probability.borel_cantelli ⟷ Mathlib.Probability.BorelCantelli

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

@@ -49,7 +49,7 @@ theorem iIndepFun.indep_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f i
   suffices
     indep (⨆ k ∈ {j}, MeasurableSpace.comap (f k) mβ)
       (⨆ k ∈ {k | k ≤ i}, MeasurableSpace.comap (f k) mβ) μ
-    by rwa [iSup_singleton] at this 
+    by rwa [iSup_singleton] at this
   exact indep_supr_of_disjoint (fun k => (hf k).Measurable.comap_le) hfi (by simpa)
 #align probability_theory.Indep_fun.indep_comap_natural_of_lt ProbabilityTheory.iIndepFun.indep_comap_natural_of_lt
 -/
@@ -109,14 +109,14 @@ theorem measure_limsup_eq_one {s : ℕ → Set Ω} (hsm : ∀ n, MeasurableSet (
     by
     rw [← ENNReal.tsum_add_one_eq_top hs' (measure_ne_top _ _)]
     exact ENNReal.tendsto_nat_tsum _
-  rw [ENNReal.tendsto_nhds_top_iff_nnreal] at htends 
+  rw [ENNReal.tendsto_nhds_top_iff_nnreal] at htends
   refine' tendsto_at_top_at_top_of_monotone' _ _
   · refine' monotone_nat_of_le_succ fun n => _
     rw [← sub_nonneg, Finset.sum_range_succ_sub_sum]
     exact ENNReal.toReal_nonneg
   · rintro ⟨B, hB⟩
     refine' not_eventually.2 (frequently_of_forall fun n => _) (htends B.to_nnreal)
-    rw [mem_upperBounds] at hB 
+    rw [mem_upperBounds] at hB
     specialize hB (∑ k : ℕ in Finset.range n, μ (s (k + 1))).toReal _
     · refine' ⟨n, _⟩
       rw [ENNReal.toReal_sum]

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

@@ -3,9 +3,9 @@ Copyright (c) 2022 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 -/
-import Mathbin.Probability.Martingale.BorelCantelli
-import Mathbin.Probability.ConditionalExpectation
-import Mathbin.Probability.Independence.Basic
+import Probability.Martingale.BorelCantelli
+import Probability.ConditionalExpectation
+import Probability.Independence.Basic
 
 #align_import probability.borel_cantelli from "leanprover-community/mathlib"@"e8e130de9dba4ed6897183c3193c752ffadbcc77"
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2022 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
-
-! This file was ported from Lean 3 source module probability.borel_cantelli
-! leanprover-community/mathlib commit e8e130de9dba4ed6897183c3193c752ffadbcc77
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Probability.Martingale.BorelCantelli
 import Mathbin.Probability.ConditionalExpectation
 import Mathbin.Probability.Independence.Basic
 
+#align_import probability.borel_cantelli from "leanprover-community/mathlib"@"e8e130de9dba4ed6897183c3193c752ffadbcc77"
+
 /-!
 
 # The second Borel-Cantelli lemma

mathlib commit https://github.com/leanprover-community/mathlib/commit/6285167a053ad0990fc88e56c48ccd9fae6550eb

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 
 ! This file was ported from Lean 3 source module probability.borel_cantelli
-! leanprover-community/mathlib commit 2f8347015b12b0864dfaf366ec4909eb70c78740
+! leanprover-community/mathlib commit e8e130de9dba4ed6897183c3193c752ffadbcc77
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Probability.Independence.Basic
 
 # The second Borel-Cantelli lemma
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains the second Borel-Cantelli lemma which states that, given a sequence of
 independent sets `(sₙ)` in a probability space, if `∑ n, μ sₙ = ∞`, then the limsup of `sₙ` has
 measure 1. We employ a proof using Lévy's generalized Borel-Cantelli by choosing an appropriate

mathlib commit https://github.com/leanprover-community/mathlib/commit/0723536a0522d24fc2f159a096fb3304bef77472

@@ -41,6 +41,7 @@ section BorelCantelli
 variable {ι β : Type _} [LinearOrder ι] [mβ : MeasurableSpace β] [NormedAddCommGroup β]
   [BorelSpace β] {f : ι → Ω → β} {i j : ι} {s : ι → Set Ω}
 
