measure_theory.function.conditional_expectation.basic ⟷ Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic

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

@@ -258,15 +258,15 @@ theorem integrable_condexp : Integrable (μ[f|m]) μ :=
 #align measure_theory.integrable_condexp MeasureTheory.integrable_condexp
 -/
 
-#print MeasureTheory.set_integral_condexp /-
+#print MeasureTheory.setIntegral_condexp /-
 /-- The integral of the conditional expectation `μ[f|hm]` over an `m`-measurable set is equal to
 the integral of `f` on that set. -/
-theorem set_integral_condexp (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : Integrable f μ)
+theorem setIntegral_condexp (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : Integrable f μ)
     (hs : measurable_set[m] s) : ∫ x in s, (μ[f|m]) x ∂μ = ∫ x in s, f x ∂μ :=
   by
   rw [set_integral_congr_ae (hm s hs) ((condexp_ae_eq_condexp_L1 hm f).mono fun x hx _ => hx)]
   exact set_integral_condexp_L1 hf hs
-#align measure_theory.set_integral_condexp MeasureTheory.set_integral_condexp
+#align measure_theory.set_integral_condexp MeasureTheory.setIntegral_condexp
 -/
 
 #print MeasureTheory.integral_condexp /-
@@ -279,11 +279,11 @@ theorem integral_condexp (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] (hf :
 #align measure_theory.integral_condexp MeasureTheory.integral_condexp
 -/
 
-#print MeasureTheory.ae_eq_condexp_of_forall_set_integral_eq /-
+#print MeasureTheory.ae_eq_condexp_of_forall_setIntegral_eq /-
 /-- **Uniqueness of the conditional expectation**
 If a function is a.e. `m`-measurable, verifies an integrability condition and has same integral
 as `f` on all `m`-measurable sets, then it is a.e. equal to `μ[f|hm]`. -/
-theorem ae_eq_condexp_of_forall_set_integral_eq (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
+theorem ae_eq_condexp_of_forall_setIntegral_eq (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     {f g : α → F'} (hf : Integrable f μ)
     (hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
     (hg_eq : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, g x ∂μ = ∫ x in s, f x ∂μ)
@@ -294,7 +294,7 @@ theorem ae_eq_condexp_of_forall_set_integral_eq (hm : m ≤ m0) [SigmaFinite (μ
       (fun s hs hμs => integrable_condexp.integrable_on) (fun s hs hμs => _) hgm
       (strongly_measurable.ae_strongly_measurable' strongly_measurable_condexp)
   rw [hg_eq s hs hμs, set_integral_condexp hm hf hs]
-#align measure_theory.ae_eq_condexp_of_forall_set_integral_eq MeasureTheory.ae_eq_condexp_of_forall_set_integral_eq
+#align measure_theory.ae_eq_condexp_of_forall_set_integral_eq MeasureTheory.ae_eq_condexp_of_forall_setIntegral_eq
 -/
 
 #print MeasureTheory.condexp_bot' /-

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

@@ -74,7 +74,7 @@ open scoped ENNReal Topology BigOperators MeasureTheory
 
 namespace MeasureTheory
 
-variable {α F F' 𝕜 : Type _} {p : ℝ≥0∞} [IsROrC 𝕜]
+variable {α F F' 𝕜 : Type _} {p : ℝ≥0∞} [RCLike 𝕜]
   -- 𝕜 for ℝ or ℂ
   -- F for a Lp submodule
   [NormedAddCommGroup F]

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

@@ -274,7 +274,7 @@ theorem integral_condexp (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] (hf :
     ∫ x, (μ[f|m]) x ∂μ = ∫ x, f x ∂μ :=
   by
   suffices ∫ x in Set.univ, (μ[f|m]) x ∂μ = ∫ x in Set.univ, f x ∂μ by
-    simp_rw [integral_univ] at this ; exact this
+    simp_rw [integral_univ] at this; exact this
   exact set_integral_condexp hm hf (@MeasurableSet.univ _ m)
 #align measure_theory.integral_condexp MeasureTheory.integral_condexp
 -/
@@ -304,7 +304,7 @@ theorem condexp_bot' [hμ : μ.ae.ne_bot] (f : α → F') :
   by_cases hμ_finite : is_finite_measure μ
   swap
   · have h : ¬sigma_finite (μ.trim bot_le) := by rwa [sigma_finite_trim_bot_iff]
-    rw [not_is_finite_measure_iff] at hμ_finite 
+    rw [not_is_finite_measure_iff] at hμ_finite
     rw [condexp_of_not_sigma_finite bot_le h]
     simp only [hμ_finite, ENNReal.top_toReal, inv_zero, zero_smul]
     rfl
@@ -315,7 +315,7 @@ theorem condexp_bot' [hμ : μ.ae.ne_bot] (f : α → F') :
   obtain ⟨c, h_eq⟩ := strongly_measurable_bot_iff.mp h_meas
   rw [h_eq]
   have h_integral : ∫ x, (μ[f|⊥]) x ∂μ = ∫ x, f x ∂μ := integral_condexp bot_le hf
-  simp_rw [h_eq, integral_const] at h_integral 
+  simp_rw [h_eq, integral_const] at h_integral
   rw [← h_integral, ← smul_assoc, smul_eq_mul, inv_mul_cancel, one_smul]
   rw [Ne.def, ENNReal.toReal_eq_zero_iff, Auto.not_or_eq, measure.measure_univ_eq_zero, ← ae_eq_bot,
     ← Ne.def, ← ne_bot_iff]
@@ -331,7 +331,7 @@ theorem condexp_bot_ae_eq (f : α → F') :
   · refine' eventually_of_forall fun x => _
     rw [condexp_bot' f]
     exact h
-  · rw [ne_bot_iff, Classical.not_not, ae_eq_bot] at h 
+  · rw [ne_bot_iff, Classical.not_not, ae_eq_bot] at h
     simp only [h, ae_zero]
 #align measure_theory.condexp_bot_ae_eq MeasureTheory.condexp_bot_ae_eq
 -/

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

@@ -169,13 +169,13 @@ theorem condexp_ae_eq_condexpL1 (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)
 #align measure_theory.condexp_ae_eq_condexp_L1 MeasureTheory.condexp_ae_eq_condexpL1
 -/
 
-#print MeasureTheory.condexp_ae_eq_condexpL1Clm /-
-theorem condexp_ae_eq_condexpL1Clm (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : Integrable f μ) :
-    μ[f|m] =ᵐ[μ] condexpL1Clm hm μ (hf.toL1 f) :=
+#print MeasureTheory.condexp_ae_eq_condexpL1CLM /-
+theorem condexp_ae_eq_condexpL1CLM (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : Integrable f μ) :
+    μ[f|m] =ᵐ[μ] condexpL1CLM hm μ (hf.toL1 f) :=
   by
   refine' (condexp_ae_eq_condexp_L1 hm f).trans (eventually_of_forall fun x => _)
   rw [condexp_L1_eq hf]
-#align measure_theory.condexp_ae_eq_condexp_L1_clm MeasureTheory.condexp_ae_eq_condexpL1Clm
+#align measure_theory.condexp_ae_eq_condexp_L1_clm MeasureTheory.condexp_ae_eq_condexpL1CLM
 -/
 
 #print MeasureTheory.condexp_undef /-

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

@@ -3,7 +3,7 @@ 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.ConditionalExpectation.CondexpL1
+import MeasureTheory.Function.ConditionalExpectation.CondexpL1
 
 #align_import measure_theory.function.conditional_expectation.basic from "leanprover-community/mathlib"@"e160cefedc932ce41c7049bf0c4b0f061d06216e"
 

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

@@ -2,14 +2,11 @@
 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.basic
-! leanprover-community/mathlib commit e160cefedc932ce41c7049bf0c4b0f061d06216e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Function.ConditionalExpectation.CondexpL1
 
+#align_import measure_theory.function.conditional_expectation.basic from "leanprover-community/mathlib"@"e160cefedc932ce41c7049bf0c4b0f061d06216e"
+
 /-! # Conditional expectation
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

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

@@ -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.basic
-! leanprover-community/mathlib commit d8bbb04e2d2a44596798a9207ceefc0fb236e41e
+! leanprover-community/mathlib commit e160cefedc932ce41c7049bf0c4b0f061d06216e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -12,6 +12,9 @@ import Mathbin.MeasureTheory.Function.ConditionalExpectation.CondexpL1
 
 /-! # Conditional expectation
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We build the conditional expectation of an integrable function `f` with value in a Banach space
 with respect to a measure `μ` (defined on a measurable space structure `m0`) and a measurable space
 structure `m` with `hm : m ≤ m0` (a sub-sigma-algebra). This is an `m`-strongly measurable

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -236,14 +236,14 @@ theorem condexp_congr_ae (h : f =ᵐ[μ] g) : μ[f|m] =ᵐ[μ] μ[g|m] :=
 #align measure_theory.condexp_congr_ae MeasureTheory.condexp_congr_ae
 -/
 
-#print MeasureTheory.condexp_of_aEStronglyMeasurable' /-
-theorem condexp_of_aEStronglyMeasurable' (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] {f : α → F'}
+#print MeasureTheory.condexp_of_aestronglyMeasurable' /-
+theorem condexp_of_aestronglyMeasurable' (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] {f : α → F'}
     (hf : AEStronglyMeasurable' m f μ) (hfi : Integrable f μ) : μ[f|m] =ᵐ[μ] f :=
   by
   refine' ((condexp_congr_ae hf.ae_eq_mk).trans _).trans hf.ae_eq_mk.symm
   rw [condexp_of_strongly_measurable hm hf.strongly_measurable_mk
       ((integrable_congr hf.ae_eq_mk).mp hfi)]
-#align measure_theory.condexp_of_ae_strongly_measurable' MeasureTheory.condexp_of_aEStronglyMeasurable'
+#align measure_theory.condexp_of_ae_strongly_measurable' MeasureTheory.condexp_of_aestronglyMeasurable'
 -/
 
