measure_theory.function.conditional_expectation.uniqueMathlib.MeasureTheory.Function.ConditionalExpectation.Unique

This file has been ported!

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

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Changes in mathlib3port

mathlib3
mathlib3port
Diff
@@ -48,8 +48,8 @@ section UniquenessOfConditionalExpectation
 /-! ## Uniqueness of the conditional expectation -/
 
 
-#print MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero /-
-theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lpMeas E' 𝕜 m p μ)
+#print MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero /-
+theorem lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero (hm : m ≤ m0) (f : lpMeas E' 𝕜 m p μ)
     (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
     (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hf_zero : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0) : f =ᵐ[μ] 0 :=
@@ -65,13 +65,13 @@ theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lp
     have hfg_restrict : f =ᵐ[μ.restrict s] g := ae_restrict_of_ae hfg
     rw [integral_congr_ae hfg_restrict.symm]
     exact hf_zero s hs hμs
-#align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero
+#align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero
 -/
 
 variable (𝕜)
 
-#print MeasureTheory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' /-
-theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
+#print MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero' /-
+theorem Lp.ae_eq_zero_of_forall_setIntegral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
     (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
     (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hf_zero : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0)
@@ -89,12 +89,12 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
     have hfg_restrict : f =ᵐ[μ.restrict s] f_meas := ae_restrict_of_ae hf_f_meas
     rw [integral_congr_ae hfg_restrict.symm]
     exact hf_zero s hs hμs
-#align measure_theory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' MeasureTheory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero'
+#align measure_theory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero'
 -/
 
-#print MeasureTheory.Lp.ae_eq_of_forall_set_integral_eq' /-
+#print MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq' /-
 /-- **Uniqueness of the conditional expectation** -/
-theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
+theorem Lp.ae_eq_of_forall_setIntegral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
     (hp_ne_top : p ≠ ∞) (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
     (hfg : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
@@ -118,13 +118,13 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
   exact
     Lp.ae_eq_zero_of_forall_set_integral_eq_zero' 𝕜 hm (f - g) hp_ne_zero hp_ne_top hfg_int hfg'
       hfg_meas
-#align measure_theory.Lp.ae_eq_of_forall_set_integral_eq' MeasureTheory.Lp.ae_eq_of_forall_set_integral_eq'
+#align measure_theory.Lp.ae_eq_of_forall_set_integral_eq' MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq'
 -/
 
 variable {𝕜}
 
-#print MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigmaFinite' /-
-theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
+#print MeasureTheory.ae_eq_of_forall_setIntegral_eq_of_sigmaFinite' /-
+theorem ae_eq_of_forall_setIntegral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     {f g : α → F'} (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
     (hfg_eq : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
@@ -160,7 +160,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
       integral_congr_ae (ae_restrict_of_ae hgm.ae_eq_mk.symm)]
     exact hfg_eq s hs hμs
   exact ae_eq_of_forall_set_integral_eq_of_sigma_finite hf_mk_int_finite hg_mk_int_finite hfg_mk_eq
-#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigmaFinite'
+#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_setIntegral_eq_of_sigmaFinite'
 -/
 
 end UniquenessOfConditionalExpectation
Diff
@@ -3,8 +3,8 @@ Copyright (c) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 -/
-import MeasureTheory.Function.AeEqOfIntegral
-import MeasureTheory.Function.ConditionalExpectation.AeMeasurable
+import MeasureTheory.Function.AEEqOfIntegral
+import MeasureTheory.Function.ConditionalExpectation.AEMeasurable
 
 #align_import measure_theory.function.conditional_expectation.unique from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
 