+#print ProbabilityTheory.iIndepFun.indep_comap_natural_of_lt /-
 theorem iIndepFun.indep_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f i))
     (hfi : iIndepFun (fun i => mβ) f μ) (hij : i < j) :
     Indep (MeasurableSpace.comap (f j) mβ) (Filtration.natural f hf i) μ :=
@@ -51,14 +52,18 @@ theorem iIndepFun.indep_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f i
     by rwa [iSup_singleton] at this 
   exact indep_supr_of_disjoint (fun k => (hf k).Measurable.comap_le) hfi (by simpa)
 #align probability_theory.Indep_fun.indep_comap_natural_of_lt ProbabilityTheory.iIndepFun.indep_comap_natural_of_lt
+-/
 
+#print ProbabilityTheory.iIndepFun.condexp_natural_ae_eq_of_lt /-
 theorem iIndepFun.condexp_natural_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]
     [NormedSpace ℝ β] (hf : ∀ i, StronglyMeasurable (f i)) (hfi : iIndepFun (fun i => mβ) f μ)
     (hij : i < j) : μ[f j|Filtration.natural f hf i] =ᵐ[μ] fun ω => μ[f j] :=
   condexp_indep_eq (hf j).Measurable.comap_le (Filtration.le _ _)
     (comap_measurable <| f j).StronglyMeasurable (hfi.indep_comap_natural_of_lt hf hij)
 #align probability_theory.Indep_fun.condexp_natural_ae_eq_of_lt ProbabilityTheory.iIndepFun.condexp_natural_ae_eq_of_lt
+-/
 
+#print ProbabilityTheory.iIndepSet.condexp_indicator_filtrationOfSet_ae_eq /-
 theorem iIndepSet.condexp_indicator_filtrationOfSet_ae_eq (hsm : ∀ n, MeasurableSet (s n))
     (hs : iIndepSet s μ) (hij : i < j) :
     μ[(s j).indicator (fun ω => 1 : Ω → ℝ)|filtrationOfSet hsm i] =ᵐ[μ] fun ω => (μ (s j)).toReal :=
@@ -68,9 +73,11 @@ theorem iIndepSet.condexp_indicator_filtrationOfSet_ae_eq (hsm : ∀ n, Measurab
   · simp only [integral_indicator_const _ (hsm _), Algebra.id.smul_eq_mul, mul_one]
   · infer_instance
 #align probability_theory.Indep_set.condexp_indicator_filtration_of_set_ae_eq ProbabilityTheory.iIndepSet.condexp_indicator_filtrationOfSet_ae_eq
+-/
 
 open Filter
 
+#print ProbabilityTheory.measure_limsup_eq_one /-
 /-- **The second Borel-Cantelli lemma**: Given a sequence of independent sets `(sₙ)` such that
 `∑ n, μ sₙ = ∞`, `limsup sₙ` has measure 1. -/
 theorem measure_limsup_eq_one {s : ℕ → Set Ω} (hsm : ∀ n, MeasurableSet (s n)) (hs : iIndepSet s μ)
@@ -118,6 +125,7 @@ theorem measure_limsup_eq_one {s : ℕ → Set Ω} (hsm : ∀ n, MeasurableSet (
       · exact hB.trans (by simp)
       · exact fun _ _ => measure_ne_top _ _
 #align probability_theory.measure_limsup_eq_one ProbabilityTheory.measure_limsup_eq_one
+-/
 
 end BorelCantelli
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -74,7 +74,7 @@ open Filter
 /-- **The second Borel-Cantelli lemma**: Given a sequence of independent sets `(sₙ)` such that
 `∑ n, μ sₙ = ∞`, `limsup sₙ` has measure 1. -/
 theorem measure_limsup_eq_one {s : ℕ → Set Ω} (hsm : ∀ n, MeasurableSet (s n)) (hs : iIndepSet s μ)
-    (hs' : (∑' n, μ (s n)) = ∞) : μ (limsup s atTop) = 1 :=
+    (hs' : ∑' n, μ (s n) = ∞) : μ (limsup s atTop) = 1 :=
   by
   rw [measure_congr
       (eventually_eq_set.2 (ae_mem_limsup_at_top_iff μ <| measurable_set_filtration_of_set' hsm) :

