probability.moments | Mathlib porting status

Changes since the initial port

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

Changes in mathlib3

85453a2a

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

1b089e3b

bump to nightly-2024-02-02-06

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

1f9867d7

Diff

@@ -67,7 +67,7 @@ def centralMoment (X : Ω → ℝ) (p : ℕ) (μ : Measure Ω) : ℝ :=
 #print ProbabilityTheory.moment_zero /-
 @[simp]
 theorem moment_zero (hp : p ≠ 0) : moment 0 p μ = 0 := by
-  simp only [moment, hp, zero_pow', Ne.def, not_false_iff, Pi.zero_apply, integral_const,
+  simp only [moment, hp, zero_pow, Ne.def, not_false_iff, Pi.zero_apply, integral_const,
     Algebra.id.smul_eq_mul, MulZeroClass.mul_zero]
 #align probability_theory.moment_zero ProbabilityTheory.moment_zero
 -/
@@ -76,7 +76,7 @@ theorem moment_zero (hp : p ≠ 0) : moment 0 p μ = 0 := by
 @[simp]
 theorem centralMoment_zero (hp : p ≠ 0) : centralMoment 0 p μ = 0 := by
   simp only [central_moment, hp, Pi.zero_apply, integral_const, Algebra.id.smul_eq_mul,
-    MulZeroClass.mul_zero, zero_sub, Pi.pow_apply, Pi.neg_apply, neg_zero, zero_pow', Ne.def,
+    MulZeroClass.mul_zero, zero_sub, Pi.pow_apply, Pi.neg_apply, neg_zero, zero_pow, Ne.def,
     not_false_iff]
 #align probability_theory.central_moment_zero ProbabilityTheory.centralMoment_zero
 -/

1b089e3b

bump to nightly-2024-02-01-06

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

5433bded

Diff

@@ -347,7 +347,16 @@ theorem aestronglyMeasurable_exp_mul_add {X Y : Ω → ℝ}
 #print ProbabilityTheory.aestronglyMeasurable_exp_mul_sum /-
 theorem aestronglyMeasurable_exp_mul_sum {X : ι → Ω → ℝ} {s : Finset ι}
     (h_int : ∀ i ∈ s, AEStronglyMeasurable (fun ω => exp (t * X i ω)) μ) :
-    AEStronglyMeasurable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by classical
+    AEStronglyMeasurable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
+  classical
+  induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
+  · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, NormedSpace.exp_zero]
+    exact ae_strongly_measurable_const
+  · have : ∀ i : ι, i ∈ s → ae_strongly_measurable (fun ω : Ω => NormedSpace.exp (t * X i ω)) μ :=
+      fun i hi => h_int i (mem_insert_of_mem hi)
+    specialize h_rec this
+    rw [sum_insert hi_notin_s]
+    apply ae_strongly_measurable_exp_mul_add (h_int i (mem_insert_self _ _)) h_rec
 #align probability_theory.ae_strongly_measurable_exp_mul_sum ProbabilityTheory.aestronglyMeasurable_exp_mul_sum
 -/
 
@@ -366,14 +375,33 @@ theorem IndepFun.integrable_exp_mul_add {X Y : Ω → ℝ} (h_indep : IndepFun X
 theorem iIndepFun.integrable_exp_mul_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : iIndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     {s : Finset ι} (h_int : ∀ i ∈ s, Integrable (fun ω => exp (t * X i ω)) μ) :
-    Integrable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by classical
+    Integrable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
+  classical
+  induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
+  · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, NormedSpace.exp_zero]
+    exact integrable_const _
+  · have : ∀ i : ι, i ∈ s → integrable (fun ω : Ω => NormedSpace.exp (t * X i ω)) μ := fun i hi =>
+      h_int i (mem_insert_of_mem hi)
+    specialize h_rec this
+    rw [sum_insert hi_notin_s]
+    refine' indep_fun.integrable_exp_mul_add _ (h_int i (mem_insert_self _ _)) h_rec
+    exact (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm
 #align probability_theory.Indep_fun.integrable_exp_mul_sum ProbabilityTheory.iIndepFun.integrable_exp_mul_sum
 -/
 
 #print ProbabilityTheory.iIndepFun.mgf_sum /-
 theorem iIndepFun.mgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : iIndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
-    (s : Finset ι) : mgf (∑ i in s, X i) μ t = ∏ i in s, mgf (X i) μ t := by classical
+    (s : Finset ι) : mgf (∑ i in s, X i) μ t = ∏ i in s, mgf (X i) μ t := by
+  classical
+  induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
+  · simp only [sum_empty, mgf_zero_fun, measure_univ, ENNReal.one_toReal, prod_empty]
+  · have h_int' : ∀ i : ι, ae_strongly_measurable (fun ω : Ω => NormedSpace.exp (t * X i ω)) μ :=
+      fun i => ((h_meas i).const_mul t).exp.AEStronglyMeasurable
+    rw [sum_insert hi_notin_s,
+      indep_fun.mgf_add (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm (h_int' i)
+        (ae_strongly_measurable_exp_mul_sum fun i hi => h_int' i),
+      h_rec, prod_insert hi_notin_s]
 #align probability_theory.Indep_fun.mgf_sum ProbabilityTheory.iIndepFun.mgf_sum
 -/

1b089e3b

bump to nightly-2024-01-31-06

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

61100fe9

Diff

@@ -347,16 +347,7 @@ theorem aestronglyMeasurable_exp_mul_add {X Y : Ω → ℝ}
 #print ProbabilityTheory.aestronglyMeasurable_exp_mul_sum /-
 theorem aestronglyMeasurable_exp_mul_sum {X : ι → Ω → ℝ} {s : Finset ι}
     (h_int : ∀ i ∈ s, AEStronglyMeasurable (fun ω => exp (t * X i ω)) μ) :
-    AEStronglyMeasurable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
-  classical
-  induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
-  · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, NormedSpace.exp_zero]
-    exact ae_strongly_measurable_const
-  · have : ∀ i : ι, i ∈ s → ae_strongly_measurable (fun ω : Ω => NormedSpace.exp (t * X i ω)) μ :=
-      fun i hi => h_int i (mem_insert_of_mem hi)
-    specialize h_rec this
-    rw [sum_insert hi_notin_s]
-    apply ae_strongly_measurable_exp_mul_add (h_int i (mem_insert_self _ _)) h_rec
+    AEStronglyMeasurable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by classical
 #align probability_theory.ae_strongly_measurable_exp_mul_sum ProbabilityTheory.aestronglyMeasurable_exp_mul_sum
 -/
 
@@ -375,33 +366,14 @@ theorem IndepFun.integrable_exp_mul_add {X Y : Ω → ℝ} (h_indep : IndepFun X
 theorem iIndepFun.integrable_exp_mul_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : iIndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     {s : Finset ι} (h_int : ∀ i ∈ s, Integrable (fun ω => exp (t * X i ω)) μ) :
-    Integrable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
-  classical
-  induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
-  · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, NormedSpace.exp_zero]
-    exact integrable_const _
-  · have : ∀ i : ι, i ∈ s → integrable (fun ω : Ω => NormedSpace.exp (t * X i ω)) μ := fun i hi =>
-      h_int i (mem_insert_of_mem hi)
-    specialize h_rec this
-    rw [sum_insert hi_notin_s]
-    refine' indep_fun.integrable_exp_mul_add _ (h_int i (mem_insert_self _ _)) h_rec
-    exact (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm
+    Integrable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by classical
 #align probability_theory.Indep_fun.integrable_exp_mul_sum ProbabilityTheory.iIndepFun.integrable_exp_mul_sum
 -/
 
 #print ProbabilityTheory.iIndepFun.mgf_sum /-
 theorem iIndepFun.mgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : iIndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
-    (s : Finset ι) : mgf (∑ i in s, X i) μ t = ∏ i in s, mgf (X i) μ t := by
-  classical
-  induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
-  · simp only [sum_empty, mgf_zero_fun, measure_univ, ENNReal.one_toReal, prod_empty]
-  · have h_int' : ∀ i : ι, ae_strongly_measurable (fun ω : Ω => NormedSpace.exp (t * X i ω)) μ :=
-      fun i => ((h_meas i).const_mul t).exp.AEStronglyMeasurable
-    rw [sum_insert hi_notin_s,
-      indep_fun.mgf_add (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm (h_int' i)
-        (ae_strongly_measurable_exp_mul_sum fun i hi => h_int' i),
-      h_rec, prod_insert hi_notin_s]
+    (s : Finset ι) : mgf (∑ i in s, X i) μ t = ∏ i in s, mgf (X i) μ t := by classical
 #align probability_theory.Indep_fun.mgf_sum ProbabilityTheory.iIndepFun.mgf_sum
 -/

1b089e3b

bump to nightly-2023-11-29-11

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

049e2cad

Diff

@@ -136,7 +136,7 @@ def cgf (X : Ω → ℝ) (μ : Measure Ω) (t : ℝ) : ℝ :=
 #print ProbabilityTheory.mgf_zero_fun /-
 @[simp]
 theorem mgf_zero_fun : mgf 0 μ t = (μ Set.univ).toReal := by
-  simp only [mgf, Pi.zero_apply, MulZeroClass.mul_zero, exp_zero, integral_const,
+  simp only [mgf, Pi.zero_apply, MulZeroClass.mul_zero, NormedSpace.exp_zero, integral_const,
     Algebra.id.smul_eq_mul, mul_one]
 #align probability_theory.mgf_zero_fun ProbabilityTheory.mgf_zero_fun
 -/
@@ -197,7 +197,8 @@ theorem cgf_const [IsProbabilityMeasure μ] (c : ℝ) : cgf (fun _ => c) μ t =
 #print ProbabilityTheory.mgf_zero' /-
 @[simp]
 theorem mgf_zero' : mgf X μ 0 = (μ Set.univ).toReal := by
-  simp only [mgf, MulZeroClass.zero_mul, exp_zero, integral_const, Algebra.id.smul_eq_mul, mul_one]
+  simp only [mgf, MulZeroClass.zero_mul, NormedSpace.exp_zero, integral_const,
+    Algebra.id.smul_eq_mul, mul_one]
 #align probability_theory.mgf_zero' ProbabilityTheory.mgf_zero'
 -/
 