@@ -34,7 +34,7 @@ open scoped ENNReal MeasureTheory
 
 namespace MeasureTheory
 
-variable {α E' F' 𝕜 : Type _} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [IsROrC 𝕜]
+variable {α E' F' 𝕜 : Type _} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [RCLike 𝕜]
   -- 𝕜 for ℝ or ℂ
   -- E' for an inner product space on which we compute integrals
   [NormedAddCommGroup E']
Diff
@@ -135,7 +135,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
     ∀ s, measurable_set[m] s → μ.trim hm s < ∞ → @integrable_on _ _ m _ (hfm.mk f) s (μ.trim hm) :=
     by
     intro s hs hμs
-    rw [trim_measurable_set_eq hm hs] at hμs 
+    rw [trim_measurable_set_eq hm hs] at hμs
     rw [integrable_on, restrict_trim hm _ hs]
     refine' integrable.trim hm _ hfm.strongly_measurable_mk
     exact integrable.congr (hf_int_finite s hs hμs) (ae_restrict_of_ae hfm.ae_eq_mk)
@@ -143,7 +143,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
     ∀ s, measurable_set[m] s → μ.trim hm s < ∞ → @integrable_on _ _ m _ (hgm.mk g) s (μ.trim hm) :=
     by
     intro s hs hμs
-    rw [trim_measurable_set_eq hm hs] at hμs 
+    rw [trim_measurable_set_eq hm hs] at hμs
     rw [integrable_on, restrict_trim hm _ hs]
     refine' integrable.trim hm _ hgm.strongly_measurable_mk
     exact integrable.congr (hg_int_finite s hs hμs) (ae_restrict_of_ae hgm.ae_eq_mk)
@@ -153,7 +153,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
         μ.trim hm s < ∞ → ∫ x in s, hfm.mk f x ∂μ.trim hm = ∫ x in s, hgm.mk g x ∂μ.trim hm :=
     by
     intro s hs hμs
-    rw [trim_measurable_set_eq hm hs] at hμs 
+    rw [trim_measurable_set_eq hm hs] at hμs
     rw [restrict_trim hm _ hs, ← integral_trim hm hfm.strongly_measurable_mk, ←
       integral_trim hm hgm.strongly_measurable_mk,
       integral_congr_ae (ae_restrict_of_ae hfm.ae_eq_mk.symm),
Diff
@@ -3,8 +3,8 @@ Copyright (c) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 -/
-import Mathbin.MeasureTheory.Function.AeEqOfIntegral
-import Mathbin.MeasureTheory.Function.ConditionalExpectation.AeMeasurable
+import MeasureTheory.Function.AeEqOfIntegral
+import MeasureTheory.Function.ConditionalExpectation.AeMeasurable
 
 #align_import measure_theory.function.conditional_expectation.unique from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
 
Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2021 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 measure_theory.function.conditional_expectation.unique
-! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Function.AeEqOfIntegral
 import Mathbin.MeasureTheory.Function.ConditionalExpectation.AeMeasurable
 
+#align_import measure_theory.function.conditional_expectation.unique from "leanprover-community/mathlib"@"8af7091a43227e179939ba132e54e54e9f3b089a"
+
 /-!
 # Uniqueness of the conditional expectation
 
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 measure_theory.function.conditional_expectation.unique
-! leanprover-community/mathlib commit d8bbb04e2d2a44596798a9207ceefc0fb236e41e
+! leanprover-community/mathlib commit 8af7091a43227e179939ba132e54e54e9f3b089a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.MeasureTheory.Function.ConditionalExpectation.AeMeasurable
 /-!
 # Uniqueness of the conditional expectation
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 Two Lp functions `f, g` which are almost everywhere strongly measurable with respect to a σ-algebra
 `m` and verify `∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ` for all `m`-measurable sets `s` are equal
 almost everywhere. This proves the uniqueness of the conditional expectation, which is not yet
Diff
@@ -48,6 +48,7 @@ section UniquenessOfConditionalExpectation
 /-! ## Uniqueness of the conditional expectation -/
 
 
+#print MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero /-
 theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lpMeas E' 𝕜 m p μ)
     (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
     (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
@@ -65,9 +66,11 @@ theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lp
     rw [integral_congr_ae hfg_restrict.symm]
     exact hf_zero s hs hμs
 #align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero
+-/
 
 variable (𝕜)
 