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

@@ -34,68 +34,68 @@ open MeasureTheory ProbabilityTheory MeasurableSpace TopologicalSpace
 
 namespace ProbabilityTheory
 
-variable {Ω : Type _} {m0 : MeasurableSpace Ω} {μ : Measure Ω} [ProbabilityMeasure μ]
+variable {Ω : Type _} {m0 : MeasurableSpace Ω} {μ : Measure Ω} [IsProbabilityMeasure μ]
 
 section BorelCantelli
 
 variable {ι β : Type _} [LinearOrder ι] [mβ : MeasurableSpace β] [NormedAddCommGroup β]
   [BorelSpace β] {f : ι → Ω → β} {i j : ι} {s : ι → Set Ω}
 
-theorem IndepFun.indepCat_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f i))
-    (hfi : IndepFun (fun i => mβ) f μ) (hij : i < j) :
-    IndepCat (MeasurableSpace.comap (f j) mβ) (Filtration.natural f hf i) μ :=
+theorem iIndepFun.indep_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f i))
+    (hfi : iIndepFun (fun i => mβ) f μ) (hij : i < j) :
+    Indep (MeasurableSpace.comap (f j) mβ) (Filtration.natural f hf i) μ :=
   by
   suffices
     indep (⨆ k ∈ {j}, MeasurableSpace.comap (f k) mβ)
-      (⨆ k ∈ { k | k ≤ i }, MeasurableSpace.comap (f k) mβ) μ
+      (⨆ k ∈ {k | k ≤ i}, MeasurableSpace.comap (f k) mβ) μ
     by rwa [iSup_singleton] at this 
   exact indep_supr_of_disjoint (fun k => (hf k).Measurable.comap_le) hfi (by simpa)
-#align probability_theory.Indep_fun.indep_comap_natural_of_lt ProbabilityTheory.IndepFun.indepCat_comap_natural_of_lt
+#align probability_theory.Indep_fun.indep_comap_natural_of_lt ProbabilityTheory.iIndepFun.indep_comap_natural_of_lt
 
-theorem IndepFun.condexp_natural_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]
-    [NormedSpace ℝ β] (hf : ∀ i, StronglyMeasurable (f i)) (hfi : IndepFun (fun i => mβ) f μ)
+theorem iIndepFun.condexp_natural_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]
+    [NormedSpace ℝ β] (hf : ∀ i, StronglyMeasurable (f i)) (hfi : iIndepFun (fun i => mβ) f μ)
     (hij : i < j) : μ[f j|Filtration.natural f hf i] =ᵐ[μ] fun ω => μ[f j] :=
-  condexp_indepCat_eq (hf j).Measurable.comap_le (Filtration.le _ _)
-    (comap_measurable <| f j).StronglyMeasurable (hfi.indepCat_comap_natural_of_lt hf hij)
-#align probability_theory.Indep_fun.condexp_natural_ae_eq_of_lt ProbabilityTheory.IndepFun.condexp_natural_ae_eq_of_lt
+  condexp_indep_eq (hf j).Measurable.comap_le (Filtration.le _ _)
+    (comap_measurable <| f j).StronglyMeasurable (hfi.indep_comap_natural_of_lt hf hij)
+#align probability_theory.Indep_fun.condexp_natural_ae_eq_of_lt ProbabilityTheory.iIndepFun.condexp_natural_ae_eq_of_lt
 
-theorem IndepSet.condexp_indicator_filtrationOfSet_ae_eq (hsm : ∀ n, MeasurableSet (s n))
-    (hs : IndepSet s μ) (hij : i < j) :
+theorem iIndepSet.condexp_indicator_filtrationOfSet_ae_eq (hsm : ∀ n, MeasurableSet (s n))
+    (hs : iIndepSet s μ) (hij : i < j) :
     μ[(s j).indicator (fun ω => 1 : Ω → ℝ)|filtrationOfSet hsm i] =ᵐ[μ] fun ω => (μ (s j)).toReal :=
   by
   rw [filtration.filtration_of_set_eq_natural hsm]
   refine' (Indep_fun.condexp_natural_ae_eq_of_lt _ hs.Indep_fun_indicator hij).trans _
   · simp only [integral_indicator_const _ (hsm _), Algebra.id.smul_eq_mul, mul_one]
   · infer_instance
-#align probability_theory.Indep_set.condexp_indicator_filtration_of_set_ae_eq ProbabilityTheory.IndepSet.condexp_indicator_filtrationOfSet_ae_eq
+#align probability_theory.Indep_set.condexp_indicator_filtration_of_set_ae_eq ProbabilityTheory.iIndepSet.condexp_indicator_filtrationOfSet_ae_eq
 
