTop {E} [NormedAddCommGroup E] {f : ι →
     coe_nnnorm, Set.mem_setOf_eq, Set.mem_compl_iff]
   rw [← dist_eq_norm (f n x) (g x)]
   rfl
-#align measure_theory.tendsto_in_measure_of_tendsto_snorm_top MeasureTheory.tendstoInMeasureOfTendstoSnormTop
+#align measure_theory.tendsto_in_measure_of_tendsto_snorm_top MeasureTheory.tendstoInMeasure_of_tendsto_snorm_top
 
 /-- Convergence in Lp implies convergence in measure. -/
-theorem tendstoInMeasureOfTendstoSnorm {l : Filter ι} (hp_ne_zero : p ≠ 0)
+theorem tendstoInMeasure_of_tendsto_snorm {l : Filter ι} (hp_ne_zero : p ≠ 0)
     (hf : ∀ n, AeStronglyMeasurable (f n) μ) (hg : AeStronglyMeasurable g μ)
     (hfg : Tendsto (fun n => snorm (f n - g) p μ) l (𝓝 0)) : TendstoInMeasure μ f l g :=
   by
@@ -375,15 +375,15 @@ theorem tendstoInMeasureOfTendstoSnorm {l : Filter ι} (hp_ne_zero : p ≠ 0)
   · subst hp_ne_top
     exact tendsto_in_measure_of_tendsto_snorm_top hfg
   · exact tendsto_in_measure_of_tendsto_snorm_of_ne_top hp_ne_zero hp_ne_top hf hg hfg
-#align measure_theory.tendsto_in_measure_of_tendsto_snorm MeasureTheory.tendstoInMeasureOfTendstoSnorm
+#align measure_theory.tendsto_in_measure_of_tendsto_snorm MeasureTheory.tendstoInMeasure_of_tendsto_snorm
 
 /-- Convergence in Lp implies convergence in measure. -/
-theorem tendstoInMeasureOfTendstoLp [hp : Fact (1 ≤ p)] {f : ι → lp E p μ} {g : lp E p μ}
+theorem tendstoInMeasure_of_tendsto_lp [hp : Fact (1 ≤ p)] {f : ι → lp E p μ} {g : lp E p μ}
     {l : Filter ι} (hfg : Tendsto f l (𝓝 g)) : TendstoInMeasure μ (fun n => f n) l g :=
-  tendstoInMeasureOfTendstoSnorm (zero_lt_one.trans_le hp.elim).Ne.symm
+  tendstoInMeasure_of_tendsto_snorm (zero_lt_one.trans_le hp.elim).Ne.symm
     (fun n => lp.aeStronglyMeasurable _) (lp.aeStronglyMeasurable _)
     ((lp.tendsto_lp_iff_tendsto_ℒp' _ _).mp hfg)
-#align measure_theory.tendsto_in_measure_of_tendsto_Lp MeasureTheory.tendstoInMeasureOfTendstoLp
+#align measure_theory.tendsto_in_measure_of_tendsto_Lp MeasureTheory.tendstoInMeasure_of_tendsto_lp
 
 end TendstoInMeasureOf
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -312,8 +312,7 @@ theorem tendstoInMeasureOfTendstoSnormOfStronglyMeasurable (hp_ne_zero : p ≠ 0
   refine' le_trans _ hn
   rw [ENNReal.ofReal_div_of_pos (Real.rpow_pos_of_pos hε _), ENNReal.ofReal_one, mul_comm,
     mul_one_div, ENNReal.le_div_iff_mul_le _ (Or.inl ENNReal.ofReal_ne_top), mul_comm]
-  · convert
-      mul_meas_ge_le_pow_snorm' μ hp_ne_zero hp_ne_top ((hf n).sub hg).AeStronglyMeasurable
+  · convert mul_meas_ge_le_pow_snorm' μ hp_ne_zero hp_ne_top ((hf n).sub hg).AeStronglyMeasurable
         (ENNReal.ofReal ε)
     · exact (ENNReal.ofReal_rpow_of_pos hε).symm
     · ext x