 #print MeasureTheory.integrable_condexp /-

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -87,6 +87,7 @@ open scoped Classical
 
 variable {𝕜} {m m0 : MeasurableSpace α} {μ : Measure α} {f g : α → F'} {s : Set α}
 
+#print MeasureTheory.condexp /-
 /-- Conditional expectation of a function. It is defined as 0 if any one of the following conditions
 is true:
 - `m` is not a sub-σ-algebra of `m0`,
@@ -98,27 +99,33 @@ noncomputable irreducible_def condexp (m : MeasurableSpace α) {m0 : MeasurableS
     if h : SigmaFinite (μ.trim hm) ∧ Integrable f μ then
       if strongly_measurable[m] f then f
       else
-        (@aEStronglyMeasurable'_condexpL1 _ _ _ _ _ m m0 μ hm h.1 _).mk
+        (@aestronglyMeasurable'_condexpL1 _ _ _ _ _ m m0 μ hm h.1 _).mk
           (@condexpL1 _ _ _ _ _ _ _ hm μ h.1 f)
     else 0
   else 0
 #align measure_theory.condexp MeasureTheory.condexp
+-/
 
 -- We define notation `μ[f|m]` for the conditional expectation of `f` with respect to `m`.
 scoped notation μ "[" f "|" m "]" => MeasureTheory.condexp m μ f
 
+#print MeasureTheory.condexp_of_not_le /-
 theorem condexp_of_not_le (hm_not : ¬m ≤ m0) : μ[f|m] = 0 := by rw [condexp, dif_neg hm_not]
 #align measure_theory.condexp_of_not_le MeasureTheory.condexp_of_not_le
+-/
 
+#print MeasureTheory.condexp_of_not_sigmaFinite /-
 theorem condexp_of_not_sigmaFinite (hm : m ≤ m0) (hμm_not : ¬SigmaFinite (μ.trim hm)) :
     μ[f|m] = 0 := by rw [condexp, dif_pos hm, dif_neg]; push_neg; exact fun h => absurd h hμm_not
 #align measure_theory.condexp_of_not_sigma_finite MeasureTheory.condexp_of_not_sigmaFinite
+-/
 
+#print MeasureTheory.condexp_of_sigmaFinite /-
 theorem condexp_of_sigmaFinite (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] :
     μ[f|m] =
       if Integrable f μ then
         if strongly_measurable[m] f then f
-        else aEStronglyMeasurable'_condexpL1.mk (condexpL1 hm μ f)
+        else aestronglyMeasurable'_condexpL1.mk (condexpL1 hm μ f)
       else 0 :=
   by
   rw [condexp, dif_pos hm]
@@ -127,17 +134,23 @@ theorem condexp_of_sigmaFinite (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)]
   · rw [dif_pos hf, if_pos hf]
   · rw [dif_neg hf, if_neg hf]
 #align measure_theory.condexp_of_sigma_finite MeasureTheory.condexp_of_sigmaFinite
+-/
 
+#print MeasureTheory.condexp_of_stronglyMeasurable /-
 theorem condexp_of_stronglyMeasurable (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] {f : α → F'}
     (hf : strongly_measurable[m] f) (hfi : Integrable f μ) : μ[f|m] = f := by
   rw [condexp_of_sigma_finite hm, if_pos hfi, if_pos hf]; infer_instance
 #align measure_theory.condexp_of_strongly_measurable MeasureTheory.condexp_of_stronglyMeasurable
+-/
 
+#print MeasureTheory.condexp_const /-
 theorem condexp_const (hm : m ≤ m0) (c : F') [IsFiniteMeasure μ] :
     μ[fun x : α => c|m] = fun _ => c :=
   condexp_of_stronglyMeasurable hm (@stronglyMeasurable_const _ _ m _ _) (integrable_const c)
 #align measure_theory.condexp_const MeasureTheory.condexp_const
+-/
 
+#print MeasureTheory.condexp_ae_eq_condexpL1 /-
 theorem condexp_ae_eq_condexpL1 (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] (f : α → F') :
     μ[f|m] =ᵐ[μ] condexpL1 hm μ f :=
   by
@@ -154,14 +167,18 @@ theorem condexp_ae_eq_condexpL1 (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)
   rw [if_neg hfi, condexp_L1_undef hfi]
   exact (coe_fn_zero _ _ _).symm
 #align measure_theory.condexp_ae_eq_condexp_L1 MeasureTheory.condexp_ae_eq_condexpL1
+-/
 
+#print MeasureTheory.condexp_ae_eq_condexpL1Clm /-
 theorem condexp_ae_eq_condexpL1Clm (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : Integrable f μ) :
     μ[f|m] =ᵐ[μ] condexpL1Clm hm μ (hf.toL1 f) :=
   by
   refine' (condexp_ae_eq_condexp_L1 hm f).trans (eventually_of_forall fun x => _)
   rw [condexp_L1_eq hf]
 #align measure_theory.condexp_ae_eq_condexp_L1_clm MeasureTheory.condexp_ae_eq_condexpL1Clm
+-/
 
+#print MeasureTheory.condexp_undef /-
 theorem condexp_undef (hf : ¬Integrable f μ) : μ[f|m] = 0 :=
   by
   by_cases hm : m ≤ m0
@@ -171,7 +188,9 @@ theorem condexp_undef (hf : ¬Integrable f μ) : μ[f|m] = 0 :=
   haveI : sigma_finite (μ.trim hm) := hμm
   rw [condexp_of_sigma_finite, if_neg hf]
 #align measure_theory.condexp_undef MeasureTheory.condexp_undef
+-/
 
+#print MeasureTheory.condexp_zero /-
 @[simp]
 theorem condexp_zero : μ[(0 : α → F')|m] = 0 :=
   by
@@ -183,7 +202,9 @@ theorem condexp_zero : μ[(0 : α → F')|m] = 0 :=
   exact
     condexp_of_strongly_measurable hm (@strongly_measurable_zero _ _ m _ _) (integrable_zero _ _ _)
 #align measure_theory.condexp_zero MeasureTheory.condexp_zero
+-/
 
+#print MeasureTheory.stronglyMeasurable_condexp /-
 theorem stronglyMeasurable_condexp : strongly_measurable[m] (μ[f|m]) :=
   by
   by_cases hm : m ≤ m0
@@ -198,7 +219,9 @@ theorem stronglyMeasurable_condexp : strongly_measurable[m] (μ[f|m]) :=
   · exact ae_strongly_measurable'.strongly_measurable_mk _
   · exact strongly_measurable_zero
 #align measure_theory.strongly_measurable_condexp MeasureTheory.stronglyMeasurable_condexp
+-/
 
+#print MeasureTheory.condexp_congr_ae /-
 theorem condexp_congr_ae (h : f =ᵐ[μ] g) : μ[f|m] =ᵐ[μ] μ[g|m] :=
   by
   by_cases hm : m ≤ m0
@@ -211,7 +234,9 @@ theorem condexp_congr_ae (h : f =ᵐ[μ] g) : μ[f|m] =ᵐ[μ] μ[g|m] :=
       (Filter.EventuallyEq.trans (by rw [condexp_L1_congr_ae hm h])
         (condexp_ae_eq_condexp_L1 hm g).symm)
 #align measure_theory.condexp_congr_ae MeasureTheory.condexp_congr_ae
+-/
 
+#print MeasureTheory.condexp_of_aEStronglyMeasurable' /-
 theorem condexp_of_aEStronglyMeasurable' (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] {f : α → F'}
     (hf : AEStronglyMeasurable' m f μ) (hfi : Integrable f μ) : μ[f|m] =ᵐ[μ] f :=
   by
@@ -219,7 +244,9 @@ theorem condexp_of_aEStronglyMeasurable' (hm : m ≤ m0) [hμm : SigmaFinite (μ
   rw [condexp_of_strongly_measurable hm hf.strongly_measurable_mk
       ((integrable_congr hf.ae_eq_mk).mp hfi)]
 #align measure_theory.condexp_of_ae_strongly_measurable' MeasureTheory.condexp_of_aEStronglyMeasurable'
+-/
 
+#print MeasureTheory.integrable_condexp /-
 theorem integrable_condexp : Integrable (μ[f|m]) μ :=
   by
   by_cases hm : m ≤ m0
@@ -229,7 +256,9 @@ theorem integrable_condexp : Integrable (μ[f|m]) μ :=
   haveI : sigma_finite (μ.trim hm) := hμm
   exact (integrable_condexp_L1 f).congr (condexp_ae_eq_condexp_L1 hm f).symm
 #align measure_theory.integrable_condexp MeasureTheory.integrable_condexp
+-/
 
+#print MeasureTheory.set_integral_condexp /-
 /-- The integral of the conditional expectation `μ[f|hm]` over an `m`-measurable set is equal to
 the integral of `f` on that set. -/
 theorem set_integral_condexp (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : Integrable f μ)
@@ -238,7 +267,9 @@ theorem set_integral_condexp (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : In
   rw [set_integral_congr_ae (hm s hs) ((condexp_ae_eq_condexp_L1 hm f).mono fun x hx _ => hx)]
   exact set_integral_condexp_L1 hf hs
 #align measure_theory.set_integral_condexp MeasureTheory.set_integral_condexp
+-/
 