 open Filter
 
 /-- **The second Borel-Cantelli lemma**: Given a sequence of independent sets `(sₙ)` such that
 `∑ n, μ sₙ = ∞`, `limsup sₙ` has measure 1. -/
-theorem measure_limsup_eq_one {s : ℕ → Set Ω} (hsm : ∀ n, MeasurableSet (s n)) (hs : IndepSet s μ)
+theorem measure_limsup_eq_one {s : ℕ → Set Ω} (hsm : ∀ n, MeasurableSet (s n)) (hs : iIndepSet s μ)
     (hs' : (∑' n, μ (s n)) = ∞) : μ (limsup s atTop) = 1 :=
   by
   rw [measure_congr
       (eventually_eq_set.2 (ae_mem_limsup_at_top_iff μ <| measurable_set_filtration_of_set' hsm) :
         (limsup s at_top : Set Ω) =ᵐ[μ]
-          { ω |
+          {ω |
             tendsto
               (fun n =>
                 ∑ k in Finset.range n,
                   (μ[(s (k + 1)).indicator (1 : Ω → ℝ)|filtration_of_set hsm k]) ω)
-              at_top at_top })]
+              at_top at_top})]
   suffices
-    { ω |
+    {ω |
         tendsto
           (fun n =>
             ∑ k in Finset.range n, (μ[(s (k + 1)).indicator (1 : Ω → ℝ)|filtration_of_set hsm k]) ω)
-          at_top at_top } =ᵐ[μ]
+          at_top at_top} =ᵐ[μ]
       Set.univ
     by rw [measure_congr this, measure_univ]
   have : ∀ᵐ ω ∂μ, ∀ n, (μ[(s (n + 1)).indicator (1 : Ω → ℝ)|filtration_of_set hsm n]) ω = _ :=
     ae_all_iff.2 fun n => hs.condexp_indicator_filtration_of_set_ae_eq hsm n.lt_succ_self
-  filter_upwards [this]with ω hω
+  filter_upwards [this] with ω hω
   refine' eq_true (_ : tendsto _ _ _)
   simp_rw [hω]
   have htends : tendsto (fun n => ∑ k in Finset.range n, μ (s (k + 1))) at_top (𝓝 ∞) :=

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

@@ -48,7 +48,7 @@ theorem IndepFun.indepCat_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f
   suffices
     indep (⨆ k ∈ {j}, MeasurableSpace.comap (f k) mβ)
       (⨆ k ∈ { k | k ≤ i }, MeasurableSpace.comap (f k) mβ) μ
-    by rwa [iSup_singleton] at this
+    by rwa [iSup_singleton] at this 
   exact indep_supr_of_disjoint (fun k => (hf k).Measurable.comap_le) hfi (by simpa)
 #align probability_theory.Indep_fun.indep_comap_natural_of_lt ProbabilityTheory.IndepFun.indepCat_comap_natural_of_lt
 
@@ -102,14 +102,14 @@ theorem measure_limsup_eq_one {s : ℕ → Set Ω} (hsm : ∀ n, MeasurableSet (
     by
     rw [← ENNReal.tsum_add_one_eq_top hs' (measure_ne_top _ _)]
     exact ENNReal.tendsto_nat_tsum _
-  rw [ENNReal.tendsto_nhds_top_iff_nnreal] at htends
+  rw [ENNReal.tendsto_nhds_top_iff_nnreal] at htends 
   refine' tendsto_at_top_at_top_of_monotone' _ _
   · refine' monotone_nat_of_le_succ fun n => _
     rw [← sub_nonneg, Finset.sum_range_succ_sub_sum]
     exact ENNReal.toReal_nonneg
   · rintro ⟨B, hB⟩
     refine' not_eventually.2 (frequently_of_forall fun n => _) (htends B.to_nnreal)
-    rw [mem_upperBounds] at hB
+    rw [mem_upperBounds] at hB 
     specialize hB (∑ k : ℕ in Finset.range n, μ (s (k + 1))).toReal _
     · refine' ⟨n, _⟩
       rw [ENNReal.toReal_sum]