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

@@ -304,7 +304,8 @@ theorem tendstoInMeasureOfTendstoSnormOfStronglyMeasurable (hp_ne_zero : p ≠ 0
   replace hfg :=
     ENNReal.Tendsto.const_mul (tendsto.ennrpow_const p.to_real hfg)
       (Or.inr <| @ENNReal.ofReal_ne_top (1 / ε ^ p.to_real))
-  simp only [mul_zero, ENNReal.zero_rpow_of_pos (ENNReal.toReal_pos hp_ne_zero hp_ne_top)] at hfg
+  simp only [MulZeroClass.mul_zero,
+    ENNReal.zero_rpow_of_pos (ENNReal.toReal_pos hp_ne_zero hp_ne_top)] at hfg
   rw [ENNReal.tendsto_nhds_zero] at hfg⊢
   intro δ hδ
   refine' (hfg δ hδ).mono fun n hn => _

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

@@ -53,8 +53,8 @@ variable {α ι E : Type _} {m : MeasurableSpace α} {μ : Measure α}
 /-- A sequence of functions `f` is said to converge in measure to some function `g` if for all
 `ε > 0`, the measure of the set `{x | ε ≤ dist (f i x) (g x)}` tends to 0 as `i` converges along
 some given filter `l`. -/
-def TendstoInMeasure [HasDist E] {m : MeasurableSpace α} (μ : Measure α) (f : ι → α → E)
-    (l : Filter ι) (g : α → E) : Prop :=
+def TendstoInMeasure [Dist E] {m : MeasurableSpace α} (μ : Measure α) (f : ι → α → E) (l : Filter ι)
+    (g : α → E) : Prop :=
   ∀ (ε) (hε : 0 < ε), Tendsto (fun i => μ { x | ε ≤ dist (f i x) (g x) }) l (𝓝 0)
 #align measure_theory.tendsto_in_measure MeasureTheory.TendstoInMeasure
 
@@ -67,7 +67,7 @@ theorem tendstoInMeasure_iff_norm [SeminormedAddCommGroup E] {l : Filter ι} {f
 
 namespace TendstoInMeasure
 
-variable [HasDist E] {l : Filter ι} {f f' : ι → α → E} {g g' : α → E}
+variable [Dist E] {l : Filter ι} {f f' : ι → α → E} {g g' : α → E}
 
 protected theorem congr' (h_left : ∀ᶠ i in l, f i =ᵐ[μ] f' i) (h_right : g =ᵐ[μ] g')
     (h_tendsto : TendstoInMeasure μ f l g) : TendstoInMeasure μ f' l g' :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne, Kexing Ying
 
 ! This file was ported from Lean 3 source module measure_theory.function.convergence_in_measure
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -380,7 +380,7 @@ theorem tendstoInMeasureOfTendstoSnorm {l : Filter ι} (hp_ne_zero : p ≠ 0)
 /-- Convergence in Lp implies convergence in measure. -/
 theorem tendstoInMeasureOfTendstoLp [hp : Fact (1 ≤ p)] {f : ι → lp E p μ} {g : lp E p μ}
     {l : Filter ι} (hfg : Tendsto f l (𝓝 g)) : TendstoInMeasure μ (fun n => f n) l g :=
-  tendstoInMeasureOfTendstoSnorm (ENNReal.zero_lt_one.trans_le hp.elim).Ne.symm
+  tendstoInMeasureOfTendstoSnorm (zero_lt_one.trans_le hp.elim).Ne.symm
     (fun n => lp.aeStronglyMeasurable _) (lp.aeStronglyMeasurable _)
     ((lp.tendsto_lp_iff_tendsto_ℒp' _ _).mp hfg)
 #align measure_theory.tendsto_in_measure_of_tendsto_Lp MeasureTheory.tendstoInMeasureOfTendstoLp

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

@@ -44,7 +44,7 @@ convergence in measure and other notions of convergence.
 