@@ -247,10 +248,11 @@ theorem mgf_nonneg : 0 ≤ mgf X μ t :=
 theorem mgf_pos' (hμ : μ ≠ 0) (h_int_X : Integrable (fun ω => exp (t * X ω)) μ) : 0 < mgf X μ t :=
   by
   simp_rw [mgf]
-  have : ∫ x : Ω, exp (t * X x) ∂μ = ∫ x : Ω in Set.univ, exp (t * X x) ∂μ := by
+  have :
+    ∫ x : Ω, NormedSpace.exp (t * X x) ∂μ = ∫ x : Ω in Set.univ, NormedSpace.exp (t * X x) ∂μ := by
     simp only [measure.restrict_univ]
   rw [this, set_integral_pos_iff_support_of_nonneg_ae _ _]
-  · have h_eq_univ : (Function.support fun x : Ω => exp (t * X x)) = Set.univ :=
+  · have h_eq_univ : (Function.support fun x : Ω => NormedSpace.exp (t * X x)) = Set.univ :=
       by
       ext1 x
       simp only [Function.mem_support, Set.mem_univ, iff_true_iff]
@@ -287,8 +289,10 @@ theorem cgf_neg : cgf (-X) μ t = cgf X μ (-t) := by simp_rw [cgf, mgf_neg]
 theorem IndepFun.exp_mul {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ) (s t : ℝ) :
     IndepFun (fun ω => exp (s * X ω)) (fun ω => exp (t * Y ω)) μ :=
   by
-  have h_meas : ∀ t, Measurable fun x => exp (t * x) := fun t => (measurable_id'.const_mul t).exp
-  change indep_fun ((fun x => exp (s * x)) ∘ X) ((fun x => exp (t * x)) ∘ Y) μ
+  have h_meas : ∀ t, Measurable fun x => NormedSpace.exp (t * x) := fun t =>
+    (measurable_id'.const_mul t).exp
+  change
+    indep_fun ((fun x => NormedSpace.exp (s * x)) ∘ X) ((fun x => NormedSpace.exp (t * x)) ∘ Y) μ
   exact indep_fun.comp h_indep (h_meas s) (h_meas t)
 #align probability_theory.indep_fun.exp_mul ProbabilityTheory.IndepFun.exp_mul
 -/
@@ -299,7 +303,7 @@ theorem IndepFun.mgf_add {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ)
     (hY : AEStronglyMeasurable (fun ω => exp (t * Y ω)) μ) :
     mgf (X + Y) μ t = mgf X μ t * mgf Y μ t :=
   by
-  simp_rw [mgf, Pi.add_apply, mul_add, exp_add]
+  simp_rw [mgf, Pi.add_apply, mul_add, NormedSpace.exp_add]
   exact (h_indep.exp_mul t t).integral_mul hX hY
 #align probability_theory.indep_fun.mgf_add ProbabilityTheory.IndepFun.mgf_add
 -/
@@ -308,10 +312,10 @@ theorem IndepFun.mgf_add {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ)
 theorem IndepFun.mgf_add' {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ) (hX : AEStronglyMeasurable X μ)
     (hY : AEStronglyMeasurable Y μ) : mgf (X + Y) μ t = mgf X μ t * mgf Y μ t :=
   by
-  have A : Continuous fun x : ℝ => exp (t * x) := by continuity
-  have h'X : ae_strongly_measurable (fun ω => exp (t * X ω)) μ :=
+  have A : Continuous fun x : ℝ => NormedSpace.exp (t * x) := by continuity
+  have h'X : ae_strongly_measurable (fun ω => NormedSpace.exp (t * X ω)) μ :=
     A.ae_strongly_measurable.comp_ae_measurable hX.ae_measurable
-  have h'Y : ae_strongly_measurable (fun ω => exp (t * Y ω)) μ :=
+  have h'Y : ae_strongly_measurable (fun ω => NormedSpace.exp (t * Y ω)) μ :=
     A.ae_strongly_measurable.comp_ae_measurable hY.ae_measurable
   exact h_indep.mgf_add h'X h'Y
 #align probability_theory.indep_fun.mgf_add' ProbabilityTheory.IndepFun.mgf_add'
@@ -335,7 +339,7 @@ theorem aestronglyMeasurable_exp_mul_add {X Y : Ω → ℝ}
     (h_int_Y : AEStronglyMeasurable (fun ω => exp (t * Y ω)) μ) :
     AEStronglyMeasurable (fun ω => exp (t * (X + Y) ω)) μ :=
   by
-  simp_rw [Pi.add_apply, mul_add, exp_add]
+  simp_rw [Pi.add_apply, mul_add, NormedSpace.exp_add]
   exact ae_strongly_measurable.mul h_int_X h_int_Y
 #align probability_theory.ae_strongly_measurable_exp_mul_add ProbabilityTheory.aestronglyMeasurable_exp_mul_add
 -/
@@ -346,10 +350,10 @@ theorem aestronglyMeasurable_exp_mul_sum {X : ι → Ω → ℝ} {s : Finset ι}
     AEStronglyMeasurable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
   classical
   induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
-  · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, exp_zero]
+  · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, NormedSpace.exp_zero]
     exact ae_strongly_measurable_const
-  · have : ∀ i : ι, i ∈ s → ae_strongly_measurable (fun ω : Ω => exp (t * X i ω)) μ := fun i hi =>
-      h_int i (mem_insert_of_mem hi)
+  · have : ∀ i : ι, i ∈ s → ae_strongly_measurable (fun ω : Ω => NormedSpace.exp (t * X i ω)) μ :=
+      fun i hi => h_int i (mem_insert_of_mem hi)
     specialize h_rec this
     rw [sum_insert hi_notin_s]
     apply ae_strongly_measurable_exp_mul_add (h_int i (mem_insert_self _ _)) h_rec
@@ -362,7 +366,7 @@ theorem IndepFun.integrable_exp_mul_add {X Y : Ω → ℝ} (h_indep : IndepFun X
     (h_int_Y : Integrable (fun ω => exp (t * Y ω)) μ) :
     Integrable (fun ω => exp (t * (X + Y) ω)) μ :=
   by
-  simp_rw [Pi.add_apply, mul_add, exp_add]
+  simp_rw [Pi.add_apply, mul_add, NormedSpace.exp_add]
   exact (h_indep.exp_mul t t).integrable_mul h_int_X h_int_Y
 #align probability_theory.indep_fun.integrable_exp_mul_add ProbabilityTheory.IndepFun.integrable_exp_mul_add
 -/
@@ -374,9 +378,9 @@ theorem iIndepFun.integrable_exp_mul_sum [IsProbabilityMeasure μ] {X : ι → 
     Integrable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
   classical
   induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
-  · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, exp_zero]
+  · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, NormedSpace.exp_zero]
     exact integrable_const _
-  · have : ∀ i : ι, i ∈ s → integrable (fun ω : Ω => exp (t * X i ω)) μ := fun i hi =>
+  · have : ∀ i : ι, i ∈ s → integrable (fun ω : Ω => NormedSpace.exp (t * X i ω)) μ := fun i hi =>
       h_int i (mem_insert_of_mem hi)
     specialize h_rec this
     rw [sum_insert hi_notin_s]
@@ -392,8 +396,8 @@ theorem iIndepFun.mgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
   classical
   induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
   · simp only [sum_empty, mgf_zero_fun, measure_univ, ENNReal.one_toReal, prod_empty]
-  · have h_int' : ∀ i : ι, ae_strongly_measurable (fun ω : Ω => exp (t * X i ω)) μ := fun i =>
-      ((h_meas i).const_mul t).exp.AEStronglyMeasurable
+  · have h_int' : ∀ i : ι, ae_strongly_measurable (fun ω : Ω => NormedSpace.exp (t * X i ω)) μ :=
+      fun i => ((h_meas i).const_mul t).exp.AEStronglyMeasurable
     rw [sum_insert hi_notin_s,
       indep_fun.mgf_add (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm (h_int' i)
         (ae_strongly_measurable_exp_mul_sum fun i hi => h_int' i),
@@ -422,23 +426,26 @@ theorem measure_ge_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
   by
   cases' ht.eq_or_lt with ht_zero_eq ht_pos
   · rw [ht_zero_eq.symm]
-    simp only [neg_zero, MulZeroClass.zero_mul, exp_zero, mgf_zero', one_mul]
+    simp only [neg_zero, MulZeroClass.zero_mul, NormedSpace.exp_zero, mgf_zero', one_mul]
     rw [ENNReal.toReal_le_toReal (measure_ne_top μ _) (measure_ne_top μ _)]
     exact measure_mono (Set.subset_univ _)
   calc
-    (μ {ω | ε ≤ X ω}).toReal = (μ {ω | exp (t * ε) ≤ exp (t * X ω)}).toReal :=
+    (μ {ω | ε ≤ X ω}).toReal =
+        (μ {ω | NormedSpace.exp (t * ε) ≤ NormedSpace.exp (t * X ω)}).toReal :=
       by
       congr with ω
       simp only [exp_le_exp, eq_iff_iff]
       exact
         ⟨fun h => mul_le_mul_of_nonneg_left h ht_pos.le, fun h => le_of_mul_le_mul_left h ht_pos⟩
-    _ ≤ (exp (t * ε))⁻¹ * μ[fun ω => exp (t * X ω)] :=
+    _ ≤ (NormedSpace.exp (t * ε))⁻¹ * μ[fun ω => NormedSpace.exp (t * X ω)] :=
       by
       have :
-        exp (t * ε) * (μ {ω | exp (t * ε) ≤ exp (t * X ω)}).toReal ≤ μ[fun ω => exp (t * X ω)] :=
+        NormedSpace.exp (t * ε) *
+            (μ {ω | NormedSpace.exp (t * ε) ≤ NormedSpace.exp (t * X ω)}).toReal ≤
+          μ[fun ω => NormedSpace.exp (t * X ω)] :=
         mul_meas_ge_le_integral_of_nonneg (fun x => (exp_pos _).le) h_int _
-      rwa [mul_comm (exp (t * ε))⁻¹, ← div_eq_mul_inv, le_div_iff' (exp_pos _)]
-    _ = exp (-t * ε) * mgf X μ t := by rw [neg_mul, exp_neg]; rfl
+      rwa [mul_comm (NormedSpace.exp (t * ε))⁻¹, ← div_eq_mul_inv, le_div_iff' (exp_pos _)]
+    _ = NormedSpace.exp (-t * ε) * mgf X μ t := by rw [neg_mul, NormedSpace.exp_neg]; rfl
 #align probability_theory.measure_ge_le_exp_mul_mgf ProbabilityTheory.measure_ge_le_exp_mul_mgf
 -/
 
@@ -464,7 +471,7 @@ theorem measure_ge_le_exp_cgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
     (μ {ω | ε ≤ X ω}).toReal ≤ exp (-t * ε + cgf X μ t) :=
   by
   refine' (measure_ge_le_exp_mul_mgf ε ht h_int).trans _
-  rw [exp_add]
+  rw [NormedSpace.exp_add]
   exact mul_le_mul le_rfl (le_exp_log _) mgf_nonneg (exp_pos _).le
 #align probability_theory.measure_ge_le_exp_cgf ProbabilityTheory.measure_ge_le_exp_cgf
 -/
@@ -476,7 +483,7 @@ theorem measure_le_le_exp_cgf [IsFiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
     (μ {ω | X ω ≤ ε}).toReal ≤ exp (-t * ε + cgf X μ t) :=
   by
   refine' (measure_le_le_exp_mul_mgf ε ht h_int).trans _
-  rw [exp_add]
+  rw [NormedSpace.exp_add]
   exact mul_le_mul le_rfl (le_exp_log _) mgf_nonneg (exp_pos _).le
 #align probability_theory.measure_le_le_exp_cgf ProbabilityTheory.measure_le_le_exp_cgf
 -/

1b089e3b

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2022 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 -/
-import Mathbin.Probability.Variance
+import Probability.Variance
 
 #align_import probability.moments from "leanprover-community/mathlib"@"1b089e3bdc3ce6b39cd472543474a0a137128c6c"

1b089e3b

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module probability.moments
-! leanprover-community/mathlib commit 1b089e3bdc3ce6b39cd472543474a0a137128c6c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Probability.Variance
 
+#align_import probability.moments from "leanprover-community/mathlib"@"1b089e3bdc3ce6b39cd472543474a0a137128c6c"
+
 /-!
 # Moments and moment generating function

1b089e3b

bump to nightly-2023-06-23-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/d30d31261cdb4d2f5e612eabc3c4bf45556350d5

2dc54ce1

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 
 ! This file was ported from Lean 3 source module probability.moments
-! leanprover-community/mathlib commit 85453a2a14be8da64caf15ca50930cf4c6e5d8de
+! leanprover-community/mathlib commit 1b089e3bdc3ce6b39cd472543474a0a137128c6c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Probability.Variance
 /-!
 # Moments and moment generating function
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main definitions
 
 * `probability_theory.moment X p μ`: `p`th moment of a real random variable `X` with respect to

85453a2a

bump to nightly-2023-06-21-13

mathlib commit https://github.com/leanprover-community/mathlib/commit/f2ad3645af9effcdb587637dc28a6074edc813f9

1b71d9e6

Diff

@@ -50,29 +50,38 @@ namespace ProbabilityTheory
 
 variable {Ω ι : Type _} {m : MeasurableSpace Ω} {X : Ω → ℝ} {p : ℕ} {μ : Measure Ω}
 
+#print ProbabilityTheory.moment /-
 /-- Moment of a real random variable, `μ[X ^ p]`. -/
 def moment (X : Ω → ℝ) (p : ℕ) (μ : Measure Ω) : ℝ :=
   μ[X ^ p]
 #align probability_theory.moment ProbabilityTheory.moment
+-/
 
+#print ProbabilityTheory.centralMoment /-
 /-- Central moment of a real random variable, `μ[(X - μ[X]) ^ p]`. -/
 def centralMoment (X : Ω → ℝ) (p : ℕ) (μ : Measure Ω) : ℝ :=
   μ[(X - fun x => μ[X]) ^ p]
 #align probability_theory.central_moment ProbabilityTheory.centralMoment
+-/
 
+#print ProbabilityTheory.moment_zero /-
 @[simp]
 theorem moment_zero (hp : p ≠ 0) : moment 0 p μ = 0 := by
   simp only [moment, hp, zero_pow', Ne.def, not_false_iff, Pi.zero_apply, integral_const,
     Algebra.id.smul_eq_mul, MulZeroClass.mul_zero]
 #align probability_theory.moment_zero ProbabilityTheory.moment_zero
+-/
 
+#print ProbabilityTheory.centralMoment_zero /-
 @[simp]
 theorem centralMoment_zero (hp : p ≠ 0) : centralMoment 0 p μ = 0 := by
   simp only [central_moment, hp, Pi.zero_apply, integral_const, Algebra.id.smul_eq_mul,
     MulZeroClass.mul_zero, zero_sub, Pi.pow_apply, Pi.neg_apply, neg_zero, zero_pow', Ne.def,
     not_false_iff]
 #align probability_theory.central_moment_zero ProbabilityTheory.centralMoment_zero
+-/
 
+#print ProbabilityTheory.centralMoment_one' /-
 theorem centralMoment_one' [IsFiniteMeasure μ] (h_int : Integrable X μ) :
     centralMoment X 1 μ = (1 - (μ Set.univ).toReal) * μ[X] :=
   by
@@ -80,7 +89,9 @@ theorem centralMoment_one' [IsFiniteMeasure μ] (h_int : Integrable X μ) :
   rw [integral_sub h_int (integrable_const _)]
   simp only [sub_mul, integral_const, Algebra.id.smul_eq_mul, one_mul]
 #align probability_theory.central_moment_one' ProbabilityTheory.centralMoment_one'
+-/
 
+#print ProbabilityTheory.centralMoment_one /-
 @[simp]
 theorem centralMoment_one [IsProbabilityMeasure μ] : centralMoment X 1 μ = 0 :=
   by
@@ -96,54 +107,74 @@ theorem centralMoment_one [IsProbabilityMeasure μ] : centralMoment X 1 μ = 0 :
       exact h_sub.add (integrable_const _)
     rw [integral_undef this]
 #align probability_theory.central_moment_one ProbabilityTheory.centralMoment_one
+-/
 
+#print ProbabilityTheory.centralMoment_two_eq_variance /-
 theorem centralMoment_two_eq_variance [IsFiniteMeasure μ] (hX : Memℒp X 2 μ) :
     centralMoment X 2 μ = variance X μ := by rw [hX.variance_eq]; rfl
 #align probability_theory.central_moment_two_eq_variance ProbabilityTheory.centralMoment_two_eq_variance
+-/
 
 section MomentGeneratingFunction
 
 variable {t : ℝ}
 
+#print ProbabilityTheory.mgf /-
 /-- Moment generating function of a real random variable `X`: `λ t, μ[exp(t*X)]`. -/
 def mgf (X : Ω → ℝ) (μ : Measure Ω) (t : ℝ) : ℝ :=
   μ[fun ω => exp (t * X ω)]
 #align probability_theory.mgf ProbabilityTheory.mgf
+-/
 
+#print ProbabilityTheory.cgf /-
 /-- Cumulant generating function of a real random variable `X`: `λ t, log μ[exp(t*X)]`. -/
 def cgf (X : Ω → ℝ) (μ : Measure Ω) (t : ℝ) : ℝ :=
   log (mgf X μ t)
 #align probability_theory.cgf ProbabilityTheory.cgf
+-/
 
+#print ProbabilityTheory.mgf_zero_fun /-
 @[simp]
 theorem mgf_zero_fun : mgf 0 μ t = (μ Set.univ).toReal := by
   simp only [mgf, Pi.zero_apply, MulZeroClass.mul_zero, exp_zero, integral_const,
     Algebra.id.smul_eq_mul, mul_one]
 #align probability_theory.mgf_zero_fun ProbabilityTheory.mgf_zero_fun
+-/
 