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

@@ -28,7 +28,7 @@ filtration.
 -/
 
 
-open MeasureTheory ProbabilityTheory ENNReal BigOperators Topology
+open scoped MeasureTheory ProbabilityTheory ENNReal BigOperators Topology
 
 open MeasureTheory ProbabilityTheory MeasurableSpace TopologicalSpace
 

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

@@ -48,7 +48,7 @@ theorem IndepFun.indepCat_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f
   suffices
     indep (⨆ k ∈ {j}, MeasurableSpace.comap (f k) mβ)
       (⨆ k ∈ { k | k ≤ i }, MeasurableSpace.comap (f k) mβ) μ
-    by rwa [supᵢ_singleton] at this
+    by rwa [iSup_singleton] at this
   exact indep_supr_of_disjoint (fun k => (hf k).Measurable.comap_le) hfi (by simpa)
 #align probability_theory.Indep_fun.indep_comap_natural_of_lt ProbabilityTheory.IndepFun.indepCat_comap_natural_of_lt
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 
 ! This file was ported from Lean 3 source module probability.borel_cantelli
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 2f8347015b12b0864dfaf366ec4909eb70c78740
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Probability.Martingale.BorelCantelli
 import Mathbin.Probability.ConditionalExpectation
-import Mathbin.Probability.Independence
+import Mathbin.Probability.Independence.Basic
 
 /-!
 
@@ -52,19 +52,19 @@ theorem IndepFun.indepCat_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f
   exact indep_supr_of_disjoint (fun k => (hf k).Measurable.comap_le) hfi (by simpa)
 #align probability_theory.Indep_fun.indep_comap_natural_of_lt ProbabilityTheory.IndepFun.indepCat_comap_natural_of_lt
 
-theorem IndepFun.condexp_natrual_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]
+theorem IndepFun.condexp_natural_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]
     [NormedSpace ℝ β] (hf : ∀ i, StronglyMeasurable (f i)) (hfi : IndepFun (fun i => mβ) f μ)
     (hij : i < j) : μ[f j|Filtration.natural f hf i] =ᵐ[μ] fun ω => μ[f j] :=
   condexp_indepCat_eq (hf j).Measurable.comap_le (Filtration.le _ _)
     (comap_measurable <| f j).StronglyMeasurable (hfi.indepCat_comap_natural_of_lt hf hij)
-#align probability_theory.Indep_fun.condexp_natrual_ae_eq_of_lt ProbabilityTheory.IndepFun.condexp_natrual_ae_eq_of_lt
+#align probability_theory.Indep_fun.condexp_natural_ae_eq_of_lt ProbabilityTheory.IndepFun.condexp_natural_ae_eq_of_lt
 
 theorem IndepSet.condexp_indicator_filtrationOfSet_ae_eq (hsm : ∀ n, MeasurableSet (s n))
     (hs : IndepSet s μ) (hij : i < j) :
     μ[(s j).indicator (fun ω => 1 : Ω → ℝ)|filtrationOfSet hsm i] =ᵐ[μ] fun ω => (μ (s j)).toReal :=
   by
   rw [filtration.filtration_of_set_eq_natural hsm]
-  refine' (Indep_fun.condexp_natrual_ae_eq_of_lt _ hs.Indep_fun_indicator hij).trans _
+  refine' (Indep_fun.condexp_natural_ae_eq_of_lt _ hs.Indep_fun_indicator hij).trans _
   · simp only [integral_indicator_const _ (hsm _), Algebra.id.smul_eq_mul, mul_one]
   · infer_instance
 #align probability_theory.Indep_set.condexp_indicator_filtration_of_set_ae_eq ProbabilityTheory.IndepSet.condexp_indicator_filtrationOfSet_ae_eq

mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398

@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 
 ! This file was ported from Lean 3 source module probability.borel_cantelli
-! leanprover-community/mathlib commit 2f8347015b12b0864dfaf366ec4909eb70c78740
+! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Probability.Martingale.BorelCantelli
 import Mathbin.Probability.ConditionalExpectation
-import Mathbin.Probability.Independence.Basic
+import Mathbin.Probability.Independence
 
 /-!
 