 open TopologicalSpace Filter
 
-open NNReal Ennreal MeasureTheory Topology
+open NNReal ENNReal MeasureTheory Topology
 
 namespace MeasureTheory
 
@@ -118,9 +118,9 @@ theorem tendstoInMeasureOfTendstoAeOfStronglyMeasurable [IsFiniteMeasure μ]
   by_cases hδi : δ = ∞
   · simp only [hδi, imp_true_iff, le_top, exists_const]
   lift δ to ℝ≥0 using hδi
-  rw [gt_iff_lt, Ennreal.coe_pos, ← NNReal.coe_pos] at hδ
+  rw [gt_iff_lt, ENNReal.coe_pos, ← NNReal.coe_pos] at hδ
   obtain ⟨t, htm, ht, hunif⟩ := tendsto_uniformly_on_of_ae_tendsto' hf hg hfg hδ
-  rw [Ennreal.ofReal_coe_nNReal] at ht
+  rw [ENNReal.ofReal_coe_nnreal] at ht
   rw [Metric.tendstoUniformlyOn_iff] at hunif
   obtain ⟨N, hN⟩ := eventually_at_top.1 (hunif ε hε)
   refine' ⟨N, fun n hn => _⟩
@@ -153,7 +153,7 @@ theorem exists_nat_measure_lt_two_inv (hfg : TendstoInMeasure μ f atTop g) (n :
     ∃ N, ∀ m ≥ N, μ { x | 2⁻¹ ^ n ≤ dist (f m x) (g x) } ≤ 2⁻¹ ^ n :=
   by
   specialize hfg (2⁻¹ ^ n) (by simp only [zero_lt_bit0, pow_pos, zero_lt_one, inv_pos])
-  rw [Ennreal.tendsto_atTop_zero] at hfg
+  rw [ENNReal.tendsto_atTop_zero] at hfg
   exact hfg (2⁻¹ ^ n) (pos_iff_ne_zero.mpr fun h_zero => by simpa using pow_eq_zero h_zero)
 #align measure_theory.exists_seq_tendsto_ae.exists_nat_measure_lt_two_inv MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv
 
@@ -223,8 +223,8 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae (hfg : TendstoInMeasure μ f atTo
   set s := filter.at_top.limsup S with hs
   have hμs : μ s = 0 :=
     by
-    refine' measure_limsup_eq_zero (ne_of_lt <| lt_of_le_of_lt (Ennreal.tsum_le_tsum hμS_le) _)
-    simp only [Ennreal.tsum_geometric, Ennreal.one_sub_inv_two, inv_inv]
+    refine' measure_limsup_eq_zero (ne_of_lt <| lt_of_le_of_lt (ENNReal.tsum_le_tsum hμS_le) _)
+    simp only [ENNReal.tsum_geometric, ENNReal.one_sub_inv_two, inv_inv]
     decide
   have h_tendsto : ∀ x ∈ sᶜ, tendsto (fun i => f (ns i) x) at_top (𝓝 (g x)) :=
     by
@@ -302,23 +302,23 @@ theorem tendstoInMeasureOfTendstoSnormOfStronglyMeasurable (hp_ne_zero : p ≠ 0
   by
   intro ε hε
   replace hfg :=
-    Ennreal.Tendsto.const_mul (tendsto.ennrpow_const p.to_real hfg)
-      (Or.inr <| @Ennreal.ofReal_ne_top (1 / ε ^ p.to_real))
-  simp only [mul_zero, Ennreal.zero_rpow_of_pos (Ennreal.toReal_pos hp_ne_zero hp_ne_top)] at hfg
-  rw [Ennreal.tendsto_nhds_zero] at hfg⊢
+    ENNReal.Tendsto.const_mul (tendsto.ennrpow_const p.to_real hfg)
+      (Or.inr <| @ENNReal.ofReal_ne_top (1 / ε ^ p.to_real))
+  simp only [mul_zero, ENNReal.zero_rpow_of_pos (ENNReal.toReal_pos hp_ne_zero hp_ne_top)] at hfg
+  rw [ENNReal.tendsto_nhds_zero] at hfg⊢
   intro δ hδ
   refine' (hfg δ hδ).mono fun n hn => _
   refine' le_trans _ hn
-  rw [Ennreal.ofReal_div_of_pos (Real.rpow_pos_of_pos hε _), Ennreal.ofReal_one, mul_comm,
-    mul_one_div, Ennreal.le_div_iff_mul_le _ (Or.inl Ennreal.ofReal_ne_top), mul_comm]
+  rw [ENNReal.ofReal_div_of_pos (Real.rpow_pos_of_pos hε _), ENNReal.ofReal_one, mul_comm,
+    mul_one_div, ENNReal.le_div_iff_mul_le _ (Or.inl ENNReal.ofReal_ne_top), mul_comm]
   · convert
       mul_meas_ge_le_pow_snorm' μ hp_ne_zero hp_ne_top ((hf n).sub hg).AeStronglyMeasurable
-        (Ennreal.ofReal ε)
-    · exact (Ennreal.ofReal_rpow_of_pos hε).symm
+        (ENNReal.ofReal ε)
+    · exact (ENNReal.ofReal_rpow_of_pos hε).symm
     · ext x
-      rw [dist_eq_norm, ← Ennreal.ofReal_le_ofReal_iff (norm_nonneg _), ofReal_norm_eq_coe_nnnorm]
+      rw [dist_eq_norm, ← ENNReal.ofReal_le_ofReal_iff (norm_nonneg _), ofReal_norm_eq_coe_nnnorm]
       exact Iff.rfl
-  · rw [Ne, Ennreal.ofReal_eq_zero, not_le]
+  · rw [Ne, ENNReal.ofReal_eq_zero, not_le]
     exact Or.inl (Real.rpow_pos_of_pos hε _)
 #align measure_theory.tendsto_in_measure_of_tendsto_snorm_of_strongly_measurable MeasureTheory.tendstoInMeasureOfTendstoSnormOfStronglyMeasurable
 