+#print ProbabilityTheory.cgf_zero_fun /-
 @[simp]
 theorem cgf_zero_fun : cgf 0 μ t = log (μ Set.univ).toReal := by simp only [cgf, mgf_zero_fun]
 #align probability_theory.cgf_zero_fun ProbabilityTheory.cgf_zero_fun
+-/
 
+#print ProbabilityTheory.mgf_zero_measure /-
 @[simp]
 theorem mgf_zero_measure : mgf X (0 : Measure Ω) t = 0 := by simp only [mgf, integral_zero_measure]
 #align probability_theory.mgf_zero_measure ProbabilityTheory.mgf_zero_measure
+-/
 
+#print ProbabilityTheory.cgf_zero_measure /-
 @[simp]
 theorem cgf_zero_measure : cgf X (0 : Measure Ω) t = 0 := by
   simp only [cgf, log_zero, mgf_zero_measure]
 #align probability_theory.cgf_zero_measure ProbabilityTheory.cgf_zero_measure
+-/
 
+#print ProbabilityTheory.mgf_const' /-
 @[simp]
 theorem mgf_const' (c : ℝ) : mgf (fun _ => c) μ t = (μ Set.univ).toReal * exp (t * c) := by
   simp only [mgf, integral_const, Algebra.id.smul_eq_mul]
 #align probability_theory.mgf_const' ProbabilityTheory.mgf_const'
+-/
 
+#print ProbabilityTheory.mgf_const /-
 @[simp]
 theorem mgf_const (c : ℝ) [IsProbabilityMeasure μ] : mgf (fun _ => c) μ t = exp (t * c) := by
   simp only [mgf_const', measure_univ, ENNReal.one_toReal, one_mul]
 #align probability_theory.mgf_const ProbabilityTheory.mgf_const
+-/
 
+#print ProbabilityTheory.cgf_const' /-
 @[simp]
 theorem cgf_const' [IsFiniteMeasure μ] (hμ : μ ≠ 0) (c : ℝ) :
     cgf (fun _ => c) μ t = log (μ Set.univ).toReal + t * c :=
@@ -154,39 +185,55 @@ theorem cgf_const' [IsFiniteMeasure μ] (hμ : μ ≠ 0) (c : ℝ) :
   · rw [Ne.def, ENNReal.toReal_eq_zero_iff, measure.measure_univ_eq_zero]
     simp only [hμ, measure_ne_top μ Set.univ, or_self_iff, not_false_iff]
 #align probability_theory.cgf_const' ProbabilityTheory.cgf_const'
+-/
 
+#print ProbabilityTheory.cgf_const /-
 @[simp]
 theorem cgf_const [IsProbabilityMeasure μ] (c : ℝ) : cgf (fun _ => c) μ t = t * c := by
   simp only [cgf, mgf_const, log_exp]
 #align probability_theory.cgf_const ProbabilityTheory.cgf_const
+-/
 
+#print ProbabilityTheory.mgf_zero' /-
 @[simp]
 theorem mgf_zero' : mgf X μ 0 = (μ Set.univ).toReal := by
   simp only [mgf, MulZeroClass.zero_mul, exp_zero, integral_const, Algebra.id.smul_eq_mul, mul_one]
 #align probability_theory.mgf_zero' ProbabilityTheory.mgf_zero'
+-/
 
+#print ProbabilityTheory.mgf_zero /-
 @[simp]
 theorem mgf_zero [IsProbabilityMeasure μ] : mgf X μ 0 = 1 := by
   simp only [mgf_zero', measure_univ, ENNReal.one_toReal]
 #align probability_theory.mgf_zero ProbabilityTheory.mgf_zero
+-/
 
+#print ProbabilityTheory.cgf_zero' /-
 @[simp]
 theorem cgf_zero' : cgf X μ 0 = log (μ Set.univ).toReal := by simp only [cgf, mgf_zero']
 #align probability_theory.cgf_zero' ProbabilityTheory.cgf_zero'
+-/
 
+#print ProbabilityTheory.cgf_zero /-
 @[simp]
 theorem cgf_zero [IsProbabilityMeasure μ] : cgf X μ 0 = 0 := by
   simp only [cgf_zero', measure_univ, ENNReal.one_toReal, log_one]
 #align probability_theory.cgf_zero ProbabilityTheory.cgf_zero
+-/
 
+#print ProbabilityTheory.mgf_undef /-
 theorem mgf_undef (hX : ¬Integrable (fun ω => exp (t * X ω)) μ) : mgf X μ t = 0 := by
   simp only [mgf, integral_undef hX]
 #align probability_theory.mgf_undef ProbabilityTheory.mgf_undef
+-/
 
+#print ProbabilityTheory.cgf_undef /-
 theorem cgf_undef (hX : ¬Integrable (fun ω => exp (t * X ω)) μ) : cgf X μ t = 0 := by
   simp only [cgf, mgf_undef hX, log_zero]
 #align probability_theory.cgf_undef ProbabilityTheory.cgf_undef
+-/
 
+#print ProbabilityTheory.mgf_nonneg /-
 theorem mgf_nonneg : 0 ≤ mgf X μ t :=
   by
   refine' integral_nonneg _
@@ -194,7 +241,9 @@ theorem mgf_nonneg : 0 ≤ mgf X μ t :=
   simp only [Pi.zero_apply]
   exact (exp_pos _).le
 #align probability_theory.mgf_nonneg ProbabilityTheory.mgf_nonneg
+-/
 
+#print ProbabilityTheory.mgf_pos' /-
 theorem mgf_pos' (hμ : μ ≠ 0) (h_int_X : Integrable (fun ω => exp (t * X ω)) μ) : 0 < mgf X μ t :=
   by
   simp_rw [mgf]
@@ -214,18 +263,26 @@ theorem mgf_pos' (hμ : μ ≠ 0) (h_int_X : Integrable (fun ω => exp (t * X ω
     exact (exp_pos _).le
   · rwa [integrable_on_univ]
 #align probability_theory.mgf_pos' ProbabilityTheory.mgf_pos'
+-/
 
+#print ProbabilityTheory.mgf_pos /-
 theorem mgf_pos [IsProbabilityMeasure μ] (h_int_X : Integrable (fun ω => exp (t * X ω)) μ) :
     0 < mgf X μ t :=
   mgf_pos' (IsProbabilityMeasure.ne_zero μ) h_int_X
 #align probability_theory.mgf_pos ProbabilityTheory.mgf_pos
+-/
 
+#print ProbabilityTheory.mgf_neg /-
 theorem mgf_neg : mgf (-X) μ t = mgf X μ (-t) := by simp_rw [mgf, Pi.neg_apply, mul_neg, neg_mul]
 #align probability_theory.mgf_neg ProbabilityTheory.mgf_neg
+-/
 
+#print ProbabilityTheory.cgf_neg /-
 theorem cgf_neg : cgf (-X) μ t = cgf X μ (-t) := by simp_rw [cgf, mgf_neg]
 #align probability_theory.cgf_neg ProbabilityTheory.cgf_neg
+-/
 
+#print ProbabilityTheory.IndepFun.exp_mul /-
 /-- This is a trivial application of `indep_fun.comp` but it will come up frequently. -/
 theorem IndepFun.exp_mul {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ) (s t : ℝ) :
     IndepFun (fun ω => exp (s * X ω)) (fun ω => exp (t * Y ω)) μ :=
@@ -234,7 +291,9 @@ theorem IndepFun.exp_mul {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ) (s t : 
   change indep_fun ((fun x => exp (s * x)) ∘ X) ((fun x => exp (t * x)) ∘ Y) μ
   exact indep_fun.comp h_indep (h_meas s) (h_meas t)
 #align probability_theory.indep_fun.exp_mul ProbabilityTheory.IndepFun.exp_mul
+-/
 
+#print ProbabilityTheory.IndepFun.mgf_add /-
 theorem IndepFun.mgf_add {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ)
     (hX : AEStronglyMeasurable (fun ω => exp (t * X ω)) μ)
     (hY : AEStronglyMeasurable (fun ω => exp (t * Y ω)) μ) :
@@ -243,7 +302,9 @@ theorem IndepFun.mgf_add {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ)
   simp_rw [mgf, Pi.add_apply, mul_add, exp_add]
   exact (h_indep.exp_mul t t).integral_mul hX hY
 #align probability_theory.indep_fun.mgf_add ProbabilityTheory.IndepFun.mgf_add
+-/
 
+#print ProbabilityTheory.IndepFun.mgf_add' /-
 theorem IndepFun.mgf_add' {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ) (hX : AEStronglyMeasurable X μ)
     (hY : AEStronglyMeasurable Y μ) : mgf (X + Y) μ t = mgf X μ t * mgf Y μ t :=
   by
@@ -254,7 +315,9 @@ theorem IndepFun.mgf_add' {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ) (hX : A
     A.ae_strongly_measurable.comp_ae_measurable hY.ae_measurable
   exact h_indep.mgf_add h'X h'Y
 #align probability_theory.indep_fun.mgf_add' ProbabilityTheory.IndepFun.mgf_add'
+-/
 
+#print ProbabilityTheory.IndepFun.cgf_add /-
 theorem IndepFun.cgf_add {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ)
     (h_int_X : Integrable (fun ω => exp (t * X ω)) μ)
     (h_int_Y : Integrable (fun ω => exp (t * Y ω)) μ) : cgf (X + Y) μ t = cgf X μ t + cgf Y μ t :=
@@ -264,17 +327,21 @@ theorem IndepFun.cgf_add {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ)
   simp only [cgf, h_indep.mgf_add h_int_X.ae_strongly_measurable h_int_Y.ae_strongly_measurable]
   exact log_mul (mgf_pos' hμ h_int_X).ne' (mgf_pos' hμ h_int_Y).ne'
 #align probability_theory.indep_fun.cgf_add ProbabilityTheory.IndepFun.cgf_add
+-/
 
-theorem aEStronglyMeasurable_exp_mul_add {X Y : Ω → ℝ}
+#print ProbabilityTheory.aestronglyMeasurable_exp_mul_add /-
+theorem aestronglyMeasurable_exp_mul_add {X Y : Ω → ℝ}
     (h_int_X : AEStronglyMeasurable (fun ω => exp (t * X ω)) μ)
     (h_int_Y : AEStronglyMeasurable (fun ω => exp (t * Y ω)) μ) :
     AEStronglyMeasurable (fun ω => exp (t * (X + Y) ω)) μ :=
   by
   simp_rw [Pi.add_apply, mul_add, exp_add]
   exact ae_strongly_measurable.mul h_int_X h_int_Y
-#align probability_theory.ae_strongly_measurable_exp_mul_add ProbabilityTheory.aEStronglyMeasurable_exp_mul_add
+#align probability_theory.ae_strongly_measurable_exp_mul_add ProbabilityTheory.aestronglyMeasurable_exp_mul_add
+-/
 
-theorem aEStronglyMeasurable_exp_mul_sum {X : ι → Ω → ℝ} {s : Finset ι}
+#print ProbabilityTheory.aestronglyMeasurable_exp_mul_sum /-
+theorem aestronglyMeasurable_exp_mul_sum {X : ι → Ω → ℝ} {s : Finset ι}
     (h_int : ∀ i ∈ s, AEStronglyMeasurable (fun ω => exp (t * X i ω)) μ) :
     AEStronglyMeasurable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
   classical
@@ -286,8 +353,10 @@ theorem aEStronglyMeasurable_exp_mul_sum {X : ι → Ω → ℝ} {s : Finset ι}
     specialize h_rec this
     rw [sum_insert hi_notin_s]
     apply ae_strongly_measurable_exp_mul_add (h_int i (mem_insert_self _ _)) h_rec
-#align probability_theory.ae_strongly_measurable_exp_mul_sum ProbabilityTheory.aEStronglyMeasurable_exp_mul_sum
+#align probability_theory.ae_strongly_measurable_exp_mul_sum ProbabilityTheory.aestronglyMeasurable_exp_mul_sum
+-/
 
+#print ProbabilityTheory.IndepFun.integrable_exp_mul_add /-
 theorem IndepFun.integrable_exp_mul_add {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ)
     (h_int_X : Integrable (fun ω => exp (t * X ω)) μ)
     (h_int_Y : Integrable (fun ω => exp (t * Y ω)) μ) :
@@ -296,7 +365,9 @@ theorem IndepFun.integrable_exp_mul_add {X Y : Ω → ℝ} (h_indep : IndepFun X
   simp_rw [Pi.add_apply, mul_add, exp_add]
   exact (h_indep.exp_mul t t).integrable_mul h_int_X h_int_Y
 #align probability_theory.indep_fun.integrable_exp_mul_add ProbabilityTheory.IndepFun.integrable_exp_mul_add
+-/
 
+#print ProbabilityTheory.iIndepFun.integrable_exp_mul_sum /-
 theorem iIndepFun.integrable_exp_mul_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : iIndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     {s : Finset ι} (h_int : ∀ i ∈ s, Integrable (fun ω => exp (t * X i ω)) μ) :
@@ -312,7 +383,9 @@ theorem iIndepFun.integrable_exp_mul_sum [IsProbabilityMeasure μ] {X : ι → 
     refine' indep_fun.integrable_exp_mul_add _ (h_int i (mem_insert_self _ _)) h_rec
     exact (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm
 #align probability_theory.Indep_fun.integrable_exp_mul_sum ProbabilityTheory.iIndepFun.integrable_exp_mul_sum
+-/
 
+#print ProbabilityTheory.iIndepFun.mgf_sum /-
 theorem iIndepFun.mgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : iIndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     (s : Finset ι) : mgf (∑ i in s, X i) μ t = ∏ i in s, mgf (X i) μ t := by
@@ -326,7 +399,9 @@ theorem iIndepFun.mgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
         (ae_strongly_measurable_exp_mul_sum fun i hi => h_int' i),
       h_rec, prod_insert hi_notin_s]
 #align probability_theory.Indep_fun.mgf_sum ProbabilityTheory.iIndepFun.mgf_sum
+-/
 
+#print ProbabilityTheory.iIndepFun.cgf_sum /-
 theorem iIndepFun.cgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : iIndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     {s : Finset ι} (h_int : ∀ i ∈ s, Integrable (fun ω => exp (t * X i ω)) μ) :
@@ -337,7 +412,9 @@ theorem iIndepFun.cgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
   · rw [h_indep.mgf_sum h_meas]
   · exact (mgf_pos (h_int j hj)).ne'
 #align probability_theory.Indep_fun.cgf_sum ProbabilityTheory.iIndepFun.cgf_sum
+-/
 