@@ -52,19 +52,19 @@ theorem IndepFun.indepCat_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f
   exact indep_supr_of_disjoint (fun k => (hf k).Measurable.comap_le) hfi (by simpa)
 #align probability_theory.Indep_fun.indep_comap_natural_of_lt ProbabilityTheory.IndepFun.indepCat_comap_natural_of_lt
 
-theorem IndepFun.condexp_natural_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]
+theorem IndepFun.condexp_natrual_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]
     [NormedSpace ℝ β] (hf : ∀ i, StronglyMeasurable (f i)) (hfi : IndepFun (fun i => mβ) f μ)
     (hij : i < j) : μ[f j|Filtration.natural f hf i] =ᵐ[μ] fun ω => μ[f j] :=
   condexp_indepCat_eq (hf j).Measurable.comap_le (Filtration.le _ _)
     (comap_measurable <| f j).StronglyMeasurable (hfi.indepCat_comap_natural_of_lt hf hij)
-#align probability_theory.Indep_fun.condexp_natural_ae_eq_of_lt ProbabilityTheory.IndepFun.condexp_natural_ae_eq_of_lt
+#align probability_theory.Indep_fun.condexp_natrual_ae_eq_of_lt ProbabilityTheory.IndepFun.condexp_natrual_ae_eq_of_lt
 
 theorem IndepSet.condexp_indicator_filtrationOfSet_ae_eq (hsm : ∀ n, MeasurableSet (s n))
     (hs : IndepSet s μ) (hij : i < j) :
     μ[(s j).indicator (fun ω => 1 : Ω → ℝ)|filtrationOfSet hsm i] =ᵐ[μ] fun ω => (μ (s j)).toReal :=
   by
   rw [filtration.filtration_of_set_eq_natural hsm]
-  refine' (Indep_fun.condexp_natural_ae_eq_of_lt _ hs.Indep_fun_indicator hij).trans _
+  refine' (Indep_fun.condexp_natrual_ae_eq_of_lt _ hs.Indep_fun_indicator hij).trans _
   · simp only [integral_indicator_const _ (hsm _), Algebra.id.smul_eq_mul, mul_one]
   · infer_instance
 #align probability_theory.Indep_set.condexp_indicator_filtration_of_set_ae_eq ProbabilityTheory.IndepSet.condexp_indicator_filtrationOfSet_ae_eq

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -4,13 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
 
 ! This file was ported from Lean 3 source module probability.borel_cantelli
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 2f8347015b12b0864dfaf366ec4909eb70c78740
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Probability.Martingale.BorelCantelli
 import Mathbin.Probability.ConditionalExpectation
-import Mathbin.Probability.Independence
+import Mathbin.Probability.Independence.Basic
 
 /-!
 
@@ -52,19 +52,19 @@ theorem IndepFun.indepCat_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f
   exact indep_supr_of_disjoint (fun k => (hf k).Measurable.comap_le) hfi (by simpa)
 #align probability_theory.Indep_fun.indep_comap_natural_of_lt ProbabilityTheory.IndepFun.indepCat_comap_natural_of_lt
 
-theorem IndepFun.condexp_natrual_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]
+theorem IndepFun.condexp_natural_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]
     [NormedSpace ℝ β] (hf : ∀ i, StronglyMeasurable (f i)) (hfi : IndepFun (fun i => mβ) f μ)
     (hij : i < j) : μ[f j|Filtration.natural f hf i] =ᵐ[μ] fun ω => μ[f j] :=
   condexp_indepCat_eq (hf j).Measurable.comap_le (Filtration.le _ _)
     (comap_measurable <| f j).StronglyMeasurable (hfi.indepCat_comap_natural_of_lt hf hij)
-#align probability_theory.Indep_fun.condexp_natrual_ae_eq_of_lt ProbabilityTheory.IndepFun.condexp_natrual_ae_eq_of_lt
+#align probability_theory.Indep_fun.condexp_natural_ae_eq_of_lt ProbabilityTheory.IndepFun.condexp_natural_ae_eq_of_lt
 
 theorem IndepSet.condexp_indicator_filtrationOfSet_ae_eq (hsm : ∀ n, MeasurableSet (s n))
     (hs : IndepSet s μ) (hij : i < j) :
     μ[(s j).indicator (fun ω => 1 : Ω → ℝ)|filtrationOfSet hsm i] =ᵐ[μ] fun ω => (μ (s j)).toReal :=
   by
   rw [filtration.filtration_of_set_eq_natural hsm]
-  refine' (Indep_fun.condexp_natrual_ae_eq_of_lt _ hs.Indep_fun_indicator hij).trans _
+  refine' (Indep_fun.condexp_natural_ae_eq_of_lt _ hs.Indep_fun_indicator hij).trans _
   · simp only [integral_indicator_const _ (hsm _), Algebra.id.smul_eq_mul, mul_one]
   · infer_instance
 #align probability_theory.Indep_set.condexp_indicator_filtration_of_set_ae_eq ProbabilityTheory.IndepSet.condexp_indicator_filtrationOfSet_ae_eq