+#print MeasureTheory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' /-
 theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
     (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
     (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
@@ -87,7 +90,9 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
     rw [integral_congr_ae hfg_restrict.symm]
     exact hf_zero s hs hμs
 #align measure_theory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' MeasureTheory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero'
+-/
 
+#print MeasureTheory.Lp.ae_eq_of_forall_set_integral_eq' /-
 /-- **Uniqueness of the conditional expectation** -/
 theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
     (hp_ne_top : p ≠ ∞) (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
@@ -114,10 +119,12 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
     Lp.ae_eq_zero_of_forall_set_integral_eq_zero' 𝕜 hm (f - g) hp_ne_zero hp_ne_top hfg_int hfg'
       hfg_meas
 #align measure_theory.Lp.ae_eq_of_forall_set_integral_eq' MeasureTheory.Lp.ae_eq_of_forall_set_integral_eq'
+-/
 
 variable {𝕜}
 
-theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
+#print MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigmaFinite' /-
+theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     {f g : α → F'} (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
     (hfg_eq : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
@@ -153,7 +160,8 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaF
       integral_congr_ae (ae_restrict_of_ae hgm.ae_eq_mk.symm)]
     exact hfg_eq s hs hμs
   exact ae_eq_of_forall_set_integral_eq_of_sigma_finite hf_mk_int_finite hg_mk_int_finite hfg_mk_eq
-#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigma_finite'
+#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigmaFinite'
+-/
 
 end UniquenessOfConditionalExpectation
 
@@ -161,6 +169,7 @@ section IntegralNormLe
 
 variable {s : Set α}
 
+#print MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eq /-
 /-- Let `m` be a sub-σ-algebra of `m0`, `f` a `m0`-measurable function and `g` a `m`-measurable
 function, such that their integrals coincide on `m`-measurable sets with finite measure.
 Then `∫ x in s, ‖g x‖ ∂μ ≤ ∫ x in s, ‖f x‖ ∂μ` on all `m`-measurable sets with finite measure. -/
@@ -193,7 +202,9 @@ theorem integral_norm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g : 
       measure.restrict_restrict h_meas_nonpos_f]
     exact set_integral_nonpos_le (hm _ h_meas_nonpos_g) hf hfi
 #align measure_theory.integral_norm_le_of_forall_fin_meas_integral_eq MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eq
+-/
 
+#print MeasureTheory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq /-
 /-- Let `m` be a sub-σ-algebra of `m0`, `f` a `m0`-measurable function and `g` a `m`-measurable
 function, such that their integrals coincide on `m`-measurable sets with finite measure.
 Then `∫⁻ x in s, ‖g x‖₊ ∂μ ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ` on all `m`-measurable sets with finite
@@ -209,6 +220,7 @@ theorem lintegral_nnnorm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g
   · exact integral_norm_le_of_forall_fin_meas_integral_eq hm hf hfi hg hgi hgf hs hμs
   · exact integral_nonneg fun x => norm_nonneg _
 #align measure_theory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq MeasureTheory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq
+-/
 
 end IntegralNormLe
 
Diff
@@ -66,8 +66,6 @@ theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lp
     exact hf_zero s hs hμs
 #align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero
 
-include 𝕜
-
 variable (𝕜)
 
 theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
@@ -119,8 +117,6 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
 