+#print MeasureTheory.integral_condexp /-
 theorem integral_condexp (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] (hf : Integrable f μ) :
     ∫ x, (μ[f|m]) x ∂μ = ∫ x, f x ∂μ :=
   by
@@ -246,7 +277,9 @@ theorem integral_condexp (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] (hf :
     simp_rw [integral_univ] at this ; exact this
   exact set_integral_condexp hm hf (@MeasurableSet.univ _ m)
 #align measure_theory.integral_condexp MeasureTheory.integral_condexp
+-/
 
+#print MeasureTheory.ae_eq_condexp_of_forall_set_integral_eq /-
 /-- **Uniqueness of the conditional expectation**
 If a function is a.e. `m`-measurable, verifies an integrability condition and has same integral
 as `f` on all `m`-measurable sets, then it is a.e. equal to `μ[f|hm]`. -/
@@ -262,7 +295,9 @@ theorem ae_eq_condexp_of_forall_set_integral_eq (hm : m ≤ m0) [SigmaFinite (μ
       (strongly_measurable.ae_strongly_measurable' strongly_measurable_condexp)
   rw [hg_eq s hs hμs, set_integral_condexp hm hf hs]
 #align measure_theory.ae_eq_condexp_of_forall_set_integral_eq MeasureTheory.ae_eq_condexp_of_forall_set_integral_eq
+-/
 
+#print MeasureTheory.condexp_bot' /-
 theorem condexp_bot' [hμ : μ.ae.ne_bot] (f : α → F') :
     μ[f|⊥] = fun _ => (μ Set.univ).toReal⁻¹ • ∫ x, f x ∂μ :=
   by
@@ -286,7 +321,9 @@ theorem condexp_bot' [hμ : μ.ae.ne_bot] (f : α → F') :
     ← Ne.def, ← ne_bot_iff]
   exact ⟨hμ, measure_ne_top μ Set.univ⟩
 #align measure_theory.condexp_bot' MeasureTheory.condexp_bot'
+-/
 
+#print MeasureTheory.condexp_bot_ae_eq /-
 theorem condexp_bot_ae_eq (f : α → F') :
     μ[f|⊥] =ᵐ[μ] fun _ => (μ Set.univ).toReal⁻¹ • ∫ x, f x ∂μ :=
   by
@@ -297,11 +334,15 @@ theorem condexp_bot_ae_eq (f : α → F') :
   · rw [ne_bot_iff, Classical.not_not, ae_eq_bot] at h 
     simp only [h, ae_zero]
 #align measure_theory.condexp_bot_ae_eq MeasureTheory.condexp_bot_ae_eq
+-/
 
+#print MeasureTheory.condexp_bot /-
 theorem condexp_bot [IsProbabilityMeasure μ] (f : α → F') : μ[f|⊥] = fun _ => ∫ x, f x ∂μ := by
   refine' (condexp_bot' f).trans _; rw [measure_univ, ENNReal.one_toReal, inv_one, one_smul]
 #align measure_theory.condexp_bot MeasureTheory.condexp_bot
+-/
 
+#print MeasureTheory.condexp_add /-
 theorem condexp_add (hf : Integrable f μ) (hg : Integrable g μ) :
     μ[f + g|m] =ᵐ[μ] μ[f|m] + μ[g|m] :=
   by
@@ -316,7 +357,9 @@ theorem condexp_add (hf : Integrable f μ) (hg : Integrable g μ) :
     (coe_fn_add _ _).trans
       ((condexp_ae_eq_condexp_L1 hm _).symm.add (condexp_ae_eq_condexp_L1 hm _).symm)
 #align measure_theory.condexp_add MeasureTheory.condexp_add
+-/
 
+#print MeasureTheory.condexp_finset_sum /-
 theorem condexp_finset_sum {ι : Type _} {s : Finset ι} {f : ι → α → F'}
     (hf : ∀ i ∈ s, Integrable (f i) μ) : μ[∑ i in s, f i|m] =ᵐ[μ] ∑ i in s, μ[f i|m] :=
   by
@@ -328,7 +371,9 @@ theorem condexp_finset_sum {ι : Type _} {s : Finset ι} {f : ι → α → F'}
             integrable_finset_sum' _ fun j hmem => hf j <| Finset.mem_insert_of_mem hmem).trans
         ((eventually_eq.refl _ _).add (HEq fun j hmem => hf j <| Finset.mem_insert_of_mem hmem))
 #align measure_theory.condexp_finset_sum MeasureTheory.condexp_finset_sum
+-/
 
+#print MeasureTheory.condexp_smul /-
 theorem condexp_smul (c : 𝕜) (f : α → F') : μ[c • f|m] =ᵐ[μ] c • μ[f|m] :=
   by
   by_cases hm : m ≤ m0
@@ -342,7 +387,9 @@ theorem condexp_smul (c : 𝕜) (f : α → F') : μ[c • f|m] =ᵐ[μ] c • 
   refine' (coe_fn_smul c (condexp_L1 hm μ f)).mono fun x hx1 hx2 => _
   rw [hx1, Pi.smul_apply, Pi.smul_apply, hx2]
 #align measure_theory.condexp_smul MeasureTheory.condexp_smul
+-/
 
+#print MeasureTheory.condexp_neg /-
 theorem condexp_neg (f : α → F') : μ[-f|m] =ᵐ[μ] -μ[f|m] := by
   letI : Module ℝ (α → F') := @Pi.module α (fun _ => F') ℝ _ _ fun _ => inferInstance <;>
     calc
@@ -350,14 +397,18 @@ theorem condexp_neg (f : α → F') : μ[-f|m] =ᵐ[μ] -μ[f|m] := by
       _ =ᵐ[μ] (-1 : ℝ) • μ[f|m] := (condexp_smul (-1) f)
       _ = -μ[f|m] := neg_one_smul ℝ (μ[f|m])
 #align measure_theory.condexp_neg MeasureTheory.condexp_neg
+-/
 
+#print MeasureTheory.condexp_sub /-
 theorem condexp_sub (hf : Integrable f μ) (hg : Integrable g μ) :
     μ[f - g|m] =ᵐ[μ] μ[f|m] - μ[g|m] :=
   by
   simp_rw [sub_eq_add_neg]
   exact (condexp_add hf hg.neg).trans (eventually_eq.rfl.add (condexp_neg g))
 #align measure_theory.condexp_sub MeasureTheory.condexp_sub
+-/
 
+#print MeasureTheory.condexp_condexp_of_le /-
 theorem condexp_condexp_of_le {m₁ m₂ m0 : MeasurableSpace α} {μ : Measure α} (hm₁₂ : m₁ ≤ m₂)
     (hm₂ : m₂ ≤ m0) [SigmaFinite (μ.trim hm₂)] : μ[μ[f|m₂]|m₁] =ᵐ[μ] μ[f|m₁] :=
   by
@@ -377,7 +428,9 @@ theorem condexp_condexp_of_le {m₁ m₂ m0 : MeasurableSpace α} {μ : Measure
   swap; · infer_instance
   rw [set_integral_condexp (hm₁₂.trans hm₂) hf hs, set_integral_condexp hm₂ hf (hm₁₂ s hs)]
 #align measure_theory.condexp_condexp_of_le MeasureTheory.condexp_condexp_of_le
+-/
 
+#print MeasureTheory.condexp_mono /-
 theorem condexp_mono {E} [NormedLatticeAddCommGroup E] [CompleteSpace E] [NormedSpace ℝ E]
     [OrderedSMul ℝ E] {f g : α → E} (hf : Integrable f μ) (hg : Integrable g μ) (hfg : f ≤ᵐ[μ] g) :
     μ[f|m] ≤ᵐ[μ] μ[g|m] := by
@@ -390,7 +443,9 @@ theorem condexp_mono {E} [NormedLatticeAddCommGroup E] [CompleteSpace E] [Normed
     (condexp_ae_eq_condexp_L1 hm _).trans_le
       ((condexp_L1_mono hf hg hfg).trans_eq (condexp_ae_eq_condexp_L1 hm _).symm)
 #align measure_theory.condexp_mono MeasureTheory.condexp_mono
+-/
 
+#print MeasureTheory.condexp_nonneg /-
 theorem condexp_nonneg {E} [NormedLatticeAddCommGroup E] [CompleteSpace E] [NormedSpace ℝ E]
     [OrderedSMul ℝ E] {f : α → E} (hf : 0 ≤ᵐ[μ] f) : 0 ≤ᵐ[μ] μ[f|m] :=
   by
@@ -399,7 +454,9 @@ theorem condexp_nonneg {E} [NormedLatticeAddCommGroup E] [CompleteSpace E] [Norm
     exact condexp_mono (integrable_zero _ _ _) hfint hf
   · rw [condexp_undef hfint]
 #align measure_theory.condexp_nonneg MeasureTheory.condexp_nonneg
+-/
 
+#print MeasureTheory.condexp_nonpos /-
 theorem condexp_nonpos {E} [NormedLatticeAddCommGroup E] [CompleteSpace E] [NormedSpace ℝ E]
     [OrderedSMul ℝ E] {f : α → E} (hf : f ≤ᵐ[μ] 0) : μ[f|m] ≤ᵐ[μ] 0 :=
   by
@@ -408,7 +465,9 @@ theorem condexp_nonpos {E} [NormedLatticeAddCommGroup E] [CompleteSpace E] [Norm
     exact condexp_mono hfint (integrable_zero _ _ _) hf
   · rw [condexp_undef hfint]
 #align measure_theory.condexp_nonpos MeasureTheory.condexp_nonpos
+-/
 