@@ -347,20 +347,20 @@ theorem tendstoInMeasureOfTendstoSnormTop {E} [NormedAddCommGroup E] {f : ι →
     TendstoInMeasure μ f l g := by
   intro δ hδ
   simp only [snorm_exponent_top, snorm_ess_sup] at hfg
-  rw [Ennreal.tendsto_nhds_zero] at hfg⊢
+  rw [ENNReal.tendsto_nhds_zero] at hfg⊢
   intro ε hε
   specialize
-    hfg (Ennreal.ofReal δ / 2)
-      (Ennreal.div_pos_iff.2 ⟨(Ennreal.ofReal_pos.2 hδ).Ne.symm, Ennreal.two_ne_top⟩)
+    hfg (ENNReal.ofReal δ / 2)
+      (ENNReal.div_pos_iff.2 ⟨(ENNReal.ofReal_pos.2 hδ).Ne.symm, ENNReal.two_ne_top⟩)
   refine' hfg.mono fun n hn => _
   simp only [true_and_iff, gt_iff_lt, ge_iff_le, zero_tsub, zero_le, zero_add, Set.mem_Icc,
     Pi.sub_apply] at *
-  have : essSup (fun x : α => (‖f n x - g x‖₊ : ℝ≥0∞)) μ < Ennreal.ofReal δ :=
+  have : essSup (fun x : α => (‖f n x - g x‖₊ : ℝ≥0∞)) μ < ENNReal.ofReal δ :=
     lt_of_le_of_lt hn
-      (Ennreal.half_lt_self (Ennreal.ofReal_pos.2 hδ).Ne.symm ennreal.of_real_lt_top.ne)
+      (ENNReal.half_lt_self (ENNReal.ofReal_pos.2 hδ).Ne.symm ennreal.of_real_lt_top.ne)
   refine' ((le_of_eq _).trans (ae_lt_of_essSup_lt this).le).trans hε.le
   congr with x
-  simp only [Ennreal.ofReal_le_iff_le_toReal ennreal.coe_lt_top.ne, Ennreal.coe_toReal, not_lt,
+  simp only [ENNReal.ofReal_le_iff_le_toReal ennreal.coe_lt_top.ne, ENNReal.coe_toReal, not_lt,
     coe_nnnorm, Set.mem_setOf_eq, Set.mem_compl_iff]
   rw [← dist_eq_norm (f n x) (g x)]
   rfl
@@ -380,7 +380,7 @@ theorem tendstoInMeasureOfTendstoSnorm {l : Filter ι} (hp_ne_zero : p ≠ 0)
 /-- Convergence in Lp implies convergence in measure. -/
 theorem tendstoInMeasureOfTendstoLp [hp : Fact (1 ≤ p)] {f : ι → lp E p μ} {g : lp E p μ}
     {l : Filter ι} (hfg : Tendsto f l (𝓝 g)) : TendstoInMeasure μ (fun n => f n) l g :=
-  tendstoInMeasureOfTendstoSnorm (Ennreal.zero_lt_one.trans_le hp.elim).Ne.symm
+  tendstoInMeasureOfTendstoSnorm (ENNReal.zero_lt_one.trans_le hp.elim).Ne.symm
     (fun n => lp.aeStronglyMeasurable _) (lp.aeStronglyMeasurable _)
     ((lp.tendsto_lp_iff_tendsto_ℒp' _ _).mp hfg)
 #align measure_theory.tendsto_in_measure_of_tendsto_Lp MeasureTheory.tendstoInMeasureOfTendstoLp