 variable {𝕜}
 
-omit 𝕜
-
 theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     {f g : α → F'} (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
Diff
@@ -74,7 +74,7 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
     (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
     (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hf_zero : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0)
-    (hf_meas : AeStronglyMeasurable' m f μ) : f =ᵐ[μ] 0 :=
+    (hf_meas : AEStronglyMeasurable' m f μ) : f =ᵐ[μ] 0 :=
   by
   let f_meas : Lp_meas E' 𝕜 m p μ := ⟨f, hf_meas⟩
   have hf_f_meas : f =ᵐ[μ] f_meas := by simp only [coeFn_coe_base', Subtype.coe_mk]
@@ -95,7 +95,7 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
     (hp_ne_top : p ≠ ∞) (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
     (hfg : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
-    (hf_meas : AeStronglyMeasurable' m f μ) (hg_meas : AeStronglyMeasurable' m g μ) : f =ᵐ[μ] g :=
+    (hf_meas : AEStronglyMeasurable' m f μ) (hg_meas : AEStronglyMeasurable' m g μ) : f =ᵐ[μ] g :=
   by
   suffices h_sub : ⇑(f - g) =ᵐ[μ] 0
   · rw [← sub_ae_eq_zero]; exact (Lp.coe_fn_sub f g).symm.trans h_sub
@@ -125,7 +125,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaF
     {f g : α → F'} (hf_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
     (hfg_eq : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
-    (hfm : AeStronglyMeasurable' m f μ) (hgm : AeStronglyMeasurable' m g μ) : f =ᵐ[μ] g :=
+    (hfm : AEStronglyMeasurable' m f μ) (hgm : AEStronglyMeasurable' m g μ) : f =ᵐ[μ] g :=
   by
   rw [← ae_eq_trim_iff_of_ae_strongly_measurable' hm hfm hgm]
   have hf_mk_int_finite :

Changes in mathlib4

mathlib3
mathlib4
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.

Diff
@@ -19,9 +19,9 @@ defined in this file but is introduced in
 
 ## Main statements
 
-* `Lp.ae_eq_of_forall_set_integral_eq'`: two `Lp` functions verifying the equality of integrals
+* `Lp.ae_eq_of_forall_setIntegral_eq'`: two `Lp` functions verifying the equality of integrals
   defining the conditional expectation are equal.
-* `ae_eq_of_forall_set_integral_eq_of_sigma_finite'`: two functions verifying the equality of
+* `ae_eq_of_forall_setIntegral_eq_of_sigma_finite'`: two functions verifying the equality of
   integrals defining the conditional expectation are equal almost everywhere.
   Requires `[SigmaFinite (μ.trim hm)]`.
 
@@ -46,7 +46,7 @@ section UniquenessOfConditionalExpectation
 
 /-! ## Uniqueness of the conditional expectation -/
 
-theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lpMeas E' 𝕜 m p μ)
+theorem lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero (hm : m ≤ m0) (f : lpMeas E' 𝕜 m p μ)
     (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
     -- Porting note: needed to add explicit casts in the next two hypotheses
     (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn (f : Lp E' p μ) s μ)
@@ -56,7 +56,7 @@ theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lp
   refine' hfg.trans _
   -- Porting note: added
   unfold Filter.EventuallyEq at hfg
-  refine' ae_eq_zero_of_forall_set_integral_eq_of_finStronglyMeasurable_trim hm _ _ hg_sm
+  refine' ae_eq_zero_of_forall_setIntegral_eq_of_finStronglyMeasurable_trim hm _ _ hg_sm
   · intro s hs hμs
     have hfg_restrict : f =ᵐ[μ.restrict s] g := ae_restrict_of_ae hfg
     rw [IntegrableOn, integrable_congr hfg_restrict.symm]
@@ -65,11 +65,15 @@ theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lp
     have hfg_restrict : f =ᵐ[μ.restrict s] g := ae_restrict_of_ae hfg
     rw [integral_congr_ae hfg_restrict.symm]
     exact hf_zero s hs hμs
-#align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero
+#align measure_theory.Lp_meas.ae_eq_zero_of_forall_set_integral_eq_zero MeasureTheory.lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero
+
+@[deprecated]
+alias lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero :=
+  lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero -- deprecated on 2024-04-17
 
 variable (𝕜)
 
-theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
+theorem Lp.ae_eq_zero_of_forall_setIntegral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
     (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
     (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hf_zero : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0)
@@ -78,7 +82,7 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
   -- Porting note: `simp only` does not call `rfl` to try to close the goal. See https://github.com/leanprover-community/mathlib4/issues/5025
   have hf_f_meas : f =ᵐ[μ] f_meas := by simp only [Subtype.coe_mk]; rfl
   refine' hf_f_meas.trans _
-  refine' lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero hm f_meas hp_ne_zero hp_ne_top _ _
+  refine' lpMeas.ae_eq_zero_of_forall_setIntegral_eq_zero hm f_meas hp_ne_zero hp_ne_top _ _
   · intro s hs hμs
     have hfg_restrict : f =ᵐ[μ.restrict s] f_meas := ae_restrict_of_ae hf_f_meas
     rw [IntegrableOn, integrable_congr hfg_restrict.symm]
@@ -87,10 +91,14 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
     have hfg_restrict : f =ᵐ[μ.restrict s] f_meas := ae_restrict_of_ae hf_f_meas
     rw [integral_congr_ae hfg_restrict.symm]
     exact hf_zero s hs hμs
-#align measure_theory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' MeasureTheory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero'
+#align measure_theory.Lp.ae_eq_zero_of_forall_set_integral_eq_zero' MeasureTheory.Lp.ae_eq_zero_of_forall_setIntegral_eq_zero'
+
+@[deprecated]
+alias Lp.ae_eq_zero_of_forall_set_integral_eq_zero' :=
+  Lp.ae_eq_zero_of_forall_setIntegral_eq_zero' -- deprecated on 2024-04-17
 
 /-- **Uniqueness of the conditional expectation** -/
-theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
+theorem Lp.ae_eq_of_forall_setIntegral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
     (hp_ne_top : p ≠ ∞) (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hg_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn g s μ)
     (hfg : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
@@ -110,13 +118,17 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
   have hfg_meas : AEStronglyMeasurable' m (⇑(f - g)) μ :=
     AEStronglyMeasurable'.congr (hf_meas.sub hg_meas) (Lp.coeFn_sub f g).symm
   exact
-    Lp.ae_eq_zero_of_forall_set_integral_eq_zero' 𝕜 hm (f - g) hp_ne_zero hp_ne_top hfg_int hfg'
+    Lp.ae_eq_zero_of_forall_setIntegral_eq_zero' 𝕜 hm (f - g) hp_ne_zero hp_ne_top hfg_int hfg'
       hfg_meas
-#align measure_theory.Lp.ae_eq_of_forall_set_integral_eq' MeasureTheory.Lp.ae_eq_of_forall_set_integral_eq'
+#align measure_theory.Lp.ae_eq_of_forall_set_integral_eq' MeasureTheory.Lp.ae_eq_of_forall_setIntegral_eq'
+
+@[deprecated]
+alias Lp.ae_eq_of_forall_set_integral_eq' :=
+  Lp.ae_eq_of_forall_setIntegral_eq' -- deprecated on 2024-04-17
 
 variable {𝕜}
 
-theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
+theorem ae_eq_of_forall_setIntegral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     {f g : α → F'} (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hg_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn g s μ)
     (hfg_eq : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
@@ -155,8 +167,12 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
       integral_congr_ae (ae_restrict_of_ae hfm.ae_eq_mk.symm),
       integral_congr_ae (ae_restrict_of_ae hgm.ae_eq_mk.symm)]
     exact hfg_eq s hs hμs
-  exact ae_eq_of_forall_set_integral_eq_of_sigmaFinite hf_mk_int_finite hg_mk_int_finite hfg_mk_eq
-#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_set_integral_eq_of_sigmaFinite'
+  exact ae_eq_of_forall_setIntegral_eq_of_sigmaFinite hf_mk_int_finite hg_mk_int_finite hfg_mk_eq
+#align measure_theory.ae_eq_of_forall_set_integral_eq_of_sigma_finite' MeasureTheory.ae_eq_of_forall_setIntegral_eq_of_sigmaFinite'
+
+@[deprecated]
+alias ae_eq_of_forall_set_integral_eq_of_sigmaFinite' :=
+  ae_eq_of_forall_setIntegral_eq_of_sigmaFinite' -- deprecated on 2024-04-17
 