+#print MeasureTheory.tendsto_condexpL1_of_dominated_convergence /-
 /-- **Lebesgue dominated convergence theorem**: sufficient conditions under which almost
   everywhere convergence of a sequence of functions implies the convergence of their image by
   `condexp_L1`. -/
@@ -420,7 +479,9 @@ theorem tendsto_condexpL1_of_dominated_convergence (hm : m ≤ m0) [SigmaFinite
     Tendsto (fun n => condexpL1 hm μ (fs n)) atTop (𝓝 (condexpL1 hm μ f)) :=
   tendsto_setToFun_of_dominated_convergence _ bound_fs hfs_meas h_int_bound_fs hfs_bound hfs
 #align measure_theory.tendsto_condexp_L1_of_dominated_convergence MeasureTheory.tendsto_condexpL1_of_dominated_convergence
+-/
 
+#print MeasureTheory.tendsto_condexp_unique /-
 /-- If two sequences of functions have a.e. equal conditional expectations at each step, converge
 and verify dominated convergence hypotheses, then the conditional expectations of their limits are
 a.e. equal. -/
@@ -451,6 +512,7 @@ theorem tendsto_condexp_unique (fs gs : ℕ → α → F') (f g : α → F')
       hgs_bound hgs
   exact tendsto_nhds_unique_of_eventuallyEq hcond_gs hcond_fs (eventually_of_forall hn_eq)
 #align measure_theory.tendsto_condexp_unique MeasureTheory.tendsto_condexp_unique
+-/
 
 end MeasureTheory
 

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

@@ -104,7 +104,6 @@ noncomputable irreducible_def condexp (m : MeasurableSpace α) {m0 : MeasurableS
   else 0
 #align measure_theory.condexp MeasureTheory.condexp
 
--- mathport name: measure_theory.condexp
 -- We define notation `μ[f|m]` for the conditional expectation of `f` with respect to `m`.
 scoped notation μ "[" f "|" m "]" => MeasureTheory.condexp m μ f
 

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

@@ -98,7 +98,7 @@ noncomputable irreducible_def condexp (m : MeasurableSpace α) {m0 : MeasurableS
     if h : SigmaFinite (μ.trim hm) ∧ Integrable f μ then
       if strongly_measurable[m] f then f
       else
-        (@aeStronglyMeasurable'_condexpL1 _ _ _ _ _ m m0 μ hm h.1 _).mk
+        (@aEStronglyMeasurable'_condexpL1 _ _ _ _ _ m m0 μ hm h.1 _).mk
           (@condexpL1 _ _ _ _ _ _ _ hm μ h.1 f)
     else 0
   else 0
@@ -119,7 +119,7 @@ theorem condexp_of_sigmaFinite (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)]
     μ[f|m] =
       if Integrable f μ then
         if strongly_measurable[m] f then f
-        else aeStronglyMeasurable'_condexpL1.mk (condexpL1 hm μ f)
+        else aEStronglyMeasurable'_condexpL1.mk (condexpL1 hm μ f)
       else 0 :=
   by
   rw [condexp, dif_pos hm]
@@ -213,13 +213,13 @@ theorem condexp_congr_ae (h : f =ᵐ[μ] g) : μ[f|m] =ᵐ[μ] μ[g|m] :=
         (condexp_ae_eq_condexp_L1 hm g).symm)
 #align measure_theory.condexp_congr_ae MeasureTheory.condexp_congr_ae
 
-theorem condexp_of_aeStronglyMeasurable' (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] {f : α → F'}
-    (hf : AeStronglyMeasurable' m f μ) (hfi : Integrable f μ) : μ[f|m] =ᵐ[μ] f :=
+theorem condexp_of_aEStronglyMeasurable' (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] {f : α → F'}
+    (hf : AEStronglyMeasurable' m f μ) (hfi : Integrable f μ) : μ[f|m] =ᵐ[μ] f :=
   by
   refine' ((condexp_congr_ae hf.ae_eq_mk).trans _).trans hf.ae_eq_mk.symm
   rw [condexp_of_strongly_measurable hm hf.strongly_measurable_mk
       ((integrable_congr hf.ae_eq_mk).mp hfi)]
-#align measure_theory.condexp_of_ae_strongly_measurable' MeasureTheory.condexp_of_aeStronglyMeasurable'
+#align measure_theory.condexp_of_ae_strongly_measurable' MeasureTheory.condexp_of_aEStronglyMeasurable'
 
 theorem integrable_condexp : Integrable (μ[f|m]) μ :=
   by
@@ -255,7 +255,7 @@ theorem ae_eq_condexp_of_forall_set_integral_eq (hm : m ≤ m0) [SigmaFinite (μ
     {f g : α → F'} (hf : Integrable f μ)
     (hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
     (hg_eq : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, g x ∂μ = ∫ x in s, f x ∂μ)
-    (hgm : AeStronglyMeasurable' m g μ) : g =ᵐ[μ] μ[f|m] :=
+    (hgm : AEStronglyMeasurable' m g μ) : g =ᵐ[μ] μ[f|m] :=
   by
   refine'
     ae_eq_of_forall_set_integral_eq_of_sigma_finite' hm hg_int_finite

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

@@ -4,13 +4,11 @@ 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.basic
-! leanprover-community/mathlib commit 00abe0695d8767201e6d008afa22393978bb324d
+! leanprover-community/mathlib commit d8bbb04e2d2a44596798a9207ceefc0fb236e41e
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.InnerProductSpace.Projection
-import Mathbin.MeasureTheory.Function.L2Space
-import Mathbin.MeasureTheory.Function.AeEqOfIntegral
+import Mathbin.MeasureTheory.Function.ConditionalExpectation.CondexpL1
 
 /-! # Conditional expectation
 
@@ -33,6 +31,10 @@ The construction is done in four steps:
   `α → E` equal to 0 if `f` is not integrable, and equal to an `m`-measurable representative of
   `condexp_L1_clm` applied to `[f]`, the equivalence class of `f` in `L¹`.
 
+The first step is done in `measure_theory.function.conditional_expectation.condexp_L2`, the two
+next steps in `measure_theory.function.conditional_expectation.condexp_L1` and the final step is
+performed in this file.
+
 ## Main results
 
 The conditional expectation and its properties
@@ -50,11 +52,6 @@ linear map `condexp_L1_clm` from `L1` to `L1`. `condexp` should be used in most
 
 Uniqueness of the conditional expectation
 
-* `Lp.ae_eq_of_forall_set_integral_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
-  integrals defining the conditional expectation are equal almost everywhere.
-  Requires `[sigma_finite (μ.trim hm)]`.
 * `ae_eq_condexp_of_forall_set_integral_eq`: an a.e. `m`-measurable function which verifies the
   equality of integrals is a.e. equal to `condexp`.
 
@@ -64,14 +61,6 @@ For a measure `μ` defined on a measurable space structure `m0`, another measura
 `m` with `hm : m ≤ m0` (a sub-σ-algebra) and a function `f`, we define the notation
 * `μ[f|m] = condexp m μ f`.
 
-## Implementation notes
-
-Most of the results in this file are valid for a complete real normed space `F`.
-However, some lemmas also use `𝕜 : is_R_or_C`:
-* `condexp_L2` is defined only for an `inner_product_space` for now, and we use `𝕜` for its field.
-* results about scalar multiplication are stated not only for `ℝ` but also for `𝕜` if we happen to
-  have `normed_space 𝕜 F`.
-
 ## Tags
 
 conditional expectation, conditional expected value
@@ -79,1976 +68,20 @@ conditional expectation, conditional expected value
 -/
 
 
-noncomputable section
+open TopologicalSpace MeasureTheory.Lp Filter
 
-open TopologicalSpace MeasureTheory.Lp Filter ContinuousLinearMap
-
-open scoped NNReal ENNReal Topology BigOperators MeasureTheory
+open scoped ENNReal Topology BigOperators MeasureTheory
 