+#print ProbabilityTheory.measure_ge_le_exp_mul_mgf /-
 /-- **Chernoff bound** on the upper tail of a real random variable. -/
 theorem measure_ge_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
@@ -363,7 +440,9 @@ theorem measure_ge_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
       rwa [mul_comm (exp (t * ε))⁻¹, ← div_eq_mul_inv, le_div_iff' (exp_pos _)]
     _ = exp (-t * ε) * mgf X μ t := by rw [neg_mul, exp_neg]; rfl
 #align probability_theory.measure_ge_le_exp_mul_mgf ProbabilityTheory.measure_ge_le_exp_mul_mgf
+-/
 
+#print ProbabilityTheory.measure_le_le_exp_mul_mgf /-
 /-- **Chernoff bound** on the lower tail of a real random variable. -/
 theorem measure_le_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
@@ -376,7 +455,9 @@ theorem measure_le_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
   · simp_rw [Pi.neg_apply, neg_mul_neg]
     exact h_int
 #align probability_theory.measure_le_le_exp_mul_mgf ProbabilityTheory.measure_le_le_exp_mul_mgf
+-/
 
+#print ProbabilityTheory.measure_ge_le_exp_cgf /-
 /-- **Chernoff bound** on the upper tail of a real random variable. -/
 theorem measure_ge_le_exp_cgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
@@ -386,7 +467,9 @@ theorem measure_ge_le_exp_cgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
   rw [exp_add]
   exact mul_le_mul le_rfl (le_exp_log _) mgf_nonneg (exp_pos _).le
 #align probability_theory.measure_ge_le_exp_cgf ProbabilityTheory.measure_ge_le_exp_cgf
+-/
 
+#print ProbabilityTheory.measure_le_le_exp_cgf /-
 /-- **Chernoff bound** on the lower tail of a real random variable. -/
 theorem measure_le_le_exp_cgf [IsFiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
@@ -396,6 +479,7 @@ theorem measure_le_le_exp_cgf [IsFiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
   rw [exp_add]
   exact mul_le_mul le_rfl (le_exp_log _) mgf_nonneg (exp_pos _).le
 #align probability_theory.measure_le_le_exp_cgf ProbabilityTheory.measure_le_le_exp_cgf
+-/
 
 end MomentGeneratingFunction

85453a2a

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -50,8 +50,6 @@ namespace ProbabilityTheory
 
 variable {Ω ι : Type _} {m : MeasurableSpace Ω} {X : Ω → ℝ} {p : ℕ} {μ : Measure Ω}
 
-include m
-
 /-- Moment of a real random variable, `μ[X ^ p]`. -/
 def moment (X : Ω → ℝ) (p : ℕ) (μ : Measure Ω) : ℝ :=
   μ[X ^ p]

85453a2a

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -200,7 +200,7 @@ theorem mgf_nonneg : 0 ≤ mgf X μ t :=
 theorem mgf_pos' (hμ : μ ≠ 0) (h_int_X : Integrable (fun ω => exp (t * X ω)) μ) : 0 < mgf X μ t :=
   by
   simp_rw [mgf]
-  have : (∫ x : Ω, exp (t * X x) ∂μ) = ∫ x : Ω in Set.univ, exp (t * X x) ∂μ := by
+  have : ∫ x : Ω, exp (t * X x) ∂μ = ∫ x : Ω in Set.univ, exp (t * X x) ∂μ := by
     simp only [measure.restrict_univ]
   rw [this, set_integral_pos_iff_support_of_nonneg_ae _ _]
   · have h_eq_univ : (Function.support fun x : Ω => exp (t * X x)) = Set.univ :=

85453a2a

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -364,7 +364,6 @@ theorem measure_ge_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
         mul_meas_ge_le_integral_of_nonneg (fun x => (exp_pos _).le) h_int _
       rwa [mul_comm (exp (t * ε))⁻¹, ← div_eq_mul_inv, le_div_iff' (exp_pos _)]
     _ = exp (-t * ε) * mgf X μ t := by rw [neg_mul, exp_neg]; rfl
-    
 #align probability_theory.measure_ge_le_exp_mul_mgf ProbabilityTheory.measure_ge_le_exp_mul_mgf
 
 /-- **Chernoff bound** on the lower tail of a real random variable. -/

85453a2a

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -75,7 +75,7 @@ theorem centralMoment_zero (hp : p ≠ 0) : centralMoment 0 p μ = 0 := by
     not_false_iff]
 #align probability_theory.central_moment_zero ProbabilityTheory.centralMoment_zero
 
-theorem centralMoment_one' [FiniteMeasure μ] (h_int : Integrable X μ) :
+theorem centralMoment_one' [IsFiniteMeasure μ] (h_int : Integrable X μ) :
     centralMoment X 1 μ = (1 - (μ Set.univ).toReal) * μ[X] :=
   by
   simp only [central_moment, Pi.sub_apply, pow_one]
@@ -84,7 +84,7 @@ theorem centralMoment_one' [FiniteMeasure μ] (h_int : Integrable X μ) :
 #align probability_theory.central_moment_one' ProbabilityTheory.centralMoment_one'
 
 @[simp]
-theorem centralMoment_one [ProbabilityMeasure μ] : centralMoment X 1 μ = 0 :=
+theorem centralMoment_one [IsProbabilityMeasure μ] : centralMoment X 1 μ = 0 :=
   by
   by_cases h_int : integrable X μ
   · rw [central_moment_one' h_int]
@@ -99,7 +99,7 @@ theorem centralMoment_one [ProbabilityMeasure μ] : centralMoment X 1 μ = 0 :=
     rw [integral_undef this]
 #align probability_theory.central_moment_one ProbabilityTheory.centralMoment_one
 
-theorem centralMoment_two_eq_variance [FiniteMeasure μ] (hX : Memℒp X 2 μ) :
+theorem centralMoment_two_eq_variance [IsFiniteMeasure μ] (hX : Memℒp X 2 μ) :
     centralMoment X 2 μ = variance X μ := by rw [hX.variance_eq]; rfl
 #align probability_theory.central_moment_two_eq_variance ProbabilityTheory.centralMoment_two_eq_variance
 
@@ -142,12 +142,12 @@ theorem mgf_const' (c : ℝ) : mgf (fun _ => c) μ t = (μ Set.univ).toReal * ex
 #align probability_theory.mgf_const' ProbabilityTheory.mgf_const'
 
 @[simp]
-theorem mgf_const (c : ℝ) [ProbabilityMeasure μ] : mgf (fun _ => c) μ t = exp (t * c) := by
+theorem mgf_const (c : ℝ) [IsProbabilityMeasure μ] : mgf (fun _ => c) μ t = exp (t * c) := by
   simp only [mgf_const', measure_univ, ENNReal.one_toReal, one_mul]
 #align probability_theory.mgf_const ProbabilityTheory.mgf_const
 
 @[simp]
-theorem cgf_const' [FiniteMeasure μ] (hμ : μ ≠ 0) (c : ℝ) :
+theorem cgf_const' [IsFiniteMeasure μ] (hμ : μ ≠ 0) (c : ℝ) :
     cgf (fun _ => c) μ t = log (μ Set.univ).toReal + t * c :=
   by
   simp only [cgf, mgf_const']
@@ -158,7 +158,7 @@ theorem cgf_const' [FiniteMeasure μ] (hμ : μ ≠ 0) (c : ℝ) :
 #align probability_theory.cgf_const' ProbabilityTheory.cgf_const'
 
 @[simp]
-theorem cgf_const [ProbabilityMeasure μ] (c : ℝ) : cgf (fun _ => c) μ t = t * c := by
+theorem cgf_const [IsProbabilityMeasure μ] (c : ℝ) : cgf (fun _ => c) μ t = t * c := by
   simp only [cgf, mgf_const, log_exp]
 #align probability_theory.cgf_const ProbabilityTheory.cgf_const
 
@@ -168,7 +168,7 @@ theorem mgf_zero' : mgf X μ 0 = (μ Set.univ).toReal := by
 #align probability_theory.mgf_zero' ProbabilityTheory.mgf_zero'
 
 @[simp]
-theorem mgf_zero [ProbabilityMeasure μ] : mgf X μ 0 = 1 := by
+theorem mgf_zero [IsProbabilityMeasure μ] : mgf X μ 0 = 1 := by
   simp only [mgf_zero', measure_univ, ENNReal.one_toReal]
 #align probability_theory.mgf_zero ProbabilityTheory.mgf_zero
 
@@ -177,7 +177,7 @@ theorem cgf_zero' : cgf X μ 0 = log (μ Set.univ).toReal := by simp only [cgf,
 #align probability_theory.cgf_zero' ProbabilityTheory.cgf_zero'
 
 @[simp]
-theorem cgf_zero [ProbabilityMeasure μ] : cgf X μ 0 = 0 := by
+theorem cgf_zero [IsProbabilityMeasure μ] : cgf X μ 0 = 0 := by
   simp only [cgf_zero', measure_univ, ENNReal.one_toReal, log_one]
 #align probability_theory.cgf_zero ProbabilityTheory.cgf_zero
 
@@ -217,9 +217,9 @@ theorem mgf_pos' (hμ : μ ≠ 0) (h_int_X : Integrable (fun ω => exp (t * X ω
   · rwa [integrable_on_univ]
 #align probability_theory.mgf_pos' ProbabilityTheory.mgf_pos'
 
-theorem mgf_pos [ProbabilityMeasure μ] (h_int_X : Integrable (fun ω => exp (t * X ω)) μ) :
+theorem mgf_pos [IsProbabilityMeasure μ] (h_int_X : Integrable (fun ω => exp (t * X ω)) μ) :
     0 < mgf X μ t :=
-  mgf_pos' (ProbabilityMeasure.ne_zero μ) h_int_X
+  mgf_pos' (IsProbabilityMeasure.ne_zero μ) h_int_X
 #align probability_theory.mgf_pos ProbabilityTheory.mgf_pos
 
 theorem mgf_neg : mgf (-X) μ t = mgf X μ (-t) := by simp_rw [mgf, Pi.neg_apply, mul_neg, neg_mul]
@@ -229,26 +229,25 @@ theorem cgf_neg : cgf (-X) μ t = cgf X μ (-t) := by simp_rw [cgf, mgf_neg]
 #align probability_theory.cgf_neg ProbabilityTheory.cgf_neg
 
 /-- This is a trivial application of `indep_fun.comp` but it will come up frequently. -/
-theorem IndepFunCat.exp_mul {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ) (s t : ℝ) :
-    IndepFunCat (fun ω => exp (s * X ω)) (fun ω => exp (t * Y ω)) μ :=
+theorem IndepFun.exp_mul {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ) (s t : ℝ) :
+    IndepFun (fun ω => exp (s * X ω)) (fun ω => exp (t * Y ω)) μ :=
   by
   have h_meas : ∀ t, Measurable fun x => exp (t * x) := fun t => (measurable_id'.const_mul t).exp
   change indep_fun ((fun x => exp (s * x)) ∘ X) ((fun x => exp (t * x)) ∘ Y) μ
   exact indep_fun.comp h_indep (h_meas s) (h_meas t)
-#align probability_theory.indep_fun.exp_mul ProbabilityTheory.IndepFunCat.exp_mul
+#align probability_theory.indep_fun.exp_mul ProbabilityTheory.IndepFun.exp_mul
 
-theorem IndepFunCat.mgf_add {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
+theorem IndepFun.mgf_add {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ)
     (hX : AEStronglyMeasurable (fun ω => exp (t * X ω)) μ)
     (hY : AEStronglyMeasurable (fun ω => exp (t * Y ω)) μ) :
     mgf (X + Y) μ t = mgf X μ t * mgf Y μ t :=
   by
   simp_rw [mgf, Pi.add_apply, mul_add, exp_add]
   exact (h_indep.exp_mul t t).integral_mul hX hY
-#align probability_theory.indep_fun.mgf_add ProbabilityTheory.IndepFunCat.mgf_add
+#align probability_theory.indep_fun.mgf_add ProbabilityTheory.IndepFun.mgf_add
 
-theorem IndepFunCat.mgf_add' {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
-    (hX : AEStronglyMeasurable X μ) (hY : AEStronglyMeasurable Y μ) :
-    mgf (X + Y) μ t = mgf X μ t * mgf Y μ t :=
+theorem IndepFun.mgf_add' {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ) (hX : AEStronglyMeasurable X μ)
+    (hY : AEStronglyMeasurable Y μ) : mgf (X + Y) μ t = mgf X μ t * mgf Y μ t :=
   by
   have A : Continuous fun x : ℝ => exp (t * x) := by continuity
   have h'X : ae_strongly_measurable (fun ω => exp (t * X ω)) μ :=
@@ -256,9 +255,9 @@ theorem IndepFunCat.mgf_add' {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
   have h'Y : ae_strongly_measurable (fun ω => exp (t * Y ω)) μ :=
     A.ae_strongly_measurable.comp_ae_measurable hY.ae_measurable
   exact h_indep.mgf_add h'X h'Y
-#align probability_theory.indep_fun.mgf_add' ProbabilityTheory.IndepFunCat.mgf_add'
+#align probability_theory.indep_fun.mgf_add' ProbabilityTheory.IndepFun.mgf_add'
 