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

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -142,7 +142,7 @@ namespace ExistsSeqTendstoAe
 
 theorem exists_nat_measure_lt_two_inv (hfg : TendstoInMeasure μ f atTop g) (n : ℕ) :
     ∃ N, ∀ m ≥ N, μ { x | (2 : ℝ)⁻¹ ^ n ≤ dist (f m x) (g x) } ≤ (2⁻¹ : ℝ≥0∞) ^ n := by
-  specialize hfg ((2⁻¹ : ℝ) ^ n) (by simp only [Real.rpow_nat_cast, inv_pos, zero_lt_two, pow_pos])
+  specialize hfg ((2⁻¹ : ℝ) ^ n) (by simp only [Real.rpow_natCast, inv_pos, zero_lt_two, pow_pos])
   rw [ENNReal.tendsto_atTop_zero] at hfg
   exact hfg ((2 : ℝ≥0∞)⁻¹ ^ n) (pos_iff_ne_zero.mpr fun h_zero => by simpa using pow_eq_zero h_zero)
 #align measure_theory.exists_seq_tendsto_ae.exists_nat_measure_lt_two_inv MeasureTheory.ExistsSeqTendstoAe.exists_nat_measure_lt_two_inv

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)

@@ -101,7 +101,6 @@ end TendstoInMeasure
 section ExistsSeqTendstoAe
 
 variable [MetricSpace E]
-
 variable {f : ℕ → α → E} {g : α → E}
 
 /-- Auxiliary lemma for `tendstoInMeasure_of_tendsto_ae`. -/
@@ -268,7 +267,6 @@ end AEMeasurableOf
 section TendstoInMeasureOf
 
 variable [NormedAddCommGroup E] {p : ℝ≥0∞}
-
 variable {f : ι → α → E} {g : α → E}
 
 /-- This lemma is superceded by `MeasureTheory.tendstoInMeasure_of_tendsto_snorm` where we

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

@@ -213,7 +213,7 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae (hfg : TendstoInMeasure μ f atTo
   have h_tendsto : ∀ x ∈ sᶜ, Tendsto (fun i => f (ns i) x) atTop (𝓝 (g x)) := by
     refine' fun x hx => Metric.tendsto_atTop.mpr fun ε hε => _
     rw [hs, limsup_eq_iInf_iSup_of_nat] at hx
-    simp only [Set.iSup_eq_iUnion, Set.iInf_eq_iInter, Set.compl_iInter, Set.compl_iUnion,
+    simp only [S, Set.iSup_eq_iUnion, Set.iInf_eq_iInter, Set.compl_iInter, Set.compl_iUnion,
       Set.mem_iUnion, Set.mem_iInter, Set.mem_compl_iff, Set.mem_setOf_eq, not_le] at hx
     obtain ⟨N, hNx⟩ := hx
     obtain ⟨k, hk_lt_ε⟩ := h_lt_ε_real ε hε