 namespace MeasureTheory
 
-/-- A function `f` verifies `ae_strongly_measurable' m f μ` if it is `μ`-a.e. equal to
-an `m`-strongly measurable function. This is similar to `ae_strongly_measurable`, but the
-`measurable_space` structures used for the measurability statement and for the measure are
-different. -/
-def AeStronglyMeasurable' {α β} [TopologicalSpace β] (m : MeasurableSpace α)
-    {m0 : MeasurableSpace α} (f : α → β) (μ : Measure α) : Prop :=
-  ∃ g : α → β, strongly_measurable[m] g ∧ f =ᵐ[μ] g
-#align measure_theory.ae_strongly_measurable' MeasureTheory.AeStronglyMeasurable'
-
-namespace AeStronglyMeasurable'
-
-variable {α β 𝕜 : Type _} {m m0 : MeasurableSpace α} {μ : Measure α} [TopologicalSpace β]
-  {f g : α → β}
-
-theorem congr (hf : AeStronglyMeasurable' m f μ) (hfg : f =ᵐ[μ] g) : AeStronglyMeasurable' m g μ :=
-  by obtain ⟨f', hf'_meas, hff'⟩ := hf; exact ⟨f', hf'_meas, hfg.symm.trans hff'⟩
-#align measure_theory.ae_strongly_measurable'.congr MeasureTheory.AeStronglyMeasurable'.congr
-
-theorem add [Add β] [ContinuousAdd β] (hf : AeStronglyMeasurable' m f μ)
-    (hg : AeStronglyMeasurable' m g μ) : AeStronglyMeasurable' m (f + g) μ :=
-  by
-  rcases hf with ⟨f', h_f'_meas, hff'⟩
-  rcases hg with ⟨g', h_g'_meas, hgg'⟩
-  exact ⟨f' + g', h_f'_meas.add h_g'_meas, hff'.add hgg'⟩
-#align measure_theory.ae_strongly_measurable'.add MeasureTheory.AeStronglyMeasurable'.add
-
-theorem neg [AddGroup β] [TopologicalAddGroup β] {f : α → β} (hfm : AeStronglyMeasurable' m f μ) :
-    AeStronglyMeasurable' m (-f) μ :=
-  by
-  rcases hfm with ⟨f', hf'_meas, hf_ae⟩
-  refine' ⟨-f', hf'_meas.neg, hf_ae.mono fun x hx => _⟩
-  simp_rw [Pi.neg_apply]
-  rw [hx]
-#align measure_theory.ae_strongly_measurable'.neg MeasureTheory.AeStronglyMeasurable'.neg
-
-theorem sub [AddGroup β] [TopologicalAddGroup β] {f g : α → β} (hfm : AeStronglyMeasurable' m f μ)
-    (hgm : AeStronglyMeasurable' m g μ) : AeStronglyMeasurable' m (f - g) μ :=
-  by
-  rcases hfm with ⟨f', hf'_meas, hf_ae⟩
-  rcases hgm with ⟨g', hg'_meas, hg_ae⟩
-  refine' ⟨f' - g', hf'_meas.sub hg'_meas, hf_ae.mp (hg_ae.mono fun x hx1 hx2 => _)⟩
-  simp_rw [Pi.sub_apply]
-  rw [hx1, hx2]
-#align measure_theory.ae_strongly_measurable'.sub MeasureTheory.AeStronglyMeasurable'.sub
-
-theorem const_smul [SMul 𝕜 β] [ContinuousConstSMul 𝕜 β] (c : 𝕜) (hf : AeStronglyMeasurable' m f μ) :
-    AeStronglyMeasurable' m (c • f) μ :=
-  by
-  rcases hf with ⟨f', h_f'_meas, hff'⟩
-  refine' ⟨c • f', h_f'_meas.const_smul c, _⟩
-  exact eventually_eq.fun_comp hff' fun x => c • x
-#align measure_theory.ae_strongly_measurable'.const_smul MeasureTheory.AeStronglyMeasurable'.const_smul
-
-theorem const_inner {𝕜 β} [IsROrC 𝕜] [NormedAddCommGroup β] [InnerProductSpace 𝕜 β] {f : α → β}
-    (hfm : AeStronglyMeasurable' m f μ) (c : β) :
-    AeStronglyMeasurable' m (fun x => (inner c (f x) : 𝕜)) μ :=
-  by
-  rcases hfm with ⟨f', hf'_meas, hf_ae⟩
-  refine'
-    ⟨fun x => (inner c (f' x) : 𝕜), (@strongly_measurable_const _ _ m _ _).inner hf'_meas,
-      hf_ae.mono fun x hx => _⟩
-  dsimp only
-  rw [hx]
-#align measure_theory.ae_strongly_measurable'.const_inner MeasureTheory.AeStronglyMeasurable'.const_inner
-
-/-- An `m`-strongly measurable function almost everywhere equal to `f`. -/
-def mk (f : α → β) (hfm : AeStronglyMeasurable' m f μ) : α → β :=
-  hfm.some
-#align measure_theory.ae_strongly_measurable'.mk MeasureTheory.AeStronglyMeasurable'.mk
-
-theorem stronglyMeasurable_mk {f : α → β} (hfm : AeStronglyMeasurable' m f μ) :
-    strongly_measurable[m] (hfm.mk f) :=
-  hfm.choose_spec.1
-#align measure_theory.ae_strongly_measurable'.strongly_measurable_mk MeasureTheory.AeStronglyMeasurable'.stronglyMeasurable_mk
-
-theorem ae_eq_mk {f : α → β} (hfm : AeStronglyMeasurable' m f μ) : f =ᵐ[μ] hfm.mk f :=
-  hfm.choose_spec.2
-#align measure_theory.ae_strongly_measurable'.ae_eq_mk MeasureTheory.AeStronglyMeasurable'.ae_eq_mk
-
-theorem continuous_comp {γ} [TopologicalSpace γ] {f : α → β} {g : β → γ} (hg : Continuous g)
-    (hf : AeStronglyMeasurable' m f μ) : AeStronglyMeasurable' m (g ∘ f) μ :=
-  ⟨fun x => g (hf.mk _ x),
-    @Continuous.comp_stronglyMeasurable _ _ _ m _ _ _ _ hg hf.stronglyMeasurable_mk,
-    hf.ae_eq_mk.mono fun x hx => by rw [Function.comp_apply, hx]⟩
-#align measure_theory.ae_strongly_measurable'.continuous_comp MeasureTheory.AeStronglyMeasurable'.continuous_comp
-
-end AeStronglyMeasurable'
-
-theorem aeStronglyMeasurable'_of_aeStronglyMeasurable'_trim {α β} {m m0 m0' : MeasurableSpace α}
-    [TopologicalSpace β] (hm0 : m0 ≤ m0') {μ : Measure α} {f : α → β}
-    (hf : AeStronglyMeasurable' m f (μ.trim hm0)) : AeStronglyMeasurable' m f μ := by
-  obtain ⟨g, hg_meas, hfg⟩ := hf; exact ⟨g, hg_meas, ae_eq_of_ae_eq_trim hfg⟩
-#align measure_theory.ae_strongly_measurable'_of_ae_strongly_measurable'_trim MeasureTheory.aeStronglyMeasurable'_of_aeStronglyMeasurable'_trim
-
-theorem StronglyMeasurable.aeStronglyMeasurable' {α β} {m m0 : MeasurableSpace α}
-    [TopologicalSpace β] {μ : Measure α} {f : α → β} (hf : strongly_measurable[m] f) :
-    AeStronglyMeasurable' m f μ :=
-  ⟨f, hf, ae_eq_refl _⟩
-#align measure_theory.strongly_measurable.ae_strongly_measurable' MeasureTheory.StronglyMeasurable.aeStronglyMeasurable'
-
-theorem ae_eq_trim_iff_of_aeStronglyMeasurable' {α β} [TopologicalSpace β] [MetrizableSpace β]
-    {m m0 : MeasurableSpace α} {μ : Measure α} {f g : α → β} (hm : m ≤ m0)
-    (hfm : AeStronglyMeasurable' m f μ) (hgm : AeStronglyMeasurable' m g μ) :
-    hfm.mk f =ᵐ[μ.trim hm] hgm.mk g ↔ f =ᵐ[μ] g :=
-  (ae_eq_trim_iff hm hfm.stronglyMeasurable_mk hgm.stronglyMeasurable_mk).trans
-    ⟨fun h => hfm.ae_eq_mk.trans (h.trans hgm.ae_eq_mk.symm), fun h =>
-      hfm.ae_eq_mk.symm.trans (h.trans hgm.ae_eq_mk)⟩
-#align measure_theory.ae_eq_trim_iff_of_ae_strongly_measurable' MeasureTheory.ae_eq_trim_iff_of_aeStronglyMeasurable'
-
-theorem AEStronglyMeasurable.comp_ae_measurable' {α β γ : Type _} [TopologicalSpace β]
-    {mα : MeasurableSpace α} {mγ : MeasurableSpace γ} {f : α → β} {μ : Measure γ} {g : γ → α}
-    (hf : AEStronglyMeasurable f (μ.map g)) (hg : AEMeasurable g μ) :
-    AeStronglyMeasurable' (mα.comap g) (f ∘ g) μ :=
-  ⟨hf.mk f ∘ g, hf.stronglyMeasurable_mk.comp_measurable (measurable_iff_comap_le.mpr le_rfl),
-    ae_eq_comp hg hf.ae_eq_mk⟩
-#align measure_theory.ae_strongly_measurable.comp_ae_measurable' MeasureTheory.AEStronglyMeasurable.comp_ae_measurable'
-
-/-- If the restriction to a set `s` of a σ-algebra `m` is included in the restriction to `s` of
-another σ-algebra `m₂` (hypothesis `hs`), the set `s` is `m` measurable and a function `f` almost