-theorem IndepFunCat.cgf_add {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
+theorem IndepFun.cgf_add {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ)
     (h_int_X : Integrable (fun ω => exp (t * X ω)) μ)
     (h_int_Y : Integrable (fun ω => exp (t * Y ω)) μ) : cgf (X + Y) μ t = cgf X μ t + cgf Y μ t :=
   by
@@ -266,7 +265,7 @@ theorem IndepFunCat.cgf_add {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
   · simp [hμ]
   simp only [cgf, h_indep.mgf_add h_int_X.ae_strongly_measurable h_int_Y.ae_strongly_measurable]
   exact log_mul (mgf_pos' hμ h_int_X).ne' (mgf_pos' hμ h_int_Y).ne'
-#align probability_theory.indep_fun.cgf_add ProbabilityTheory.IndepFunCat.cgf_add
+#align probability_theory.indep_fun.cgf_add ProbabilityTheory.IndepFun.cgf_add
 
 theorem aEStronglyMeasurable_exp_mul_add {X Y : Ω → ℝ}
     (h_int_X : AEStronglyMeasurable (fun ω => exp (t * X ω)) μ)
@@ -281,57 +280,57 @@ theorem aEStronglyMeasurable_exp_mul_sum {X : ι → Ω → ℝ} {s : Finset ι}
     (h_int : ∀ i ∈ s, AEStronglyMeasurable (fun ω => exp (t * X i ω)) μ) :
     AEStronglyMeasurable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
   classical
-    induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
-    · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, exp_zero]
-      exact ae_strongly_measurable_const
-    · have : ∀ i : ι, i ∈ s → ae_strongly_measurable (fun ω : Ω => exp (t * X i ω)) μ := fun i hi =>
-        h_int i (mem_insert_of_mem hi)
-      specialize h_rec this
-      rw [sum_insert hi_notin_s]
-      apply ae_strongly_measurable_exp_mul_add (h_int i (mem_insert_self _ _)) h_rec
+  induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
+  · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, exp_zero]
+    exact ae_strongly_measurable_const
+  · have : ∀ i : ι, i ∈ s → ae_strongly_measurable (fun ω : Ω => exp (t * X i ω)) μ := fun i hi =>
+      h_int i (mem_insert_of_mem hi)
+    specialize h_rec this
+    rw [sum_insert hi_notin_s]
+    apply ae_strongly_measurable_exp_mul_add (h_int i (mem_insert_self _ _)) h_rec
 #align probability_theory.ae_strongly_measurable_exp_mul_sum ProbabilityTheory.aEStronglyMeasurable_exp_mul_sum
 
-theorem IndepFunCat.integrable_exp_mul_add {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
+theorem IndepFun.integrable_exp_mul_add {X Y : Ω → ℝ} (h_indep : IndepFun X Y μ)
     (h_int_X : Integrable (fun ω => exp (t * X ω)) μ)
     (h_int_Y : Integrable (fun ω => exp (t * Y ω)) μ) :
     Integrable (fun ω => exp (t * (X + Y) ω)) μ :=
   by
   simp_rw [Pi.add_apply, mul_add, exp_add]
   exact (h_indep.exp_mul t t).integrable_mul h_int_X h_int_Y
-#align probability_theory.indep_fun.integrable_exp_mul_add ProbabilityTheory.IndepFunCat.integrable_exp_mul_add
+#align probability_theory.indep_fun.integrable_exp_mul_add ProbabilityTheory.IndepFun.integrable_exp_mul_add
 
-theorem IndepFun.integrable_exp_mul_sum [ProbabilityMeasure μ] {X : ι → Ω → ℝ}
-    (h_indep : IndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
+theorem iIndepFun.integrable_exp_mul_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
+    (h_indep : iIndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     {s : Finset ι} (h_int : ∀ i ∈ s, Integrable (fun ω => exp (t * X i ω)) μ) :
     Integrable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
   classical
-    induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
-    · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, exp_zero]
-      exact integrable_const _
-    · have : ∀ i : ι, i ∈ s → integrable (fun ω : Ω => exp (t * X i ω)) μ := fun i hi =>
-        h_int i (mem_insert_of_mem hi)
-      specialize h_rec this
-      rw [sum_insert hi_notin_s]
-      refine' indep_fun.integrable_exp_mul_add _ (h_int i (mem_insert_self _ _)) h_rec
-      exact (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm
-#align probability_theory.Indep_fun.integrable_exp_mul_sum ProbabilityTheory.IndepFun.integrable_exp_mul_sum
-
-theorem IndepFun.mgf_sum [ProbabilityMeasure μ] {X : ι → Ω → ℝ}
-    (h_indep : IndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
+  induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
+  · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, exp_zero]
+    exact integrable_const _
+  · have : ∀ i : ι, i ∈ s → integrable (fun ω : Ω => exp (t * X i ω)) μ := fun i hi =>
+      h_int i (mem_insert_of_mem hi)
+    specialize h_rec this
+    rw [sum_insert hi_notin_s]
+    refine' indep_fun.integrable_exp_mul_add _ (h_int i (mem_insert_self _ _)) h_rec
+    exact (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm
+#align probability_theory.Indep_fun.integrable_exp_mul_sum ProbabilityTheory.iIndepFun.integrable_exp_mul_sum
+
+theorem iIndepFun.mgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
+    (h_indep : iIndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     (s : Finset ι) : mgf (∑ i in s, X i) μ t = ∏ i in s, mgf (X i) μ t := by
   classical
-    induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
-    · simp only [sum_empty, mgf_zero_fun, measure_univ, ENNReal.one_toReal, prod_empty]
-    · have h_int' : ∀ i : ι, ae_strongly_measurable (fun ω : Ω => exp (t * X i ω)) μ := fun i =>
-        ((h_meas i).const_mul t).exp.AEStronglyMeasurable
-      rw [sum_insert hi_notin_s,
-        indep_fun.mgf_add (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm
-          (h_int' i) (ae_strongly_measurable_exp_mul_sum fun i hi => h_int' i),
-        h_rec, prod_insert hi_notin_s]
-#align probability_theory.Indep_fun.mgf_sum ProbabilityTheory.IndepFun.mgf_sum
-
-theorem IndepFun.cgf_sum [ProbabilityMeasure μ] {X : ι → Ω → ℝ}
-    (h_indep : IndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
+  induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
+  · simp only [sum_empty, mgf_zero_fun, measure_univ, ENNReal.one_toReal, prod_empty]
+  · have h_int' : ∀ i : ι, ae_strongly_measurable (fun ω : Ω => exp (t * X i ω)) μ := fun i =>
+      ((h_meas i).const_mul t).exp.AEStronglyMeasurable
+    rw [sum_insert hi_notin_s,
+      indep_fun.mgf_add (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm (h_int' i)
+        (ae_strongly_measurable_exp_mul_sum fun i hi => h_int' i),
+      h_rec, prod_insert hi_notin_s]
+#align probability_theory.Indep_fun.mgf_sum ProbabilityTheory.iIndepFun.mgf_sum
+
+theorem iIndepFun.cgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
+    (h_indep : iIndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     {s : Finset ι} (h_int : ∀ i ∈ s, Integrable (fun ω => exp (t * X i ω)) μ) :
     cgf (∑ i in s, X i) μ t = ∑ i in s, cgf (X i) μ t :=
   by
@@ -339,12 +338,12 @@ theorem IndepFun.cgf_sum [ProbabilityMeasure μ] {X : ι → Ω → ℝ}
   rw [← log_prod _ _ fun j hj => _]
   · rw [h_indep.mgf_sum h_meas]
   · exact (mgf_pos (h_int j hj)).ne'
-#align probability_theory.Indep_fun.cgf_sum ProbabilityTheory.IndepFun.cgf_sum
+#align probability_theory.Indep_fun.cgf_sum ProbabilityTheory.iIndepFun.cgf_sum
 
 /-- **Chernoff bound** on the upper tail of a real random variable. -/
-theorem measure_ge_le_exp_mul_mgf [FiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
+theorem measure_ge_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
-    (μ { ω | ε ≤ X ω }).toReal ≤ exp (-t * ε) * mgf X μ t :=
+    (μ {ω | ε ≤ X ω}).toReal ≤ exp (-t * ε) * mgf X μ t :=
   by
   cases' ht.eq_or_lt with ht_zero_eq ht_pos
   · rw [ht_zero_eq.symm]
@@ -352,7 +351,7 @@ theorem measure_ge_le_exp_mul_mgf [FiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
     rw [ENNReal.toReal_le_toReal (measure_ne_top μ _) (measure_ne_top μ _)]
     exact measure_mono (Set.subset_univ _)
   calc
-    (μ { ω | ε ≤ X ω }).toReal = (μ { ω | exp (t * ε) ≤ exp (t * X ω) }).toReal :=
+    (μ {ω | ε ≤ X ω}).toReal = (μ {ω | exp (t * ε) ≤ exp (t * X ω)}).toReal :=
       by
       congr with ω
       simp only [exp_le_exp, eq_iff_iff]
@@ -361,7 +360,7 @@ theorem measure_ge_le_exp_mul_mgf [FiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
     _ ≤ (exp (t * ε))⁻¹ * μ[fun ω => exp (t * X ω)] :=
       by
       have :
-        exp (t * ε) * (μ { ω | exp (t * ε) ≤ exp (t * X ω) }).toReal ≤ μ[fun ω => exp (t * X ω)] :=
+        exp (t * ε) * (μ {ω | exp (t * ε) ≤ exp (t * X ω)}).toReal ≤ μ[fun ω => exp (t * X ω)] :=
         mul_meas_ge_le_integral_of_nonneg (fun x => (exp_pos _).le) h_int _
       rwa [mul_comm (exp (t * ε))⁻¹, ← div_eq_mul_inv, le_div_iff' (exp_pos _)]
     _ = exp (-t * ε) * mgf X μ t := by rw [neg_mul, exp_neg]; rfl
@@ -369,9 +368,9 @@ theorem measure_ge_le_exp_mul_mgf [FiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
 #align probability_theory.measure_ge_le_exp_mul_mgf ProbabilityTheory.measure_ge_le_exp_mul_mgf
 
 /-- **Chernoff bound** on the lower tail of a real random variable. -/
-theorem measure_le_le_exp_mul_mgf [FiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
+theorem measure_le_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
-    (μ { ω | X ω ≤ ε }).toReal ≤ exp (-t * ε) * mgf X μ t :=
+    (μ {ω | X ω ≤ ε}).toReal ≤ exp (-t * ε) * mgf X μ t :=
   by
   rw [← neg_neg t, ← mgf_neg, neg_neg, ← neg_mul_neg (-t)]
   refine' Eq.trans_le _ (measure_ge_le_exp_mul_mgf (-ε) (neg_nonneg.mpr ht) _)
@@ -382,9 +381,9 @@ theorem measure_le_le_exp_mul_mgf [FiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
 #align probability_theory.measure_le_le_exp_mul_mgf ProbabilityTheory.measure_le_le_exp_mul_mgf
 
 /-- **Chernoff bound** on the upper tail of a real random variable. -/
-theorem measure_ge_le_exp_cgf [FiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
+theorem measure_ge_le_exp_cgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
-    (μ { ω | ε ≤ X ω }).toReal ≤ exp (-t * ε + cgf X μ t) :=
+    (μ {ω | ε ≤ X ω}).toReal ≤ exp (-t * ε + cgf X μ t) :=
   by
   refine' (measure_ge_le_exp_mul_mgf ε ht h_int).trans _
   rw [exp_add]
@@ -392,9 +391,9 @@ theorem measure_ge_le_exp_cgf [FiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
 #align probability_theory.measure_ge_le_exp_cgf ProbabilityTheory.measure_ge_le_exp_cgf
 
 /-- **Chernoff bound** on the lower tail of a real random variable. -/
-theorem measure_le_le_exp_cgf [FiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
+theorem measure_le_le_exp_cgf [IsFiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
-    (μ { ω | X ω ≤ ε }).toReal ≤ exp (-t * ε + cgf X μ t) :=
+    (μ {ω | X ω ≤ ε}).toReal ≤ exp (-t * ε + cgf X μ t) :=
   by
   refine' (measure_le_le_exp_mul_mgf ε ht h_int).trans _
   rw [exp_add]

85453a2a

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -44,7 +44,7 @@ open MeasureTheory Filter Finset Real
 
 noncomputable section
 
-open BigOperators MeasureTheory ProbabilityTheory ENNReal NNReal
+open scoped BigOperators MeasureTheory ProbabilityTheory ENNReal NNReal
 
 namespace ProbabilityTheory

85453a2a

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -93,20 +93,14 @@ theorem centralMoment_one [ProbabilityMeasure μ] : centralMoment X 1 μ = 0 :=
     have : ¬integrable (fun x => X x - integral μ X) μ :=
       by
       refine' fun h_sub => h_int _
-      have h_add : X = (fun x => X x - integral μ X) + fun x => integral μ X :=
-        by
-        ext1 x
-        simp
+      have h_add : X = (fun x => X x - integral μ X) + fun x => integral μ X := by ext1 x; simp
       rw [h_add]
       exact h_sub.add (integrable_const _)
     rw [integral_undef this]
 #align probability_theory.central_moment_one ProbabilityTheory.centralMoment_one
 
 theorem centralMoment_two_eq_variance [FiniteMeasure μ] (hX : Memℒp X 2 μ) :
-    centralMoment X 2 μ = variance X μ :=
-  by
-  rw [hX.variance_eq]
-  rfl
+    centralMoment X 2 μ = variance X μ := by rw [hX.variance_eq]; rfl
 #align probability_theory.central_moment_two_eq_variance ProbabilityTheory.centralMoment_two_eq_variance
 
 section MomentGeneratingFunction
@@ -370,9 +364,7 @@ theorem measure_ge_le_exp_mul_mgf [FiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
         exp (t * ε) * (μ { ω | exp (t * ε) ≤ exp (t * X ω) }).toReal ≤ μ[fun ω => exp (t * X ω)] :=
         mul_meas_ge_le_integral_of_nonneg (fun x => (exp_pos _).le) h_int _
       rwa [mul_comm (exp (t * ε))⁻¹, ← div_eq_mul_inv, le_div_iff' (exp_pos _)]
-    _ = exp (-t * ε) * mgf X μ t := by
-      rw [neg_mul, exp_neg]
-      rfl
+    _ = exp (-t * ε) * mgf X μ t := by rw [neg_mul, exp_neg]; rfl
     
 #align probability_theory.measure_ge_le_exp_mul_mgf ProbabilityTheory.measure_ge_le_exp_mul_mgf