 end UniquenessOfConditionalExpectation
 
@@ -187,13 +203,13 @@ theorem integral_norm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g : 
         ((measure_mono (Set.inter_subset_right _ _)).trans_lt (lt_top_iff_ne_top.mpr hμs)),
       ← Measure.restrict_restrict (hm _ h_meas_nonneg_g), ←
       Measure.restrict_restrict h_meas_nonneg_f]
-    exact set_integral_le_nonneg (hm _ h_meas_nonneg_g) hf hfi
+    exact setIntegral_le_nonneg (hm _ h_meas_nonneg_g) hf hfi
   · rw [Measure.restrict_restrict (hm _ h_meas_nonpos_g), Measure.restrict_restrict h_meas_nonpos_f,
       hgf _ (@MeasurableSet.inter α m _ _ h_meas_nonpos_g hs)
         ((measure_mono (Set.inter_subset_right _ _)).trans_lt (lt_top_iff_ne_top.mpr hμs)),
       ← Measure.restrict_restrict (hm _ h_meas_nonpos_g), ←
       Measure.restrict_restrict h_meas_nonpos_f]
-    exact set_integral_nonpos_le (hm _ h_meas_nonpos_g) hf hfi
+    exact setIntegral_nonpos_le (hm _ h_meas_nonpos_g) hf hfi
 #align measure_theory.integral_norm_le_of_forall_fin_meas_integral_eq MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eq
 
 /-- Let `m` be a sub-σ-algebra of `m0`, `f` an `m0`-measurable function and `g` an `m`-measurable
chore: Rename IsROrC to RCLike (#10819)

IsROrC contains data, which goes against the expectation that classes prefixed with Is are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC to RCLike.

Diff
@@ -33,7 +33,7 @@ open scoped ENNReal MeasureTheory
 
 namespace MeasureTheory
 
-variable {α E' F' 𝕜 : Type*} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [IsROrC 𝕜]
+variable {α E' F' 𝕜 : Type*} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [RCLike 𝕜]
   -- 𝕜 for ℝ or ℂ
   -- E' for an inner product space on which we compute integrals
   [NormedAddCommGroup E']
feat: Positivity extension for Bochner integral (#10661)

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

Diff
@@ -208,7 +208,7 @@ theorem lintegral_nnnorm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g
   rw [← ofReal_integral_norm_eq_lintegral_nnnorm hfi, ←
     ofReal_integral_norm_eq_lintegral_nnnorm hgi, ENNReal.ofReal_le_ofReal_iff]
   · exact integral_norm_le_of_forall_fin_meas_integral_eq hm hf hfi hg hgi hgf hs hμs
-  · exact integral_nonneg fun x => norm_nonneg _
+  · positivity
 #align measure_theory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq MeasureTheory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq
 
 end IntegralNormLE
chore: remove stream-of-consciousness uses of have, replace and suffices (#10640)

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

This follows on from #6964.

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

Diff
@@ -96,8 +96,8 @@ theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (
     (hfg : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
     (hf_meas : AEStronglyMeasurable' m f μ) (hg_meas : AEStronglyMeasurable' m g μ) :
     f =ᵐ[μ] g := by
-  suffices h_sub : ⇑(f - g) =ᵐ[μ] 0
-  · rw [← sub_ae_eq_zero]; exact (Lp.coeFn_sub f g).symm.trans h_sub
+  suffices h_sub : ⇑(f - g) =ᵐ[μ] 0 by
+    rw [← sub_ae_eq_zero]; exact (Lp.coeFn_sub f g).symm.trans h_sub
   have hfg' : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → (∫ x in s, (f - g) x ∂μ) = 0 := by
     intro s hs hμs
     rw [integral_congr_ae (ae_restrict_of_ae (Lp.coeFn_sub f g))]
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.