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>

@@ -118,7 +118,7 @@ theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [IsFiniteMeasure μ
   rw [Metric.tendstoUniformlyOn_iff] at hunif
   obtain ⟨N, hN⟩ := eventually_atTop.1 (hunif ε hε)
   refine' ⟨N, fun n hn => _⟩
-  suffices : { x : α | ε ≤ dist (f n x) (g x) } ⊆ t; exact (measure_mono this).trans ht
+  suffices { x : α | ε ≤ dist (f n x) (g x) } ⊆ t from (measure_mono this).trans ht
   rw [← Set.compl_subset_compl]
   intro x hx
   rw [Set.mem_compl_iff, Set.nmem_setOf_iff, dist_comm, not_le]

Follow-up #9184

@@ -52,13 +52,13 @@ variable {α ι E : Type*} {m : MeasurableSpace α} {μ : Measure α}
 some given filter `l`. -/
 def TendstoInMeasure [Dist E] {_ : MeasurableSpace α} (μ : Measure α) (f : ι → α → E) (l : Filter ι)
     (g : α → E) : Prop :=
-  ∀ (ε) (_ : 0 < ε), Tendsto (fun i => μ { x | ε ≤ dist (f i x) (g x) }) l (𝓝 0)
+  ∀ ε, 0 < ε → Tendsto (fun i => μ { x | ε ≤ dist (f i x) (g x) }) l (𝓝 0)
 #align measure_theory.tendsto_in_measure MeasureTheory.TendstoInMeasure
 
 theorem tendstoInMeasure_iff_norm [SeminormedAddCommGroup E] {l : Filter ι} {f : ι → α → E}
     {g : α → E} :
     TendstoInMeasure μ f l g ↔
-      ∀ (ε) (hε : 0 < ε), Tendsto (fun i => μ { x | ε ≤ ‖f i x - g x‖ }) l (𝓝 0) := by
+      ∀ ε, 0 < ε → Tendsto (fun i => μ { x | ε ≤ ‖f i x - g x‖ }) l (𝓝 0) := by
   simp_rw [TendstoInMeasure, dist_eq_norm]
 #align measure_theory.tendsto_in_measure_iff_norm MeasureTheory.tendstoInMeasure_iff_norm
 

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -139,8 +139,6 @@ theorem tendstoInMeasure_of_tendsto_ae [IsFiniteMeasure μ] (hf : ∀ n, AEStron
   exact hxfg
 #align measure_theory.tendsto_in_measure_of_tendsto_ae MeasureTheory.tendstoInMeasure_of_tendsto_ae
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 namespace ExistsSeqTendstoAe
 
 theorem exists_nat_measure_lt_two_inv (hfg : TendstoInMeasure μ f atTop g) (n : ℕ) :
@@ -211,7 +209,7 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae (hfg : TendstoInMeasure μ f atTo
   set s := Filter.atTop.limsup S with hs
   have hμs : μ s = 0 := by
     refine' measure_limsup_eq_zero (ne_of_lt <| lt_of_le_of_lt (ENNReal.tsum_le_tsum hμS_le) _)
-    simp only [ENNReal.tsum_geometric, ENNReal.one_sub_inv_two, inv_inv]
+    simp only [ENNReal.tsum_geometric, ENNReal.one_sub_inv_two, ENNReal.two_lt_top, inv_inv]
   have h_tendsto : ∀ x ∈ sᶜ, Tendsto (fun i => f (ns i) x) atTop (𝓝 (g x)) := by
     refine' fun x hx => Metric.tendsto_atTop.mpr fun ε hε => _
     rw [hs, limsup_eq_iInf_iSup_of_nat] at hx