85453a2a

bump to nightly-2023-05-23-20

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

4d066d3b

Diff

@@ -244,8 +244,8 @@ theorem IndepFunCat.exp_mul {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ) (s
 #align probability_theory.indep_fun.exp_mul ProbabilityTheory.IndepFunCat.exp_mul
 
 theorem IndepFunCat.mgf_add {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
-    (hX : AeStronglyMeasurable (fun ω => exp (t * X ω)) μ)
-    (hY : AeStronglyMeasurable (fun ω => exp (t * Y ω)) μ) :
+    (hX : AEStronglyMeasurable (fun ω => exp (t * X ω)) μ)
+    (hY : AEStronglyMeasurable (fun ω => exp (t * Y ω)) μ) :
     mgf (X + Y) μ t = mgf X μ t * mgf Y μ t :=
   by
   simp_rw [mgf, Pi.add_apply, mul_add, exp_add]
@@ -253,7 +253,7 @@ theorem IndepFunCat.mgf_add {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
 #align probability_theory.indep_fun.mgf_add ProbabilityTheory.IndepFunCat.mgf_add
 
 theorem IndepFunCat.mgf_add' {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
-    (hX : AeStronglyMeasurable X μ) (hY : AeStronglyMeasurable Y μ) :
+    (hX : AEStronglyMeasurable X μ) (hY : AEStronglyMeasurable Y μ) :
     mgf (X + Y) μ t = mgf X μ t * mgf Y μ t :=
   by
   have A : Continuous fun x : ℝ => exp (t * x) := by continuity
@@ -274,18 +274,18 @@ theorem IndepFunCat.cgf_add {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
   exact log_mul (mgf_pos' hμ h_int_X).ne' (mgf_pos' hμ h_int_Y).ne'
 #align probability_theory.indep_fun.cgf_add ProbabilityTheory.IndepFunCat.cgf_add
 
-theorem aeStronglyMeasurable_exp_mul_add {X Y : Ω → ℝ}
-    (h_int_X : AeStronglyMeasurable (fun ω => exp (t * X ω)) μ)
-    (h_int_Y : AeStronglyMeasurable (fun ω => exp (t * Y ω)) μ) :
-    AeStronglyMeasurable (fun ω => exp (t * (X + Y) ω)) μ :=
+theorem aEStronglyMeasurable_exp_mul_add {X Y : Ω → ℝ}
+    (h_int_X : AEStronglyMeasurable (fun ω => exp (t * X ω)) μ)
+    (h_int_Y : AEStronglyMeasurable (fun ω => exp (t * Y ω)) μ) :
+    AEStronglyMeasurable (fun ω => exp (t * (X + Y) ω)) μ :=
   by
   simp_rw [Pi.add_apply, mul_add, exp_add]
   exact ae_strongly_measurable.mul h_int_X h_int_Y
-#align probability_theory.ae_strongly_measurable_exp_mul_add ProbabilityTheory.aeStronglyMeasurable_exp_mul_add
+#align probability_theory.ae_strongly_measurable_exp_mul_add ProbabilityTheory.aEStronglyMeasurable_exp_mul_add
 
-theorem aeStronglyMeasurable_exp_mul_sum {X : ι → Ω → ℝ} {s : Finset ι}
-    (h_int : ∀ i ∈ s, AeStronglyMeasurable (fun ω => exp (t * X i ω)) μ) :
-    AeStronglyMeasurable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
+theorem aEStronglyMeasurable_exp_mul_sum {X : ι → Ω → ℝ} {s : Finset ι}
+    (h_int : ∀ i ∈ s, AEStronglyMeasurable (fun ω => exp (t * X i ω)) μ) :
+    AEStronglyMeasurable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
   classical
     induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
     · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, exp_zero]
@@ -295,7 +295,7 @@ theorem aeStronglyMeasurable_exp_mul_sum {X : ι → Ω → ℝ} {s : Finset ι}
       specialize h_rec this
       rw [sum_insert hi_notin_s]
       apply ae_strongly_measurable_exp_mul_add (h_int i (mem_insert_self _ _)) h_rec
-#align probability_theory.ae_strongly_measurable_exp_mul_sum ProbabilityTheory.aeStronglyMeasurable_exp_mul_sum
+#align probability_theory.ae_strongly_measurable_exp_mul_sum ProbabilityTheory.aEStronglyMeasurable_exp_mul_sum
 
 theorem IndepFunCat.integrable_exp_mul_add {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
     (h_int_X : Integrable (fun ω => exp (t * X ω)) μ)
@@ -329,7 +329,7 @@ theorem IndepFun.mgf_sum [ProbabilityMeasure μ] {X : ι → Ω → ℝ}
     induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
     · simp only [sum_empty, mgf_zero_fun, measure_univ, ENNReal.one_toReal, prod_empty]
     · have h_int' : ∀ i : ι, ae_strongly_measurable (fun ω : Ω => exp (t * X i ω)) μ := fun i =>
-        ((h_meas i).const_mul t).exp.AeStronglyMeasurable
+        ((h_meas i).const_mul t).exp.AEStronglyMeasurable
       rw [sum_insert hi_notin_s,
         indep_fun.mgf_add (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm
           (h_int' i) (ae_strongly_measurable_exp_mul_sum fun i hi => h_int' i),

85453a2a

bump to nightly-2023-05-09-08

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

244524af

Diff

@@ -75,7 +75,7 @@ theorem centralMoment_zero (hp : p ≠ 0) : centralMoment 0 p μ = 0 := by
     not_false_iff]
 #align probability_theory.central_moment_zero ProbabilityTheory.centralMoment_zero
 
-theorem centralMoment_one' [IsFiniteMeasure μ] (h_int : Integrable X μ) :
+theorem centralMoment_one' [FiniteMeasure μ] (h_int : Integrable X μ) :
     centralMoment X 1 μ = (1 - (μ Set.univ).toReal) * μ[X] :=
   by
   simp only [central_moment, Pi.sub_apply, pow_one]
@@ -84,7 +84,7 @@ theorem centralMoment_one' [IsFiniteMeasure μ] (h_int : Integrable X μ) :
 #align probability_theory.central_moment_one' ProbabilityTheory.centralMoment_one'
 
 @[simp]
-theorem centralMoment_one [IsProbabilityMeasure μ] : centralMoment X 1 μ = 0 :=
+theorem centralMoment_one [ProbabilityMeasure μ] : centralMoment X 1 μ = 0 :=
   by
   by_cases h_int : integrable X μ
   · rw [central_moment_one' h_int]
@@ -102,7 +102,7 @@ theorem centralMoment_one [IsProbabilityMeasure μ] : centralMoment X 1 μ = 0 :
     rw [integral_undef this]
 #align probability_theory.central_moment_one ProbabilityTheory.centralMoment_one
 
-theorem centralMoment_two_eq_variance [IsFiniteMeasure μ] (hX : Memℒp X 2 μ) :
+theorem centralMoment_two_eq_variance [FiniteMeasure μ] (hX : Memℒp X 2 μ) :
     centralMoment X 2 μ = variance X μ :=
   by
   rw [hX.variance_eq]
@@ -148,12 +148,12 @@ theorem mgf_const' (c : ℝ) : mgf (fun _ => c) μ t = (μ Set.univ).toReal * ex
 #align probability_theory.mgf_const' ProbabilityTheory.mgf_const'
 
 @[simp]
-theorem mgf_const (c : ℝ) [IsProbabilityMeasure μ] : mgf (fun _ => c) μ t = exp (t * c) := by
+theorem mgf_const (c : ℝ) [ProbabilityMeasure μ] : mgf (fun _ => c) μ t = exp (t * c) := by
   simp only [mgf_const', measure_univ, ENNReal.one_toReal, one_mul]
 #align probability_theory.mgf_const ProbabilityTheory.mgf_const
 
 @[simp]
-theorem cgf_const' [IsFiniteMeasure μ] (hμ : μ ≠ 0) (c : ℝ) :
+theorem cgf_const' [FiniteMeasure μ] (hμ : μ ≠ 0) (c : ℝ) :
     cgf (fun _ => c) μ t = log (μ Set.univ).toReal + t * c :=
   by
   simp only [cgf, mgf_const']
@@ -164,7 +164,7 @@ theorem cgf_const' [IsFiniteMeasure μ] (hμ : μ ≠ 0) (c : ℝ) :
 #align probability_theory.cgf_const' ProbabilityTheory.cgf_const'
 
 @[simp]
-theorem cgf_const [IsProbabilityMeasure μ] (c : ℝ) : cgf (fun _ => c) μ t = t * c := by
+theorem cgf_const [ProbabilityMeasure μ] (c : ℝ) : cgf (fun _ => c) μ t = t * c := by
   simp only [cgf, mgf_const, log_exp]
 #align probability_theory.cgf_const ProbabilityTheory.cgf_const
 
@@ -174,7 +174,7 @@ theorem mgf_zero' : mgf X μ 0 = (μ Set.univ).toReal := by
 #align probability_theory.mgf_zero' ProbabilityTheory.mgf_zero'
 
 @[simp]
-theorem mgf_zero [IsProbabilityMeasure μ] : mgf X μ 0 = 1 := by
+theorem mgf_zero [ProbabilityMeasure μ] : mgf X μ 0 = 1 := by
   simp only [mgf_zero', measure_univ, ENNReal.one_toReal]
 #align probability_theory.mgf_zero ProbabilityTheory.mgf_zero
 
@@ -183,7 +183,7 @@ theorem cgf_zero' : cgf X μ 0 = log (μ Set.univ).toReal := by simp only [cgf,
 #align probability_theory.cgf_zero' ProbabilityTheory.cgf_zero'
 
 @[simp]
-theorem cgf_zero [IsProbabilityMeasure μ] : cgf X μ 0 = 0 := by
+theorem cgf_zero [ProbabilityMeasure μ] : cgf X μ 0 = 0 := by
   simp only [cgf_zero', measure_univ, ENNReal.one_toReal, log_one]
 #align probability_theory.cgf_zero ProbabilityTheory.cgf_zero
 
@@ -223,9 +223,9 @@ theorem mgf_pos' (hμ : μ ≠ 0) (h_int_X : Integrable (fun ω => exp (t * X ω
   · rwa [integrable_on_univ]
 #align probability_theory.mgf_pos' ProbabilityTheory.mgf_pos'
 
-theorem mgf_pos [IsProbabilityMeasure μ] (h_int_X : Integrable (fun ω => exp (t * X ω)) μ) :
+theorem mgf_pos [ProbabilityMeasure μ] (h_int_X : Integrable (fun ω => exp (t * X ω)) μ) :
     0 < mgf X μ t :=
-  mgf_pos' (IsProbabilityMeasure.ne_zero μ) h_int_X
+  mgf_pos' (ProbabilityMeasure.ne_zero μ) h_int_X
 #align probability_theory.mgf_pos ProbabilityTheory.mgf_pos
 
 theorem mgf_neg : mgf (-X) μ t = mgf X μ (-t) := by simp_rw [mgf, Pi.neg_apply, mul_neg, neg_mul]
@@ -306,7 +306,7 @@ theorem IndepFunCat.integrable_exp_mul_add {X Y : Ω → ℝ} (h_indep : IndepFu
   exact (h_indep.exp_mul t t).integrable_mul h_int_X h_int_Y
 #align probability_theory.indep_fun.integrable_exp_mul_add ProbabilityTheory.IndepFunCat.integrable_exp_mul_add
 
-theorem IndepFun.integrable_exp_mul_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
+theorem IndepFun.integrable_exp_mul_sum [ProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : IndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     {s : Finset ι} (h_int : ∀ i ∈ s, Integrable (fun ω => exp (t * X i ω)) μ) :
     Integrable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
@@ -322,7 +322,7 @@ theorem IndepFun.integrable_exp_mul_sum [IsProbabilityMeasure μ] {X : ι → Ω
       exact (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm
 #align probability_theory.Indep_fun.integrable_exp_mul_sum ProbabilityTheory.IndepFun.integrable_exp_mul_sum
 
-theorem IndepFun.mgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
+theorem IndepFun.mgf_sum [ProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : IndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     (s : Finset ι) : mgf (∑ i in s, X i) μ t = ∏ i in s, mgf (X i) μ t := by
   classical
@@ -336,7 +336,7 @@ theorem IndepFun.mgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
         h_rec, prod_insert hi_notin_s]
 #align probability_theory.Indep_fun.mgf_sum ProbabilityTheory.IndepFun.mgf_sum
 
-theorem IndepFun.cgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
+theorem IndepFun.cgf_sum [ProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : IndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     {s : Finset ι} (h_int : ∀ i ∈ s, Integrable (fun ω => exp (t * X i ω)) μ) :
     cgf (∑ i in s, X i) μ t = ∑ i in s, cgf (X i) μ t :=
@@ -348,7 +348,7 @@ theorem IndepFun.cgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
 #align probability_theory.Indep_fun.cgf_sum ProbabilityTheory.IndepFun.cgf_sum
 
 /-- **Chernoff bound** on the upper tail of a real random variable. -/
-theorem measure_ge_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
+theorem measure_ge_le_exp_mul_mgf [FiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
     (μ { ω | ε ≤ X ω }).toReal ≤ exp (-t * ε) * mgf X μ t :=
   by
@@ -377,7 +377,7 @@ theorem measure_ge_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
 #align probability_theory.measure_ge_le_exp_mul_mgf ProbabilityTheory.measure_ge_le_exp_mul_mgf
 
 /-- **Chernoff bound** on the lower tail of a real random variable. -/
-theorem measure_le_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
+theorem measure_le_le_exp_mul_mgf [FiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
     (μ { ω | X ω ≤ ε }).toReal ≤ exp (-t * ε) * mgf X μ t :=
   by
@@ -390,7 +390,7 @@ theorem measure_le_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
 #align probability_theory.measure_le_le_exp_mul_mgf ProbabilityTheory.measure_le_le_exp_mul_mgf
 
 /-- **Chernoff bound** on the upper tail of a real random variable. -/
-theorem measure_ge_le_exp_cgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
+theorem measure_ge_le_exp_cgf [FiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
     (μ { ω | ε ≤ X ω }).toReal ≤ exp (-t * ε + cgf X μ t) :=
   by
@@ -400,7 +400,7 @@ theorem measure_ge_le_exp_cgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
 #align probability_theory.measure_ge_le_exp_cgf ProbabilityTheory.measure_ge_le_exp_cgf
 