Diff
@@ -33,7 +33,7 @@ open scoped ENNReal MeasureTheory
 
 namespace MeasureTheory
 
-variable {α E' F' 𝕜 : Type _} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [IsROrC 𝕜]
+variable {α E' F' 𝕜 : Type*} {p : ℝ≥0∞} {m m0 : MeasurableSpace α} {μ : Measure α} [IsROrC 𝕜]
   -- 𝕜 for ℝ or ℂ
   -- E' for an inner product space on which we compute integrals
   [NormedAddCommGroup E']
chore: script to replace headers with #align_import statements (#5979)

Open in Gitpod

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

Diff
@@ -2,15 +2,12 @@
 Copyright (c) 2021 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 measure_theory.function.conditional_expectation.unique
-! leanprover-community/mathlib commit d8bbb04e2d2a44596798a9207ceefc0fb236e41e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Function.AEEqOfIntegral
 import Mathlib.MeasureTheory.Function.ConditionalExpectation.AEMeasurable
 
+#align_import measure_theory.function.conditional_expectation.unique from "leanprover-community/mathlib"@"d8bbb04e2d2a44596798a9207ceefc0fb236e41e"
+
 /-!
 # Uniqueness of the conditional expectation
 
chore: fix grammar in docs (#5668)
Diff
@@ -167,7 +167,7 @@ section IntegralNormLE
 
 variable {s : Set α}
 
-/-- Let `m` be a sub-σ-algebra of `m0`, `f` a `m0`-measurable function and `g` a `m`-measurable
+/-- Let `m` be a sub-σ-algebra of `m0`, `f` an `m0`-measurable function and `g` an `m`-measurable
 function, such that their integrals coincide on `m`-measurable sets with finite measure.
 Then `∫ x in s, ‖g x‖ ∂μ ≤ ∫ x in s, ‖f x‖ ∂μ` on all `m`-measurable sets with finite measure. -/
 theorem integral_norm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g : α → ℝ}
@@ -199,7 +199,7 @@ theorem integral_norm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g : 
     exact set_integral_nonpos_le (hm _ h_meas_nonpos_g) hf hfi
 #align measure_theory.integral_norm_le_of_forall_fin_meas_integral_eq MeasureTheory.integral_norm_le_of_forall_fin_meas_integral_eq
 