-everywhere supported on `s` is `m`-ae-strongly-measurable, then `f` is also
-`m₂`-ae-strongly-measurable. -/
-theorem AeStronglyMeasurable'.aeStronglyMeasurable'_of_measurableSpace_le_on {α E}
-    {m m₂ m0 : MeasurableSpace α} {μ : Measure α} [TopologicalSpace E] [Zero E] (hm : m ≤ m0)
-    {s : Set α} {f : α → E} (hs_m : measurable_set[m] s)
-    (hs : ∀ t, measurable_set[m] (s ∩ t) → measurable_set[m₂] (s ∩ t))
-    (hf : AeStronglyMeasurable' m f μ) (hf_zero : f =ᵐ[μ.restrict (sᶜ)] 0) :
-    AeStronglyMeasurable' m₂ f μ := by
-  let f' := hf.mk f
-  have h_ind_eq : s.indicator (hf.mk f) =ᵐ[μ] f :=
-    by
-    refine'
-      Filter.EventuallyEq.trans _ (indicator_ae_eq_of_restrict_compl_ae_eq_zero (hm _ hs_m) hf_zero)
-    filter_upwards [hf.ae_eq_mk] with x hx
-    by_cases hxs : x ∈ s
-    · simp [hxs, hx]
-    · simp [hxs]
-  suffices : strongly_measurable[m₂] (s.indicator (hf.mk f))
-  exact ae_strongly_measurable'.congr this.ae_strongly_measurable' h_ind_eq
-  have hf_ind : strongly_measurable[m] (s.indicator (hf.mk f)) :=
-    hf.strongly_measurable_mk.indicator hs_m
-  exact
-    hf_ind.strongly_measurable_of_measurable_space_le_on hs_m hs fun x hxs =>
-      Set.indicator_of_not_mem hxs _
-#align measure_theory.ae_strongly_measurable'.ae_strongly_measurable'_of_measurable_space_le_on MeasureTheory.AeStronglyMeasurable'.aeStronglyMeasurable'_of_measurableSpace_le_on
-
-variable {α β γ E E' F F' G G' H 𝕜 : Type _} {p : ℝ≥0∞} [IsROrC 𝕜]
+variable {α F F' 𝕜 : Type _} {p : ℝ≥0∞} [IsROrC 𝕜]
   -- 𝕜 for ℝ or ℂ
-  [TopologicalSpace β]
-  -- β for a generic topological space
-  -- E for an inner product space
-  [NormedAddCommGroup E]
-  [InnerProductSpace 𝕜 E]
-  -- E' for an inner product space on which we compute integrals
-  [NormedAddCommGroup E']
-  [InnerProductSpace 𝕜 E'] [CompleteSpace E'] [NormedSpace ℝ E']
   -- F for a Lp submodule
   [NormedAddCommGroup F]
   [NormedSpace 𝕜 F]
   -- F' for integrals on a Lp submodule
   [NormedAddCommGroup F']
   [NormedSpace 𝕜 F'] [NormedSpace ℝ F'] [CompleteSpace F']
-  -- G for a Lp add_subgroup
-  [NormedAddCommGroup G]
-  -- G' for integrals on a Lp add_subgroup
-  [NormedAddCommGroup G']
-  [NormedSpace ℝ G'] [CompleteSpace G']
-  -- H for a normed group (hypotheses of mem_ℒp)
-  [NormedAddCommGroup H]
-
-section LpMeas
-
-/-! ## The subset `Lp_meas` of `Lp` functions a.e. measurable with respect to a sub-sigma-algebra -/
-
-
-variable (F)
-
-/-- `Lp_meas_subgroup F m p μ` is the subspace of `Lp F p μ` containing functions `f` verifying
-`ae_strongly_measurable' m f μ`, i.e. functions which are `μ`-a.e. equal to
-an `m`-strongly measurable function. -/
-def lpMeasSubgroup (m : MeasurableSpace α) [MeasurableSpace α] (p : ℝ≥0∞) (μ : Measure α) :
-    AddSubgroup (Lp F p μ)
-    where
-  carrier := {f : Lp F p μ | AeStronglyMeasurable' m f μ}
-  zero_mem' := ⟨(0 : α → F), @stronglyMeasurable_zero _ _ m _ _, Lp.coeFn_zero _ _ _⟩
-  add_mem' f g hf hg := (hf.add hg).congr (Lp.coeFn_add f g).symm
-  neg_mem' f hf := AeStronglyMeasurable'.congr hf.neg (Lp.coeFn_neg f).symm
-#align measure_theory.Lp_meas_subgroup MeasureTheory.lpMeasSubgroup
-
-variable (𝕜)
-
-/-- `Lp_meas F 𝕜 m p μ` is the subspace of `Lp F p μ` containing functions `f` verifying
-`ae_strongly_measurable' m f μ`, i.e. functions which are `μ`-a.e. equal to
-an `m`-strongly measurable function. -/
-def lpMeas (m : MeasurableSpace α) [MeasurableSpace α] (p : ℝ≥0∞) (μ : Measure α) :
-    Submodule 𝕜 (Lp F p μ)
-    where
-  carrier := {f : Lp F p μ | AeStronglyMeasurable' m f μ}
-  zero_mem' := ⟨(0 : α → F), @stronglyMeasurable_zero _ _ m _ _, Lp.coeFn_zero _ _ _⟩
-  add_mem' f g hf hg := (hf.add hg).congr (Lp.coeFn_add f g).symm
-  smul_mem' c f hf := (hf.const_smul c).congr (Lp.coeFn_smul c f).symm
-#align measure_theory.Lp_meas MeasureTheory.lpMeas
-
-variable {F 𝕜}
-
-variable ()
-
-theorem mem_lpMeasSubgroup_iff_aeStronglyMeasurable' {m m0 : MeasurableSpace α} {μ : Measure α}
-    {f : Lp F p μ} : f ∈ lpMeasSubgroup F m p μ ↔ AeStronglyMeasurable' m f μ := by
-  rw [← AddSubgroup.mem_carrier, Lp_meas_subgroup, Set.mem_setOf_eq]
-#align measure_theory.mem_Lp_meas_subgroup_iff_ae_strongly_measurable' MeasureTheory.mem_lpMeasSubgroup_iff_aeStronglyMeasurable'
-
-theorem mem_lpMeas_iff_aeStronglyMeasurable' {m m0 : MeasurableSpace α} {μ : Measure α}
-    {f : Lp F p μ} : f ∈ lpMeas F 𝕜 m p μ ↔ AeStronglyMeasurable' m f μ := by
-  rw [← SetLike.mem_coe, ← Submodule.mem_carrier, Lp_meas, Set.mem_setOf_eq]
-#align measure_theory.mem_Lp_meas_iff_ae_strongly_measurable' MeasureTheory.mem_lpMeas_iff_aeStronglyMeasurable'
-
-theorem lpMeas.aeStronglyMeasurable' {m m0 : MeasurableSpace α} {μ : Measure α}
-    (f : lpMeas F 𝕜 m p μ) : AeStronglyMeasurable' m f μ :=
-  mem_lpMeas_iff_aeStronglyMeasurable'.mp f.Mem
-#align measure_theory.Lp_meas.ae_strongly_measurable' MeasureTheory.lpMeas.aeStronglyMeasurable'
-
-theorem mem_lpMeas_self {m0 : MeasurableSpace α} (μ : Measure α) (f : Lp F p μ) :
-    f ∈ lpMeas F 𝕜 m0 p μ :=
-  mem_lpMeas_iff_aeStronglyMeasurable'.mpr (Lp.aestronglyMeasurable f)
-#align measure_theory.mem_Lp_meas_self MeasureTheory.mem_lpMeas_self
-
-theorem lpMeasSubgroup_coe {m m0 : MeasurableSpace α} {μ : Measure α} {f : lpMeasSubgroup F m p μ} :
-    ⇑f = (f : Lp F p μ) :=
-  coeFn_coeBase f
-#align measure_theory.Lp_meas_subgroup_coe MeasureTheory.lpMeasSubgroup_coe
-
-theorem lpMeas_coe {m m0 : MeasurableSpace α} {μ : Measure α} {f : lpMeas F 𝕜 m p μ} :
-    ⇑f = (f : Lp F p μ) :=
-  coeFn_coeBase f
-#align measure_theory.Lp_meas_coe MeasureTheory.lpMeas_coe
-
-theorem mem_lpMeas_indicatorConstLp {m m0 : MeasurableSpace α} (hm : m ≤ m0) {μ : Measure α}
-    {s : Set α} (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) {c : F} :
-    indicatorConstLp p (hm s hs) hμs c ∈ lpMeas F 𝕜 m p μ :=
-  ⟨s.indicator fun x : α => c, (@stronglyMeasurable_const _ _ m _ _).indicator hs,
-    indicatorConstLp_coeFn⟩
-#align measure_theory.mem_Lp_meas_indicator_const_Lp MeasureTheory.mem_lpMeas_indicatorConstLp
-
-section CompleteSubspace
-
-/-! ## The subspace `Lp_meas` is complete.
-
-We define an `isometry_equiv` between `Lp_meas_subgroup` and the `Lp` space corresponding to the
-measure `μ.trim hm`. As a consequence, the completeness of `Lp` implies completeness of
-`Lp_meas_subgroup` (and `Lp_meas`). -/
-
-
-variable {ι : Type _} {m m0 : MeasurableSpace α} {μ : Measure α}
-
-/-- If `f` belongs to `Lp_meas_subgroup F m p μ`, then the measurable function it is almost
-everywhere equal to (given by `ae_measurable.mk`) belongs to `ℒp` for the measure `μ.trim hm`. -/
-theorem memℒp_trim_of_mem_lpMeasSubgroup (hm : m ≤ m0) (f : Lp F p μ)
-    (hf_meas : f ∈ lpMeasSubgroup F m p μ) :