@@ -206,12 +206,8 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae (hfg : TendstoInMeasure μ f atTo
   set ns := ExistsSeqTendstoAe.seqTendstoAeSeq hfg
   use ns
   let S := fun k => { x | (2 : ℝ)⁻¹ ^ k ≤ dist (f (ns k) x) (g x) }
-  have hμS_le : ∀ k, μ (S k) ≤ (2 : ℝ≥0∞)⁻¹ ^ k := by
-    intro k
-    have := ExistsSeqTendstoAe.seqTendstoAeSeq_spec hfg k (ns k) le_rfl
-    convert this
-
-  --  fun k => ExistsSeqTendstoAe.seqTendstoAeSeq_spec hfg k (ns k) le_rfl
+  have hμS_le : ∀ k, μ (S k) ≤ (2 : ℝ≥0∞)⁻¹ ^ k :=
+    fun k => ExistsSeqTendstoAe.seqTendstoAeSeq_spec hfg k (ns k) le_rfl
   set s := Filter.atTop.limsup S with hs
   have hμs : μ s = 0 := by
     refine' measure_limsup_eq_zero (ne_of_lt <| lt_of_le_of_lt (ENNReal.tsum_le_tsum hμS_le) _)
@@ -258,18 +254,18 @@ theorem TendstoInMeasure.exists_seq_tendsto_ae' {u : Filter ι} [NeBot u] [IsCou
 
 end ExistsSeqTendstoAe
 
-section AeMeasurableOf
+section AEMeasurableOf
 
 variable [MeasurableSpace E] [NormedAddCommGroup E] [BorelSpace E]
 
-theorem TendstoInMeasure.aeMeasurable {u : Filter ι} [NeBot u] [IsCountablyGenerated u]
+theorem TendstoInMeasure.aemeasurable {u : Filter ι} [NeBot u] [IsCountablyGenerated u]
     {f : ι → α → E} {g : α → E} (hf : ∀ n, AEMeasurable (f n) μ)
     (h_tendsto : TendstoInMeasure μ f u g) : AEMeasurable g μ := by
   obtain ⟨ns, hns⟩ := h_tendsto.exists_seq_tendsto_ae'
   exact aemeasurable_of_tendsto_metrizable_ae atTop (fun n => hf (ns n)) hns
-#align measure_theory.tendsto_in_measure.ae_measurable MeasureTheory.TendstoInMeasure.aeMeasurable
+#align measure_theory.tendsto_in_measure.ae_measurable MeasureTheory.TendstoInMeasure.aemeasurable
 
-end AeMeasurableOf
+end AEMeasurableOf
 
 section TendstoInMeasureOf
 

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).

@@ -286,7 +286,7 @@ theorem tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable (hp_ne_zero : p
   intro ε hε
   replace hfg := ENNReal.Tendsto.const_mul
     (Tendsto.ennrpow_const p.toReal hfg) (Or.inr <| @ENNReal.ofReal_ne_top (1 / ε ^ p.toReal))
-  simp only [MulZeroClass.mul_zero,
+  simp only [mul_zero,
     ENNReal.zero_rpow_of_pos (ENNReal.toReal_pos hp_ne_zero hp_ne_top)] at hfg
   rw [ENNReal.tendsto_nhds_zero] at hfg ⊢
   intro δ hδ

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

This has nice performance benefits.

@@ -45,7 +45,7 @@ open scoped NNReal ENNReal MeasureTheory Topology
 
 namespace MeasureTheory
 
-variable {α ι E : Type _} {m : MeasurableSpace α} {μ : Measure α}
+variable {α ι E : Type*} {m : MeasurableSpace α} {μ : Measure α}
 
 /-- A sequence of functions `f` is said to converge in measure to some function `g` if for all
 `ε > 0`, the measure of the set `{x | ε ≤ dist (f i x) (g x)}` tends to 0 as `i` converges along

@@ -139,8 +139,7 @@ theorem tendstoInMeasure_of_tendsto_ae [IsFiniteMeasure μ] (hf : ∀ n, AEStron
   exact hxfg
 #align measure_theory.tendsto_in_measure_of_tendsto_ae MeasureTheory.tendstoInMeasure_of_tendsto_ae
 