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

@@ -34,7 +34,7 @@ open MeasureTheory ProbabilityTheory MeasurableSpace TopologicalSpace
 
 namespace ProbabilityTheory
 
-variable {Ω : Type _} {m0 : MeasurableSpace Ω} {μ : Measure Ω} [IsProbabilityMeasure μ]
+variable {Ω : Type _} {m0 : MeasurableSpace Ω} {μ : Measure Ω} [ProbabilityMeasure μ]
 
 section BorelCantelli
 

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

@@ -41,7 +41,7 @@ section BorelCantelli
 variable {ι β : Type _} [LinearOrder ι] [mβ : MeasurableSpace β] [NormedAddCommGroup β]
   [BorelSpace β] {f : ι → Ω → β} {i j : ι} {s : ι → Set Ω}
 
-theorem IndepFun.indepComapNaturalOfLt (hf : ∀ i, StronglyMeasurable (f i))
+theorem IndepFun.indepCat_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f i))
     (hfi : IndepFun (fun i => mβ) f μ) (hij : i < j) :
     IndepCat (MeasurableSpace.comap (f j) mβ) (Filtration.natural f hf i) μ :=
   by
@@ -50,13 +50,13 @@ theorem IndepFun.indepComapNaturalOfLt (hf : ∀ i, StronglyMeasurable (f i))
       (⨆ k ∈ { k | k ≤ i }, MeasurableSpace.comap (f k) mβ) μ
     by rwa [supᵢ_singleton] at this
   exact indep_supr_of_disjoint (fun k => (hf k).Measurable.comap_le) hfi (by simpa)
-#align probability_theory.Indep_fun.indep_comap_natural_of_lt ProbabilityTheory.IndepFun.indepComapNaturalOfLt
+#align probability_theory.Indep_fun.indep_comap_natural_of_lt ProbabilityTheory.IndepFun.indepCat_comap_natural_of_lt
 
 theorem IndepFun.condexp_natrual_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]
     [NormedSpace ℝ β] (hf : ∀ i, StronglyMeasurable (f i)) (hfi : IndepFun (fun i => mβ) f μ)
     (hij : i < j) : μ[f j|Filtration.natural f hf i] =ᵐ[μ] fun ω => μ[f j] :=
   condexp_indepCat_eq (hf j).Measurable.comap_le (Filtration.le _ _)
-    (comap_measurable <| f j).StronglyMeasurable (hfi.indepComapNaturalOfLt hf hij)
+    (comap_measurable <| f j).StronglyMeasurable (hfi.indepCat_comap_natural_of_lt hf hij)
 #align probability_theory.Indep_fun.condexp_natrual_ae_eq_of_lt ProbabilityTheory.IndepFun.condexp_natrual_ae_eq_of_lt
 
 theorem IndepSet.condexp_indicator_filtrationOfSet_ae_eq (hsm : ∀ n, MeasurableSet (s n))

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

@@ -102,7 +102,7 @@ theorem measure_limsup_eq_one {s : ℕ → Set Ω} (hsm : ∀ n, MeasurableSet (
     by
     rw [← ENNReal.tsum_add_one_eq_top hs' (measure_ne_top _ _)]
     exact ENNReal.tendsto_nat_tsum _
-  rw [ENNReal.tendsto_nhds_top_iff_nNReal] at htends
+  rw [ENNReal.tendsto_nhds_top_iff_nnreal] at htends
   refine' tendsto_at_top_at_top_of_monotone' _ _
   · refine' monotone_nat_of_le_succ fun n => _
     rw [← sub_nonneg, Finset.sum_range_succ_sub_sum]

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

@@ -28,7 +28,7 @@ filtration.
 -/
 
 
-open MeasureTheory ProbabilityTheory Ennreal BigOperators Topology
+open MeasureTheory ProbabilityTheory ENNReal BigOperators Topology
 