 /-- **Chernoff bound** on the lower tail of a real random variable. -/
-theorem measure_le_le_exp_cgf [IsFiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
+theorem measure_le_le_exp_cgf [FiniteMeasure μ] (ε : ℝ) (ht : t ≤ 0)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
     (μ { ω | X ω ≤ ε }).toReal ≤ exp (-t * ε + cgf X μ t) :=
   by

85453a2a

bump to nightly-2023-05-04-10

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

3d8894bd

Diff

@@ -235,13 +235,13 @@ theorem cgf_neg : cgf (-X) μ t = cgf X μ (-t) := by simp_rw [cgf, mgf_neg]
 #align probability_theory.cgf_neg ProbabilityTheory.cgf_neg
 
 /-- This is a trivial application of `indep_fun.comp` but it will come up frequently. -/
-theorem IndepFunCat.expMul {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ) (s t : ℝ) :
+theorem IndepFunCat.exp_mul {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ) (s t : ℝ) :
     IndepFunCat (fun ω => exp (s * X ω)) (fun ω => exp (t * Y ω)) μ :=
   by
   have h_meas : ∀ t, Measurable fun x => exp (t * x) := fun t => (measurable_id'.const_mul t).exp
   change indep_fun ((fun x => exp (s * x)) ∘ X) ((fun x => exp (t * x)) ∘ Y) μ
   exact indep_fun.comp h_indep (h_meas s) (h_meas t)
-#align probability_theory.indep_fun.exp_mul ProbabilityTheory.IndepFunCat.expMul
+#align probability_theory.indep_fun.exp_mul ProbabilityTheory.IndepFunCat.exp_mul
 
 theorem IndepFunCat.mgf_add {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
     (hX : AeStronglyMeasurable (fun ω => exp (t * X ω)) μ)
@@ -274,16 +274,16 @@ theorem IndepFunCat.cgf_add {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
   exact log_mul (mgf_pos' hμ h_int_X).ne' (mgf_pos' hμ h_int_Y).ne'
 #align probability_theory.indep_fun.cgf_add ProbabilityTheory.IndepFunCat.cgf_add
 
-theorem aeStronglyMeasurableExpMulAdd {X Y : Ω → ℝ}
+theorem aeStronglyMeasurable_exp_mul_add {X Y : Ω → ℝ}
     (h_int_X : AeStronglyMeasurable (fun ω => exp (t * X ω)) μ)
     (h_int_Y : AeStronglyMeasurable (fun ω => exp (t * Y ω)) μ) :
     AeStronglyMeasurable (fun ω => exp (t * (X + Y) ω)) μ :=
   by
   simp_rw [Pi.add_apply, mul_add, exp_add]
   exact ae_strongly_measurable.mul h_int_X h_int_Y
-#align probability_theory.ae_strongly_measurable_exp_mul_add ProbabilityTheory.aeStronglyMeasurableExpMulAdd
+#align probability_theory.ae_strongly_measurable_exp_mul_add ProbabilityTheory.aeStronglyMeasurable_exp_mul_add
 
-theorem aeStronglyMeasurableExpMulSum {X : ι → Ω → ℝ} {s : Finset ι}
+theorem aeStronglyMeasurable_exp_mul_sum {X : ι → Ω → ℝ} {s : Finset ι}
     (h_int : ∀ i ∈ s, AeStronglyMeasurable (fun ω => exp (t * X i ω)) μ) :
     AeStronglyMeasurable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
   classical
@@ -295,18 +295,18 @@ theorem aeStronglyMeasurableExpMulSum {X : ι → Ω → ℝ} {s : Finset ι}
       specialize h_rec this
       rw [sum_insert hi_notin_s]
       apply ae_strongly_measurable_exp_mul_add (h_int i (mem_insert_self _ _)) h_rec
-#align probability_theory.ae_strongly_measurable_exp_mul_sum ProbabilityTheory.aeStronglyMeasurableExpMulSum
+#align probability_theory.ae_strongly_measurable_exp_mul_sum ProbabilityTheory.aeStronglyMeasurable_exp_mul_sum
 
-theorem IndepFunCat.integrableExpMulAdd {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
+theorem IndepFunCat.integrable_exp_mul_add {X Y : Ω → ℝ} (h_indep : IndepFunCat X Y μ)
     (h_int_X : Integrable (fun ω => exp (t * X ω)) μ)
     (h_int_Y : Integrable (fun ω => exp (t * Y ω)) μ) :
     Integrable (fun ω => exp (t * (X + Y) ω)) μ :=
   by
   simp_rw [Pi.add_apply, mul_add, exp_add]
-  exact (h_indep.exp_mul t t).integrableMul h_int_X h_int_Y
-#align probability_theory.indep_fun.integrable_exp_mul_add ProbabilityTheory.IndepFunCat.integrableExpMulAdd
+  exact (h_indep.exp_mul t t).integrable_mul h_int_X h_int_Y
+#align probability_theory.indep_fun.integrable_exp_mul_add ProbabilityTheory.IndepFunCat.integrable_exp_mul_add
 
-theorem IndepFun.integrableExpMulSum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
+theorem IndepFun.integrable_exp_mul_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : IndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))
     {s : Finset ι} (h_int : ∀ i ∈ s, Integrable (fun ω => exp (t * X i ω)) μ) :
     Integrable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
@@ -320,7 +320,7 @@ theorem IndepFun.integrableExpMulSum [IsProbabilityMeasure μ] {X : ι → Ω 
       rw [sum_insert hi_notin_s]
       refine' indep_fun.integrable_exp_mul_add _ (h_int i (mem_insert_self _ _)) h_rec
       exact (h_indep.indep_fun_finset_sum_of_not_mem h_meas hi_notin_s).symm
-#align probability_theory.Indep_fun.integrable_exp_mul_sum ProbabilityTheory.IndepFun.integrableExpMulSum
+#align probability_theory.Indep_fun.integrable_exp_mul_sum ProbabilityTheory.IndepFun.integrable_exp_mul_sum
 
 theorem IndepFun.mgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (h_indep : IndepFun (fun i => inferInstance) X μ) (h_meas : ∀ i, Measurable (X i))

85453a2a

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -65,13 +65,14 @@ def centralMoment (X : Ω → ℝ) (p : ℕ) (μ : Measure Ω) : ℝ :=
 @[simp]
 theorem moment_zero (hp : p ≠ 0) : moment 0 p μ = 0 := by
   simp only [moment, hp, zero_pow', Ne.def, not_false_iff, Pi.zero_apply, integral_const,
-    Algebra.id.smul_eq_mul, mul_zero]
+    Algebra.id.smul_eq_mul, MulZeroClass.mul_zero]
 #align probability_theory.moment_zero ProbabilityTheory.moment_zero
 
 @[simp]
 theorem centralMoment_zero (hp : p ≠ 0) : centralMoment 0 p μ = 0 := by
-  simp only [central_moment, hp, Pi.zero_apply, integral_const, Algebra.id.smul_eq_mul, mul_zero,
-    zero_sub, Pi.pow_apply, Pi.neg_apply, neg_zero, zero_pow', Ne.def, not_false_iff]
+  simp only [central_moment, hp, Pi.zero_apply, integral_const, Algebra.id.smul_eq_mul,
+    MulZeroClass.mul_zero, zero_sub, Pi.pow_apply, Pi.neg_apply, neg_zero, zero_pow', Ne.def,
+    not_false_iff]
 #align probability_theory.central_moment_zero ProbabilityTheory.centralMoment_zero
 
 theorem centralMoment_one' [IsFiniteMeasure μ] (h_int : Integrable X μ) :
@@ -87,7 +88,7 @@ theorem centralMoment_one [IsProbabilityMeasure μ] : centralMoment X 1 μ = 0 :
   by
   by_cases h_int : integrable X μ
   · rw [central_moment_one' h_int]
-    simp only [measure_univ, ENNReal.one_toReal, sub_self, zero_mul]
+    simp only [measure_univ, ENNReal.one_toReal, sub_self, MulZeroClass.zero_mul]
   · simp only [central_moment, Pi.sub_apply, pow_one]
     have : ¬integrable (fun x => X x - integral μ X) μ :=
       by
@@ -124,8 +125,8 @@ def cgf (X : Ω → ℝ) (μ : Measure Ω) (t : ℝ) : ℝ :=
 
 @[simp]
 theorem mgf_zero_fun : mgf 0 μ t = (μ Set.univ).toReal := by
-  simp only [mgf, Pi.zero_apply, mul_zero, exp_zero, integral_const, Algebra.id.smul_eq_mul,
-    mul_one]
+  simp only [mgf, Pi.zero_apply, MulZeroClass.mul_zero, exp_zero, integral_const,
+    Algebra.id.smul_eq_mul, mul_one]
 #align probability_theory.mgf_zero_fun ProbabilityTheory.mgf_zero_fun
 
 @[simp]
@@ -169,7 +170,7 @@ theorem cgf_const [IsProbabilityMeasure μ] (c : ℝ) : cgf (fun _ => c) μ t =
 
 @[simp]
 theorem mgf_zero' : mgf X μ 0 = (μ Set.univ).toReal := by
-  simp only [mgf, zero_mul, exp_zero, integral_const, Algebra.id.smul_eq_mul, mul_one]
+  simp only [mgf, MulZeroClass.zero_mul, exp_zero, integral_const, Algebra.id.smul_eq_mul, mul_one]
 #align probability_theory.mgf_zero' ProbabilityTheory.mgf_zero'
 
 @[simp]
@@ -287,7 +288,7 @@ theorem aeStronglyMeasurableExpMulSum {X : ι → Ω → ℝ} {s : Finset ι}
     AeStronglyMeasurable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
   classical
     induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
-    · simp only [Pi.zero_apply, sum_apply, sum_empty, mul_zero, exp_zero]
+    · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, exp_zero]
       exact ae_strongly_measurable_const
     · have : ∀ i : ι, i ∈ s → ae_strongly_measurable (fun ω : Ω => exp (t * X i ω)) μ := fun i hi =>
         h_int i (mem_insert_of_mem hi)
@@ -311,7 +312,7 @@ theorem IndepFun.integrableExpMulSum [IsProbabilityMeasure μ] {X : ι → Ω 
     Integrable (fun ω => exp (t * (∑ i in s, X i) ω)) μ := by
   classical
     induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
-    · simp only [Pi.zero_apply, sum_apply, sum_empty, mul_zero, exp_zero]
+    · simp only [Pi.zero_apply, sum_apply, sum_empty, MulZeroClass.mul_zero, exp_zero]
       exact integrable_const _
     · have : ∀ i : ι, i ∈ s → integrable (fun ω : Ω => exp (t * X i ω)) μ := fun i hi =>
         h_int i (mem_insert_of_mem hi)
@@ -353,7 +354,7 @@ theorem measure_ge_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
   by
   cases' ht.eq_or_lt with ht_zero_eq ht_pos
   · rw [ht_zero_eq.symm]
-    simp only [neg_zero, zero_mul, exp_zero, mgf_zero', one_mul]
+    simp only [neg_zero, MulZeroClass.zero_mul, exp_zero, mgf_zero', one_mul]
     rw [ENNReal.toReal_le_toReal (measure_ne_top μ _) (measure_ne_top μ _)]
     exact measure_mono (Set.subset_univ _)
   calc

85453a2a

bump to nightly-2023-02-27-10

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

49ff026a

Diff

@@ -44,7 +44,7 @@ open MeasureTheory Filter Finset Real
 
 noncomputable section
 
-open BigOperators MeasureTheory ProbabilityTheory Ennreal NNReal
+open BigOperators MeasureTheory ProbabilityTheory ENNReal NNReal
 
 namespace ProbabilityTheory
 
@@ -87,7 +87,7 @@ theorem centralMoment_one [IsProbabilityMeasure μ] : centralMoment X 1 μ = 0 :
   by
   by_cases h_int : integrable X μ
   · rw [central_moment_one' h_int]
-    simp only [measure_univ, Ennreal.one_toReal, sub_self, zero_mul]
+    simp only [measure_univ, ENNReal.one_toReal, sub_self, zero_mul]
   · simp only [central_moment, Pi.sub_apply, pow_one]
     have : ¬integrable (fun x => X x - integral μ X) μ :=
       by
@@ -148,7 +148,7 @@ theorem mgf_const' (c : ℝ) : mgf (fun _ => c) μ t = (μ Set.univ).toReal * ex
 
 @[simp]
 theorem mgf_const (c : ℝ) [IsProbabilityMeasure μ] : mgf (fun _ => c) μ t = exp (t * c) := by
-  simp only [mgf_const', measure_univ, Ennreal.one_toReal, one_mul]
+  simp only [mgf_const', measure_univ, ENNReal.one_toReal, one_mul]
 #align probability_theory.mgf_const ProbabilityTheory.mgf_const
 
 @[simp]
@@ -158,7 +158,7 @@ theorem cgf_const' [IsFiniteMeasure μ] (hμ : μ ≠ 0) (c : ℝ) :
   simp only [cgf, mgf_const']
   rw [log_mul _ (exp_pos _).ne']
   · rw [log_exp _]
-  · rw [Ne.def, Ennreal.toReal_eq_zero_iff, measure.measure_univ_eq_zero]
+  · rw [Ne.def, ENNReal.toReal_eq_zero_iff, measure.measure_univ_eq_zero]
     simp only [hμ, measure_ne_top μ Set.univ, or_self_iff, not_false_iff]
 #align probability_theory.cgf_const' ProbabilityTheory.cgf_const'
 
@@ -174,7 +174,7 @@ theorem mgf_zero' : mgf X μ 0 = (μ Set.univ).toReal := by
 
 @[simp]
 theorem mgf_zero [IsProbabilityMeasure μ] : mgf X μ 0 = 1 := by
-  simp only [mgf_zero', measure_univ, Ennreal.one_toReal]
+  simp only [mgf_zero', measure_univ, ENNReal.one_toReal]
 #align probability_theory.mgf_zero ProbabilityTheory.mgf_zero
 
 @[simp]
@@ -183,7 +183,7 @@ theorem cgf_zero' : cgf X μ 0 = log (μ Set.univ).toReal := by simp only [cgf,
 