--- Porting note: See issue #2220
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y)
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 namespace ExistsSeqTendstoAe
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Rémy Degenne, Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne, Kexing Ying
-
-! This file was ported from Lean 3 source module measure_theory.function.convergence_in_measure
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.SpecialFunctions.Pow.Real
 import Mathlib.MeasureTheory.Function.Egorov
 import Mathlib.MeasureTheory.Function.LpSpace
 
+#align_import measure_theory.function.convergence_in_measure from "leanprover-community/mathlib"@"0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8"
+
 /-!
 # Convergence in measure
 

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -292,7 +292,7 @@ theorem tendstoInMeasure_of_tendsto_snorm_of_stronglyMeasurable (hp_ne_zero : p
     (Tendsto.ennrpow_const p.toReal hfg) (Or.inr <| @ENNReal.ofReal_ne_top (1 / ε ^ p.toReal))
   simp only [MulZeroClass.mul_zero,
     ENNReal.zero_rpow_of_pos (ENNReal.toReal_pos hp_ne_zero hp_ne_top)] at hfg
-  rw [ENNReal.tendsto_nhds_zero] at hfg⊢
+  rw [ENNReal.tendsto_nhds_zero] at hfg ⊢
   intro δ hδ
   refine' (hfg δ hδ).mono fun n hn => _
   refine' le_trans _ hn
@@ -328,7 +328,7 @@ theorem tendstoInMeasure_of_tendsto_snorm_top {E} [NormedAddCommGroup E] {f : ι
     TendstoInMeasure μ f l g := by
   intro δ hδ
   simp only [snorm_exponent_top, snormEssSup] at hfg
-  rw [ENNReal.tendsto_nhds_zero] at hfg⊢
+  rw [ENNReal.tendsto_nhds_zero] at hfg ⊢
   intro ε hε
   specialize hfg (ENNReal.ofReal δ / 2)
       (ENNReal.div_pos_iff.2 ⟨(ENNReal.ofReal_pos.2 hδ).ne.symm, ENNReal.two_ne_top⟩)

I have misported is_foo to Foo because I misunderstood the rule for IsLawfulFoo. This PR recover Is of Foo which is ported from is_foo. This PR also renames some misported theorems.

@@ -108,7 +108,7 @@ variable [MetricSpace E]
 variable {f : ℕ → α → E} {g : α → E}
 
 /-- Auxiliary lemma for `tendstoInMeasure_of_tendsto_ae`. -/
-theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [FiniteMeasure μ]
+theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [IsFiniteMeasure μ]
     (hf : ∀ n, StronglyMeasurable (f n)) (hg : StronglyMeasurable g)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) : TendstoInMeasure μ f atTop g := by
   refine' fun ε hε => ENNReal.tendsto_atTop_zero.mpr fun δ hδ => _
@@ -129,7 +129,7 @@ theorem tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable [FiniteMeasure μ]
 #align measure_theory.tendsto_in_measure_of_tendsto_ae_of_strongly_measurable MeasureTheory.tendstoInMeasure_of_tendsto_ae_of_stronglyMeasurable
 
 /-- Convergence a.e. implies convergence in measure in a finite measure space. -/
-theorem tendstoInMeasure_of_tendsto_ae [FiniteMeasure μ] (hf : ∀ n, AEStronglyMeasurable (f n) μ)
+theorem tendstoInMeasure_of_tendsto_ae [IsFiniteMeasure μ] (hf : ∀ n, AEStronglyMeasurable (f n) μ)
     (hfg : ∀ᵐ x ∂μ, Tendsto (fun n => f n x) atTop (𝓝 (g x))) : TendstoInMeasure μ f atTop g := by
   have hg : AEStronglyMeasurable g μ := aestronglyMeasurable_of_tendsto_ae _ hf hfg
   refine' TendstoInMeasure.congr (fun i => (hf i).ae_eq_mk.symm) hg.ae_eq_mk.symm _

Co-authored-by: Xavier-François Roblot <46200072+xroblot@users.noreply.github.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>