-    Memℒp (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp hf_meas).some p (μ.trim hm) :=
-  by
-  have hf : ae_strongly_measurable' m f μ :=
-    mem_Lp_meas_subgroup_iff_ae_strongly_measurable'.mp hf_meas
-  let g := hf.some
-  obtain ⟨hg, hfg⟩ := hf.some_spec
-  change mem_ℒp g p (μ.trim hm)
-  refine' ⟨hg.ae_strongly_measurable, _⟩
-  have h_snorm_fg : snorm g p (μ.trim hm) = snorm f p μ := by rw [snorm_trim hm hg];
-    exact snorm_congr_ae hfg.symm
-  rw [h_snorm_fg]
-  exact Lp.snorm_lt_top f
-#align measure_theory.mem_ℒp_trim_of_mem_Lp_meas_subgroup MeasureTheory.memℒp_trim_of_mem_lpMeasSubgroup
-
-/-- If `f` belongs to `Lp` for the measure `μ.trim hm`, then it belongs to the subgroup
-`Lp_meas_subgroup F m p μ`. -/
-theorem mem_lpMeasSubgroup_toLp_of_trim (hm : m ≤ m0) (f : Lp F p (μ.trim hm)) :
-    (memℒp_of_memℒp_trim hm (Lp.memℒp f)).toLp f ∈ lpMeasSubgroup F m p μ :=
-  by
-  let hf_mem_ℒp := mem_ℒp_of_mem_ℒp_trim hm (Lp.mem_ℒp f)
-  rw [mem_Lp_meas_subgroup_iff_ae_strongly_measurable']
-  refine' ae_strongly_measurable'.congr _ (mem_ℒp.coe_fn_to_Lp hf_mem_ℒp).symm
-  refine' ae_strongly_measurable'_of_ae_strongly_measurable'_trim hm _
-  exact Lp.ae_strongly_measurable f
-#align measure_theory.mem_Lp_meas_subgroup_to_Lp_of_trim MeasureTheory.mem_lpMeasSubgroup_toLp_of_trim
-
-variable (F p μ)
-
-/-- Map from `Lp_meas_subgroup` to `Lp F p (μ.trim hm)`. -/
-def lpMeasSubgroupToLpTrim (hm : m ≤ m0) (f : lpMeasSubgroup F m p μ) : Lp F p (μ.trim hm) :=
-  Memℒp.toLp (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp f.Mem).some
-    (memℒp_trim_of_mem_lpMeasSubgroup hm f f.Mem)
-#align measure_theory.Lp_meas_subgroup_to_Lp_trim MeasureTheory.lpMeasSubgroupToLpTrim
-
-variable (𝕜)
-
-/-- Map from `Lp_meas` to `Lp F p (μ.trim hm)`. -/
-def lpMeasToLpTrim (hm : m ≤ m0) (f : lpMeas F 𝕜 m p μ) : Lp F p (μ.trim hm) :=
-  Memℒp.toLp (mem_lpMeas_iff_aeStronglyMeasurable'.mp f.Mem).some
-    (memℒp_trim_of_mem_lpMeasSubgroup hm f f.Mem)
-#align measure_theory.Lp_meas_to_Lp_trim MeasureTheory.lpMeasToLpTrim
-
-variable {𝕜}
-
-/-- Map from `Lp F p (μ.trim hm)` to `Lp_meas_subgroup`, inverse of
-`Lp_meas_subgroup_to_Lp_trim`. -/
-def lpTrimToLpMeasSubgroup (hm : m ≤ m0) (f : Lp F p (μ.trim hm)) : lpMeasSubgroup F m p μ :=
-  ⟨(memℒp_of_memℒp_trim hm (Lp.memℒp f)).toLp f, mem_lpMeasSubgroup_toLp_of_trim hm f⟩
-#align measure_theory.Lp_trim_to_Lp_meas_subgroup MeasureTheory.lpTrimToLpMeasSubgroup
-
-variable (𝕜)
-
-/-- Map from `Lp F p (μ.trim hm)` to `Lp_meas`, inverse of `Lp_meas_to_Lp_trim`. -/
-def lpTrimToLpMeas (hm : m ≤ m0) (f : Lp F p (μ.trim hm)) : lpMeas F 𝕜 m p μ :=
-  ⟨(memℒp_of_memℒp_trim hm (Lp.memℒp f)).toLp f, mem_lpMeasSubgroup_toLp_of_trim hm f⟩
-#align measure_theory.Lp_trim_to_Lp_meas MeasureTheory.lpTrimToLpMeas
-
-variable {F 𝕜 p μ}
-
-theorem lpMeasSubgroupToLpTrim_ae_eq (hm : m ≤ m0) (f : lpMeasSubgroup F m p μ) :
-    lpMeasSubgroupToLpTrim F p μ hm f =ᵐ[μ] f :=
-  (ae_eq_of_ae_eq_trim (Memℒp.coeFn_toLp (memℒp_trim_of_mem_lpMeasSubgroup hm (↑f) f.Mem))).trans
-    (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp f.Mem).choose_spec.2.symm
-#align measure_theory.Lp_meas_subgroup_to_Lp_trim_ae_eq MeasureTheory.lpMeasSubgroupToLpTrim_ae_eq
-
-theorem lpTrimToLpMeasSubgroup_ae_eq (hm : m ≤ m0) (f : Lp F p (μ.trim hm)) :
-    lpTrimToLpMeasSubgroup F p μ hm f =ᵐ[μ] f :=
-  Memℒp.coeFn_toLp _
-#align measure_theory.Lp_trim_to_Lp_meas_subgroup_ae_eq MeasureTheory.lpTrimToLpMeasSubgroup_ae_eq
-
-theorem lpMeasToLpTrim_ae_eq (hm : m ≤ m0) (f : lpMeas F 𝕜 m p μ) :
-    lpMeasToLpTrim F 𝕜 p μ hm f =ᵐ[μ] f :=
-  (ae_eq_of_ae_eq_trim (Memℒp.coeFn_toLp (memℒp_trim_of_mem_lpMeasSubgroup hm (↑f) f.Mem))).trans
-    (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp f.Mem).choose_spec.2.symm
-#align measure_theory.Lp_meas_to_Lp_trim_ae_eq MeasureTheory.lpMeasToLpTrim_ae_eq
-
-theorem lpTrimToLpMeas_ae_eq (hm : m ≤ m0) (f : Lp F p (μ.trim hm)) :
-    lpTrimToLpMeas F 𝕜 p μ hm f =ᵐ[μ] f :=
-  Memℒp.coeFn_toLp _
-#align measure_theory.Lp_trim_to_Lp_meas_ae_eq MeasureTheory.lpTrimToLpMeas_ae_eq
-
-/-- `Lp_trim_to_Lp_meas_subgroup` is a right inverse of `Lp_meas_subgroup_to_Lp_trim`. -/
-theorem lpMeasSubgroupToLpTrim_right_inv (hm : m ≤ m0) :
-    Function.RightInverse (lpTrimToLpMeasSubgroup F p μ hm) (lpMeasSubgroupToLpTrim F p μ hm) :=
-  by
-  intro f
-  ext1
-  refine'
-    ae_eq_trim_of_strongly_measurable hm (Lp.strongly_measurable _) (Lp.strongly_measurable _) _
-  exact (Lp_meas_subgroup_to_Lp_trim_ae_eq hm _).trans (Lp_trim_to_Lp_meas_subgroup_ae_eq hm _)
-#align measure_theory.Lp_meas_subgroup_to_Lp_trim_right_inv MeasureTheory.lpMeasSubgroupToLpTrim_right_inv
-
-/-- `Lp_trim_to_Lp_meas_subgroup` is a left inverse of `Lp_meas_subgroup_to_Lp_trim`. -/
-theorem lpMeasSubgroupToLpTrim_left_inv (hm : m ≤ m0) :
-    Function.LeftInverse (lpTrimToLpMeasSubgroup F p μ hm) (lpMeasSubgroupToLpTrim F p μ hm) :=
-  by
-  intro f
-  ext1
-  ext1
-  rw [← Lp_meas_subgroup_coe]
-  exact (Lp_trim_to_Lp_meas_subgroup_ae_eq hm _).trans (Lp_meas_subgroup_to_Lp_trim_ae_eq hm _)
-#align measure_theory.Lp_meas_subgroup_to_Lp_trim_left_inv MeasureTheory.lpMeasSubgroupToLpTrim_left_inv
-
-theorem lpMeasSubgroupToLpTrim_add (hm : m ≤ m0) (f g : lpMeasSubgroup F m p μ) :
-    lpMeasSubgroupToLpTrim F p μ hm (f + g) =
-      lpMeasSubgroupToLpTrim F p μ hm f + lpMeasSubgroupToLpTrim F p μ hm g :=
-  by
-  ext1
-  refine' eventually_eq.trans _ (Lp.coe_fn_add _ _).symm
-  refine' ae_eq_trim_of_strongly_measurable hm (Lp.strongly_measurable _) _ _
-  · exact (Lp.strongly_measurable _).add (Lp.strongly_measurable _)
-  refine' (Lp_meas_subgroup_to_Lp_trim_ae_eq hm _).trans _
-  refine'
-    eventually_eq.trans _
-      (eventually_eq.add (Lp_meas_subgroup_to_Lp_trim_ae_eq hm f).symm
-        (Lp_meas_subgroup_to_Lp_trim_ae_eq hm g).symm)
-  refine' (Lp.coe_fn_add _ _).trans _
-  simp_rw [Lp_meas_subgroup_coe]
-  exact eventually_of_forall fun x => by rfl
-#align measure_theory.Lp_meas_subgroup_to_Lp_trim_add MeasureTheory.lpMeasSubgroupToLpTrim_add
-
-theorem lpMeasSubgroupToLpTrim_neg (hm : m ≤ m0) (f : lpMeasSubgroup F m p μ) :
-    lpMeasSubgroupToLpTrim F p μ hm (-f) = -lpMeasSubgroupToLpTrim F p μ hm f :=
-  by
-  ext1
-  refine' eventually_eq.trans _ (Lp.coe_fn_neg _).symm
-  refine' ae_eq_trim_of_strongly_measurable hm (Lp.strongly_measurable _) _ _
-  · exact @strongly_measurable.neg _ _ _ m _ _ _ (Lp.strongly_measurable _)
-  refine' (Lp_meas_subgroup_to_Lp_trim_ae_eq hm _).trans _
-  refine' eventually_eq.trans _ (eventually_eq.neg (Lp_meas_subgroup_to_Lp_trim_ae_eq hm f).symm)
-  refine' (Lp.coe_fn_neg _).trans _
-  simp_rw [Lp_meas_subgroup_coe]