 @[simp]
 theorem cgf_zero [IsProbabilityMeasure μ] : cgf X μ 0 = 0 := by
-  simp only [cgf_zero', measure_univ, Ennreal.one_toReal, log_one]
+  simp only [cgf_zero', measure_univ, ENNReal.one_toReal, log_one]
 #align probability_theory.cgf_zero ProbabilityTheory.cgf_zero
 
 theorem mgf_undef (hX : ¬Integrable (fun ω => exp (t * X ω)) μ) : mgf X μ t = 0 := by
@@ -215,7 +215,7 @@ theorem mgf_pos' (hμ : μ ≠ 0) (h_int_X : Integrable (fun ω => exp (t * X ω
       exact (exp_pos _).ne'
     rw [h_eq_univ, Set.inter_univ _]
     refine' Ne.bot_lt _
-    simp only [hμ, Ennreal.bot_eq_zero, Ne.def, measure.measure_univ_eq_zero, not_false_iff]
+    simp only [hμ, ENNReal.bot_eq_zero, Ne.def, measure.measure_univ_eq_zero, not_false_iff]
   · refine' eventually_of_forall fun x => _
     rw [Pi.zero_apply]
     exact (exp_pos _).le
@@ -326,7 +326,7 @@ theorem IndepFun.mgf_sum [IsProbabilityMeasure μ] {X : ι → Ω → ℝ}
     (s : Finset ι) : mgf (∑ i in s, X i) μ t = ∏ i in s, mgf (X i) μ t := by
   classical
     induction' s using Finset.induction_on with i s hi_notin_s h_rec h_int
-    · simp only [sum_empty, mgf_zero_fun, measure_univ, Ennreal.one_toReal, prod_empty]
+    · simp only [sum_empty, mgf_zero_fun, measure_univ, ENNReal.one_toReal, prod_empty]
     · have h_int' : ∀ i : ι, ae_strongly_measurable (fun ω : Ω => exp (t * X i ω)) μ := fun i =>
         ((h_meas i).const_mul t).exp.AeStronglyMeasurable
       rw [sum_insert hi_notin_s,
@@ -354,7 +354,7 @@ theorem measure_ge_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
   cases' ht.eq_or_lt with ht_zero_eq ht_pos
   · rw [ht_zero_eq.symm]
     simp only [neg_zero, zero_mul, exp_zero, mgf_zero', one_mul]
-    rw [Ennreal.toReal_le_toReal (measure_ne_top μ _) (measure_ne_top μ _)]
+    rw [ENNReal.toReal_le_toReal (measure_ne_top μ _) (measure_ne_top μ _)]
     exact measure_mono (Set.subset_univ _)
   calc
     (μ { ω | ε ≤ X ω }).toReal = (μ { ω | exp (t * ε) ≤ exp (t * X ω) }).toReal :=

85453a2a

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

85453a2a

chore: Rename a few lemmas about Pi.mulSingle (#12317)

Before this PR, the MonoidHom version of Pi.mulSingle was called MonoidHom.single for brevity; but this is confusing when contrasted with MulHom.single which is about Pi.single.

After this PR, the name is MonoidHom.mulSingle.

Also fix the name of Pi.single_div since it is about Pi.mulSingle (and we don't have the lemma that would be called Pi.single_div).

01ce6da3

Diff

@@ -61,7 +61,7 @@ def centralMoment (X : Ω → ℝ) (p : ℕ) (μ : Measure Ω) : ℝ := by
 @[simp]
 theorem moment_zero (hp : p ≠ 0) : moment 0 p μ = 0 := by
   simp only [moment, hp, zero_pow, Ne, not_false_iff, Pi.zero_apply, integral_const,
-    smul_eq_mul, mul_zero]
+    smul_eq_mul, mul_zero, integral_zero]
 #align probability_theory.moment_zero ProbabilityTheory.moment_zero
 
 @[simp]

85453a2a

chore: replace set_integral with setIntegral (#12215)

Done with a global search and replace, and then (to fix the #align lines), replace (#align \S*)setIntegral with $1set_integral.

f4b4298b

Diff

@@ -188,7 +188,7 @@ theorem mgf_pos' (hμ : μ ≠ 0) (h_int_X : Integrable (fun ω => exp (t * X ω
   simp_rw [mgf]
   have : ∫ x : Ω, exp (t * X x) ∂μ = ∫ x : Ω in Set.univ, exp (t * X x) ∂μ := by
     simp only [Measure.restrict_univ]
-  rw [this, set_integral_pos_iff_support_of_nonneg_ae _ _]
+  rw [this, setIntegral_pos_iff_support_of_nonneg_ae _ _]
   · have h_eq_univ : (Function.support fun x : Ω => exp (t * X x)) = Set.univ := by
       ext1 x
       simp only [Function.mem_support, Set.mem_univ, iff_true_iff]

85453a2a

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11813)

08686b25

Diff

@@ -60,14 +60,14 @@ def centralMoment (X : Ω → ℝ) (p : ℕ) (μ : Measure Ω) : ℝ := by
 
 @[simp]
 theorem moment_zero (hp : p ≠ 0) : moment 0 p μ = 0 := by
-  simp only [moment, hp, zero_pow, Ne.def, not_false_iff, Pi.zero_apply, integral_const,
+  simp only [moment, hp, zero_pow, Ne, not_false_iff, Pi.zero_apply, integral_const,
     smul_eq_mul, mul_zero]
 #align probability_theory.moment_zero ProbabilityTheory.moment_zero
 
 @[simp]
 theorem centralMoment_zero (hp : p ≠ 0) : centralMoment 0 p μ = 0 := by
   simp only [centralMoment, hp, Pi.zero_apply, integral_const, smul_eq_mul,
-    mul_zero, zero_sub, Pi.pow_apply, Pi.neg_apply, neg_zero, zero_pow, Ne.def, not_false_iff]
+    mul_zero, zero_sub, Pi.pow_apply, Pi.neg_apply, neg_zero, zero_pow, Ne, not_false_iff]
 #align probability_theory.central_moment_zero ProbabilityTheory.centralMoment_zero
 
 theorem centralMoment_one' [IsFiniteMeasure μ] (h_int : Integrable X μ) :
@@ -143,7 +143,7 @@ theorem cgf_const' [IsFiniteMeasure μ] (hμ : μ ≠ 0) (c : ℝ) :
   simp only [cgf, mgf_const']
   rw [log_mul _ (exp_pos _).ne']
   · rw [log_exp _]
-  · rw [Ne.def, ENNReal.toReal_eq_zero_iff, Measure.measure_univ_eq_zero]
+  · rw [Ne, ENNReal.toReal_eq_zero_iff, Measure.measure_univ_eq_zero]
     simp only [hμ, measure_ne_top μ Set.univ, or_self_iff, not_false_iff]
 #align probability_theory.cgf_const' ProbabilityTheory.cgf_const'
 
@@ -195,7 +195,7 @@ theorem mgf_pos' (hμ : μ ≠ 0) (h_int_X : Integrable (fun ω => exp (t * X ω
       exact (exp_pos _).ne'
     rw [h_eq_univ, Set.inter_univ _]
     refine' Ne.bot_lt _
-    simp only [hμ, ENNReal.bot_eq_zero, Ne.def, Measure.measure_univ_eq_zero, not_false_iff]
+    simp only [hμ, ENNReal.bot_eq_zero, Ne, Measure.measure_univ_eq_zero, not_false_iff]
   · filter_upwards with x
     rw [Pi.zero_apply]
     exact (exp_pos _).le

85453a2a

feat: Positivity extension for Bochner integral (#10661)

Inspired by #10538 add a positivity extension for Bochner integrals.

8b3fbc92

Diff

@@ -180,10 +180,7 @@ theorem cgf_undef (hX : ¬Integrable (fun ω => exp (t * X ω)) μ) : cgf X μ t
 #align probability_theory.cgf_undef ProbabilityTheory.cgf_undef
 
 theorem mgf_nonneg : 0 ≤ mgf X μ t := by
-  refine' integral_nonneg _
-  intro ω
-  simp only [Pi.zero_apply]
-  exact (exp_pos _).le
+  unfold mgf; positivity
 #align probability_theory.mgf_nonneg ProbabilityTheory.mgf_nonneg
 
 theorem mgf_pos' (hμ : μ ≠ 0) (h_int_X : Integrable (fun ω => exp (t * X ω)) μ) :

85453a2a

chore: golf using filter_upwards (#11208)

This is presumably not exhaustive, but covers about a hundred instances.

Style opinions (e.g., why a particular change is great/not a good idea) are very welcome; I'm still forming my own.

f637899e

Diff

@@ -199,7 +199,7 @@ theorem mgf_pos' (hμ : μ ≠ 0) (h_int_X : Integrable (fun ω => exp (t * X ω
     rw [h_eq_univ, Set.inter_univ _]
     refine' Ne.bot_lt _
     simp only [hμ, ENNReal.bot_eq_zero, Ne.def, Measure.measure_univ_eq_zero, not_false_iff]
-  · refine' eventually_of_forall fun x => _
+  · filter_upwards with x
     rw [Pi.zero_apply]
     exact (exp_pos _).le
   · rwa [integrableOn_univ]

85453a2a

feat: The support of f ^ n (#9617)

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

9d1a7d26

Diff

@@ -60,14 +60,14 @@ def centralMoment (X : Ω → ℝ) (p : ℕ) (μ : Measure Ω) : ℝ := by
 
 @[simp]
 theorem moment_zero (hp : p ≠ 0) : moment 0 p μ = 0 := by
-  simp only [moment, hp, zero_pow', Ne.def, not_false_iff, Pi.zero_apply, integral_const,
+  simp only [moment, hp, zero_pow, Ne.def, not_false_iff, Pi.zero_apply, integral_const,
     smul_eq_mul, mul_zero]
 #align probability_theory.moment_zero ProbabilityTheory.moment_zero
 
 @[simp]
 theorem centralMoment_zero (hp : p ≠ 0) : centralMoment 0 p μ = 0 := by
   simp only [centralMoment, hp, Pi.zero_apply, integral_const, smul_eq_mul,
-    mul_zero, zero_sub, Pi.pow_apply, Pi.neg_apply, neg_zero, zero_pow', Ne.def, not_false_iff]
+    mul_zero, zero_sub, Pi.pow_apply, Pi.neg_apply, neg_zero, zero_pow, Ne.def, not_false_iff]
 #align probability_theory.central_moment_zero ProbabilityTheory.centralMoment_zero
 
 theorem centralMoment_one' [IsFiniteMeasure μ] (h_int : Integrable X μ) :

85453a2a

chore: remove uses of cases' (#9171)

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

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

3fca282c

Diff

@@ -329,7 +329,7 @@ set_option linter.uppercaseLean3 false in
 theorem measure_ge_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
     (h_int : Integrable (fun ω => exp (t * X ω)) μ) :
     (μ {ω | ε ≤ X ω}).toReal ≤ exp (-t * ε) * mgf X μ t := by
-  cases' ht.eq_or_lt with ht_zero_eq ht_pos
+  rcases ht.eq_or_lt with ht_zero_eq | ht_pos
   · rw [ht_zero_eq.symm]
     simp only [neg_zero, zero_mul, exp_zero, mgf_zero', one_mul]
     rw [ENNReal.toReal_le_toReal (measure_ne_top μ _) (measure_ne_top μ _)]

85453a2a

feat(Integral/Bochner): golf Markov's inequality, drop an assumption (#7619)

Golf the proof of MeasureTheory.mul_meas_ge_le_integral_of_nonneg.
Drop the assumption [IsFiniteMeasure μ].
Assume 0 ≤ᵐ[μ] f instead of 0 ≤ f.

780c5bab

Diff

@@ -343,7 +343,7 @@ theorem measure_ge_le_exp_mul_mgf [IsFiniteMeasure μ] (ε : ℝ) (ht : 0 ≤ t)
     _ ≤ (exp (t * ε))⁻¹ * μ[fun ω => exp (t * X ω)] := by
       have : exp (t * ε) * (μ {ω | exp (t * ε) ≤ exp (t * X ω)}).toReal ≤
           μ[fun ω => exp (t * X ω)] :=
-        mul_meas_ge_le_integral_of_nonneg (fun x => (exp_pos _).le) h_int _
+        mul_meas_ge_le_integral_of_nonneg (ae_of_all _ fun x => (exp_pos _).le) h_int _
       rwa [mul_comm (exp (t * ε))⁻¹, ← div_eq_mul_inv, le_div_iff' (exp_pos _)]
     _ = exp (-t * ε) * mgf X μ t := by rw [neg_mul, exp_neg]; rfl
 #align probability_theory.measure_ge_le_exp_mul_mgf ProbabilityTheory.measure_ge_le_exp_mul_mgf

85453a2a

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

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

This has nice performance benefits.

32de3f67

Diff

@@ -45,7 +45,7 @@ open scoped BigOperators MeasureTheory ProbabilityTheory ENNReal NNReal
 
 namespace ProbabilityTheory
 
-variable {Ω ι : Type _} {m : MeasurableSpace Ω} {X : Ω → ℝ} {p : ℕ} {μ : Measure Ω}
+variable {Ω ι : Type*} {m : MeasurableSpace Ω} {X : Ω → ℝ} {p : ℕ} {μ : Measure Ω}
 
 /-- Moment of a real random variable, `μ[X ^ p]`. -/
 def moment (X : Ω → ℝ) (p : ℕ) (μ : Measure Ω) : ℝ :=

85453a2a

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

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2022 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module probability.moments
-! leanprover-community/mathlib commit 85453a2a14be8da64caf15ca50930cf4c6e5d8de
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Probability.Variance
 
+#align_import probability.moments from "leanprover-community/mathlib"@"85453a2a14be8da64caf15ca50930cf4c6e5d8de"
+
 /-!
 # Moments and moment generating function

85453a2a

feat: port Probability.Moments (#5338)

This PR completes the port of the entire Probability folder to mathlib4.

9da26a02

`probability.moments` ⟷ `Mathlib.Probability.Moments`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 999

probability.moments ⟷ Mathlib.Probability.Moments

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 12 + 999

`probability.moments` ⟷ `Mathlib.Probability.Moments`