 open MeasureTheory ProbabilityTheory MeasurableSpace TopologicalSpace
 
@@ -100,21 +100,21 @@ theorem measure_limsup_eq_one {s : ℕ → Set Ω} (hsm : ∀ n, MeasurableSet (
   simp_rw [hω]
   have htends : tendsto (fun n => ∑ k in Finset.range n, μ (s (k + 1))) at_top (𝓝 ∞) :=
     by
-    rw [← Ennreal.tsum_add_one_eq_top hs' (measure_ne_top _ _)]
-    exact Ennreal.tendsto_nat_tsum _
-  rw [Ennreal.tendsto_nhds_top_iff_nNReal] at htends
+    rw [← ENNReal.tsum_add_one_eq_top hs' (measure_ne_top _ _)]
+    exact ENNReal.tendsto_nat_tsum _
+  rw [ENNReal.tendsto_nhds_top_iff_nNReal] at htends
   refine' tendsto_at_top_at_top_of_monotone' _ _
   · refine' monotone_nat_of_le_succ fun n => _
     rw [← sub_nonneg, Finset.sum_range_succ_sub_sum]
-    exact Ennreal.toReal_nonneg
+    exact ENNReal.toReal_nonneg
   · rintro ⟨B, hB⟩
     refine' not_eventually.2 (frequently_of_forall fun n => _) (htends B.to_nnreal)
     rw [mem_upperBounds] at hB
     specialize hB (∑ k : ℕ in Finset.range n, μ (s (k + 1))).toReal _
     · refine' ⟨n, _⟩
-      rw [Ennreal.toReal_sum]
+      rw [ENNReal.toReal_sum]
       exact fun _ _ => measure_ne_top _ _
-    · rw [not_lt, ← Ennreal.toReal_le_toReal (Ennreal.sum_lt_top _).Ne Ennreal.coe_ne_top]
+    · rw [not_lt, ← ENNReal.toReal_le_toReal (ENNReal.sum_lt_top _).Ne ENNReal.coe_ne_top]
       · exact hB.trans (by simp)
       · exact fun _ _ => measure_ne_top _ _
 #align probability_theory.measure_limsup_eq_one ProbabilityTheory.measure_limsup_eq_one

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

Some of the students from my Lean seminar got quite confused trying to find the Borel-Cantelli lemmas in Mathlib, because there is a file Probability.Martingale.BorelCantelli but neither of the Borel-Cantelli lemmas are in it! This PR adds cross-links between the documentation strings for the various files concerned. (There are no changes to actual code.)

@@ -13,7 +13,7 @@ import Mathlib.Probability.Independence.Basic
 
 # The second Borel-Cantelli lemma
 
-This file contains the second Borel-Cantelli lemma which states that, given a sequence of
+This file contains the *second Borel-Cantelli lemma* which states that, given a sequence of
 independent sets `(sₙ)` in a probability space, if `∑ n, μ sₙ = ∞`, then the limsup of `sₙ` has
 measure 1. We employ a proof using Lévy's generalized Borel-Cantelli by choosing an appropriate
 filtration.
@@ -22,6 +22,8 @@ filtration.
 
 - `ProbabilityTheory.measure_limsup_eq_one`: the second Borel-Cantelli lemma.
 
+**Note**: for the *first Borel-Cantelli lemma*, which holds in general measure spaces (not only
+in probability spaces), see `MeasureTheory.measure_limsup_eq_zero`.
 -/
 
 

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

This has nice performance benefits.

@@ -31,11 +31,11 @@ open MeasureTheory ProbabilityTheory MeasurableSpace TopologicalSpace
 
 namespace ProbabilityTheory
 
-variable {Ω : Type _} {m0 : MeasurableSpace Ω} {μ : Measure Ω} [IsProbabilityMeasure μ]
+variable {Ω : Type*} {m0 : MeasurableSpace Ω} {μ : Measure Ω} [IsProbabilityMeasure μ]
 
 section BorelCantelli
 
-variable {ι β : Type _} [LinearOrder ι] [mβ : MeasurableSpace β] [NormedAddCommGroup β]
+variable {ι β : Type*} [LinearOrder ι] [mβ : MeasurableSpace β] [NormedAddCommGroup β]
   [BorelSpace β] {f : ι → Ω → β} {i j : ι} {s : ι → Set Ω}
 
 theorem iIndepFun.indep_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f i))

• 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 Kexing Ying. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Kexing Ying
-
-! This file was ported from Lean 3 source module probability.borel_cantelli
-! leanprover-community/mathlib commit 2f8347015b12b0864dfaf366ec4909eb70c78740
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Probability.Martingale.BorelCantelli
 import Mathlib.Probability.ConditionalExpectation
 import Mathlib.Probability.Independence.Basic
 
+#align_import probability.borel_cantelli from "leanprover-community/mathlib"@"2f8347015b12b0864dfaf366ec4909eb70c78740"
+
 /-!
 
 # The second Borel-Cantelli lemma