-/-- Let `m` be a sub-σ-algebra of `m0`, `f` a `m0`-measurable function and `g` a `m`-measurable
+/-- Let `m` be a sub-σ-algebra of `m0`, `f` an `m0`-measurable function and `g` an `m`-measurable
 function, such that their integrals coincide on `m`-measurable sets with finite measure.
 Then `∫⁻ x in s, ‖g x‖₊ ∂μ ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ` on all `m`-measurable sets with finite
 measure. -/
chore: remove superfluous parentheses around integrals (#5591)
Diff
@@ -75,7 +75,7 @@ variable (𝕜)
 theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E' p μ)
     (hp_ne_zero : p ≠ 0) (hp_ne_top : p ≠ ∞)
     (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
-    (hf_zero : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → (∫ x in s, f x ∂μ) = 0)
+    (hf_zero : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0)
     (hf_meas : AEStronglyMeasurable' m f μ) : f =ᵐ[μ] 0 := by
   let f_meas : lpMeas E' 𝕜 m p μ := ⟨f, hf_meas⟩
   -- Porting note: `simp only` does not call `rfl` to try to close the goal. See https://github.com/leanprover-community/mathlib4/issues/5025
@@ -96,7 +96,7 @@ theorem Lp.ae_eq_zero_of_forall_set_integral_eq_zero' (hm : m ≤ m0) (f : Lp E'
 theorem Lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : Lp E' p μ) (hp_ne_zero : p ≠ 0)
     (hp_ne_top : p ≠ ∞) (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hg_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn g s μ)
-    (hfg : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ)
+    (hfg : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
     (hf_meas : AEStronglyMeasurable' m f μ) (hg_meas : AEStronglyMeasurable' m g μ) :
     f =ᵐ[μ] g := by
   suffices h_sub : ⇑(f - g) =ᵐ[μ] 0
@@ -122,7 +122,7 @@ variable {𝕜}
 theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     {f g : α → F'} (hf_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn f s μ)
     (hg_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn g s μ)
-    (hfg_eq : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂μ)
+    (hfg_eq : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = ∫ x in s, g x ∂μ)
     (hfm : AEStronglyMeasurable' m f μ) (hgm : AEStronglyMeasurable' m g μ) : f =ᵐ[μ] g := by
   rw [← ae_eq_trim_iff_of_aeStronglyMeasurable' hm hfm hgm]
   have hf_mk_int_finite :
@@ -150,7 +150,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm : m ≤ m0) [SigmaFi
   have hfg_mk_eq :
     ∀ s : Set α,
       MeasurableSet[m] s →
-        μ.trim hm s < ∞ → (∫ x in s, hfm.mk f x ∂μ.trim hm) = ∫ x in s, hgm.mk g x ∂μ.trim hm := by
+        μ.trim hm s < ∞ → ∫ x in s, hfm.mk f x ∂μ.trim hm = ∫ x in s, hgm.mk g x ∂μ.trim hm := by
     intro s hs hμs
     rw [trim_measurableSet_eq hm hs] at hμs
     rw [restrict_trim hm _ hs, ← integral_trim hm hfm.stronglyMeasurable_mk, ←
@@ -173,7 +173,7 @@ Then `∫ x in s, ‖g x‖ ∂μ ≤ ∫ x in s, ‖f x‖ ∂μ` on all `m`-me
 theorem integral_norm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g : α → ℝ}
     (hf : StronglyMeasurable f) (hfi : IntegrableOn f s μ) (hg : StronglyMeasurable[m] g)
     (hgi : IntegrableOn g s μ)
-    (hgf : ∀ t, MeasurableSet[m] t → μ t < ∞ → (∫ x in t, g x ∂μ) = ∫ x in t, f x ∂μ)
+    (hgf : ∀ t, MeasurableSet[m] t → μ t < ∞ → ∫ x in t, g x ∂μ = ∫ x in t, f x ∂μ)
     (hs : MeasurableSet[m] s) (hμs : μ s ≠ ∞) : (∫ x in s, ‖g x‖ ∂μ) ≤ ∫ x in s, ‖f x‖ ∂μ := by
   rw [integral_norm_eq_pos_sub_neg hgi, integral_norm_eq_pos_sub_neg hfi]
   have h_meas_nonneg_g : MeasurableSet[m] {x | 0 ≤ g x} :=
@@ -206,7 +206,7 @@ measure. -/
 theorem lintegral_nnnorm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g : α → ℝ}
     (hf : StronglyMeasurable f) (hfi : IntegrableOn f s μ) (hg : StronglyMeasurable[m] g)
     (hgi : IntegrableOn g s μ)
-    (hgf : ∀ t, MeasurableSet[m] t → μ t < ∞ → (∫ x in t, g x ∂μ) = ∫ x in t, f x ∂μ)
+    (hgf : ∀ t, MeasurableSet[m] t → μ t < ∞ → ∫ x in t, g x ∂μ = ∫ x in t, f x ∂μ)
     (hs : MeasurableSet[m] s) (hμs : μ s ≠ ∞) : (∫⁻ x in s, ‖g x‖₊ ∂μ) ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ := by
   rw [← ofReal_integral_norm_eq_lintegral_nnnorm hfi, ←
     ofReal_integral_norm_eq_lintegral_nnnorm hgi, ENNReal.ofReal_le_ofReal_iff]
feat: port MeasureTheory.Function.ConditionalExpectation.Unique (#5008)

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

Dependencies 12 + 975

976 files ported (98.8%)
445153 lines ported (98.8%)
Show graph

The unported dependencies are

The following 1 dependencies have changed in mathlib3 since they were ported, which may complicate porting this file