-  exact eventually_of_forall fun x => by rfl
-#align measure_theory.Lp_meas_subgroup_to_Lp_trim_neg MeasureTheory.lpMeasSubgroupToLpTrim_neg
-
-theorem lpMeasSubgroupToLpTrim_sub (hm : m ≤ m0) (f g : lpMeasSubgroup F m p μ) :
-    lpMeasSubgroupToLpTrim F p μ hm (f - g) =
-      lpMeasSubgroupToLpTrim F p μ hm f - lpMeasSubgroupToLpTrim F p μ hm g :=
-  by
-  rw [sub_eq_add_neg, sub_eq_add_neg, Lp_meas_subgroup_to_Lp_trim_add,
-    Lp_meas_subgroup_to_Lp_trim_neg]
-#align measure_theory.Lp_meas_subgroup_to_Lp_trim_sub MeasureTheory.lpMeasSubgroupToLpTrim_sub
-
-theorem lpMeasToLpTrim_smul (hm : m ≤ m0) (c : 𝕜) (f : lpMeas F 𝕜 m p μ) :
-    lpMeasToLpTrim F 𝕜 p μ hm (c • f) = c • lpMeasToLpTrim F 𝕜 p μ hm f :=
-  by
-  ext1
-  refine' eventually_eq.trans _ (Lp.coe_fn_smul _ _).symm
-  refine' ae_eq_trim_of_strongly_measurable hm (Lp.strongly_measurable _) _ _
-  · exact (Lp.strongly_measurable _).const_smul c
-  refine' (Lp_meas_to_Lp_trim_ae_eq hm _).trans _
-  refine' (Lp.coe_fn_smul _ _).trans _
-  refine' (Lp_meas_to_Lp_trim_ae_eq hm f).mono fun x hx => _
-  rw [Pi.smul_apply, Pi.smul_apply, hx]
-  rfl
-#align measure_theory.Lp_meas_to_Lp_trim_smul MeasureTheory.lpMeasToLpTrim_smul
-
-/-- `Lp_meas_subgroup_to_Lp_trim` preserves the norm. -/
-theorem lpMeasSubgroupToLpTrim_norm_map [hp : Fact (1 ≤ p)] (hm : m ≤ m0)
-    (f : lpMeasSubgroup F m p μ) : ‖lpMeasSubgroupToLpTrim F p μ hm f‖ = ‖f‖ :=
-  by
-  rw [Lp.norm_def, snorm_trim hm (Lp.strongly_measurable _),
-    snorm_congr_ae (Lp_meas_subgroup_to_Lp_trim_ae_eq hm _), Lp_meas_subgroup_coe, ← Lp.norm_def]
-  congr
-#align measure_theory.Lp_meas_subgroup_to_Lp_trim_norm_map MeasureTheory.lpMeasSubgroupToLpTrim_norm_map
-
-theorem isometry_lpMeasSubgroupToLpTrim [hp : Fact (1 ≤ p)] (hm : m ≤ m0) :
-    Isometry (lpMeasSubgroupToLpTrim F p μ hm) :=
-  Isometry.of_dist_eq fun f g => by
-    rw [dist_eq_norm, ← Lp_meas_subgroup_to_Lp_trim_sub, Lp_meas_subgroup_to_Lp_trim_norm_map,
-      dist_eq_norm]
-#align measure_theory.isometry_Lp_meas_subgroup_to_Lp_trim MeasureTheory.isometry_lpMeasSubgroupToLpTrim
-
-variable (F p μ)
-
-/-- `Lp_meas_subgroup` and `Lp F p (μ.trim hm)` are isometric. -/
-def lpMeasSubgroupToLpTrimIso [hp : Fact (1 ≤ p)] (hm : m ≤ m0) :
-    lpMeasSubgroup F m p μ ≃ᵢ Lp F p (μ.trim hm)
-    where
-  toFun := lpMeasSubgroupToLpTrim F p μ hm
-  invFun := lpTrimToLpMeasSubgroup F p μ hm
-  left_inv := lpMeasSubgroupToLpTrim_left_inv hm
-  right_inv := lpMeasSubgroupToLpTrim_right_inv hm
-  isometry_toFun := isometry_lpMeasSubgroupToLpTrim hm
-#align measure_theory.Lp_meas_subgroup_to_Lp_trim_iso MeasureTheory.lpMeasSubgroupToLpTrimIso
-
-variable (𝕜)
-
-/-- `Lp_meas_subgroup` and `Lp_meas` are isometric. -/
-def lpMeasSubgroupToLpMeasIso [hp : Fact (1 ≤ p)] : lpMeasSubgroup F m p μ ≃ᵢ lpMeas F 𝕜 m p μ :=
-  IsometryEquiv.refl (lpMeasSubgroup F m p μ)
-#align measure_theory.Lp_meas_subgroup_to_Lp_meas_iso MeasureTheory.lpMeasSubgroupToLpMeasIso
-
-/-- `Lp_meas` and `Lp F p (μ.trim hm)` are isometric, with a linear equivalence. -/
-def lpMeasToLpTrimLie [hp : Fact (1 ≤ p)] (hm : m ≤ m0) : lpMeas F 𝕜 m p μ ≃ₗᵢ[𝕜] Lp F p (μ.trim hm)
-    where
-  toFun := lpMeasToLpTrim F 𝕜 p μ hm
-  invFun := lpTrimToLpMeas F 𝕜 p μ hm
-  left_inv := lpMeasSubgroupToLpTrim_left_inv hm
-  right_inv := lpMeasSubgroupToLpTrim_right_inv hm
-  map_add' := lpMeasSubgroupToLpTrim_add hm
-  map_smul' := lpMeasToLpTrim_smul hm
-  norm_map' := lpMeasSubgroupToLpTrim_norm_map hm
-#align measure_theory.Lp_meas_to_Lp_trim_lie MeasureTheory.lpMeasToLpTrimLie
-
-variable {F 𝕜 p μ}
-
-instance [hm : Fact (m ≤ m0)] [CompleteSpace F] [hp : Fact (1 ≤ p)] :
-    CompleteSpace (lpMeasSubgroup F m p μ) := by
-  rw [(Lp_meas_subgroup_to_Lp_trim_iso F p μ hm.elim).completeSpace_iff]; infer_instance
-
--- For now just no-lint this; lean4's tree-based logging will make this easier to debug.
--- One possible change might be to generalize `𝕜` from `is_R_or_C` to `normed_field`, as this
--- result may well hold there.
-@[nolint fails_quickly]
-instance [hm : Fact (m ≤ m0)] [CompleteSpace F] [hp : Fact (1 ≤ p)] :
-    CompleteSpace (lpMeas F 𝕜 m p μ) := by
-  rw [(Lp_meas_subgroup_to_Lp_meas_iso F 𝕜 p μ).symm.completeSpace_iff]; infer_instance
-
-theorem isComplete_aeStronglyMeasurable' [hp : Fact (1 ≤ p)] [CompleteSpace F] (hm : m ≤ m0) :
-    IsComplete {f : Lp F p μ | AeStronglyMeasurable' m f μ} :=
-  by
-  rw [← completeSpace_coe_iff_isComplete]
-  haveI : Fact (m ≤ m0) := ⟨hm⟩
-  change CompleteSpace (Lp_meas_subgroup F m p μ)
-  infer_instance
-#align measure_theory.is_complete_ae_strongly_measurable' MeasureTheory.isComplete_aeStronglyMeasurable'
-
-theorem isClosed_aeStronglyMeasurable' [hp : Fact (1 ≤ p)] [CompleteSpace F] (hm : m ≤ m0) :
-    IsClosed {f : Lp F p μ | AeStronglyMeasurable' m f μ} :=
-  IsComplete.isClosed (isComplete_aeStronglyMeasurable' hm)
-#align measure_theory.is_closed_ae_strongly_measurable' MeasureTheory.isClosed_aeStronglyMeasurable'
-
-end CompleteSubspace
-
-section StronglyMeasurable
-
-variable {m m0 : MeasurableSpace α} {μ : Measure α}
-
-/-- We do not get `ae_fin_strongly_measurable f (μ.trim hm)`, since we don't have
-`f =ᵐ[μ.trim hm] Lp_meas_to_Lp_trim F 𝕜 p μ hm f` but only the weaker
-`f =ᵐ[μ] Lp_meas_to_Lp_trim F 𝕜 p μ hm f`. -/
-theorem lpMeas.ae_fin_strongly_measurable' (hm : m ≤ m0) (f : lpMeas F 𝕜 m p μ) (hp_ne_zero : p ≠ 0)
-    (hp_ne_top : p ≠ ∞) : ∃ g, FinStronglyMeasurable g (μ.trim hm) ∧ f =ᵐ[μ] g :=
-  ⟨lpMeasSubgroupToLpTrim F p μ hm f, Lp.finStronglyMeasurable _ hp_ne_zero hp_ne_top,
-    (lpMeasSubgroupToLpTrim_ae_eq hm f).symm⟩
-#align measure_theory.Lp_meas.ae_fin_strongly_measurable' MeasureTheory.lpMeas.ae_fin_strongly_measurable'
-
-/-- When applying the inverse of `Lp_meas_to_Lp_trim_lie` (which takes a function in the Lp space of
-the sub-sigma algebra and returns its version in the larger Lp space) to an indicator of the
-sub-sigma-algebra, we obtain an indicator in the Lp space of the larger sigma-algebra. -/
-theorem lpMeasToLpTrimLie_symm_indicator [one_le_p : Fact (1 ≤ p)] [NormedSpace ℝ F] {hm : m ≤ m0}
-    {s : Set α} {μ : Measure α} (hs : measurable_set[m] s) (hμs : μ.trim hm s ≠ ∞) (c : F) :
-    ((lpMeasToLpTrimLie F ℝ p μ hm).symm (indicatorConstLp p hs hμs c) : Lp F p μ) =
-      indicatorConstLp p (hm s hs) ((le_trim hm).trans_lt hμs.lt_top).Ne c :=
-  by
-  ext1
-  rw [← Lp_meas_coe]
-  change
-    Lp_trim_to_Lp_meas F ℝ p μ hm (indicator_const_Lp p hs hμs c) =ᵐ[μ]
-      (indicator_const_Lp p _ _ c : α → F)
-  refine' (Lp_trim_to_Lp_meas_ae_eq hm _).trans _
-  exact (ae_eq_of_ae_eq_trim indicator_const_Lp_coe_fn).trans indicator_const_Lp_coe_fn.symm
-#align measure_theory.Lp_meas_to_Lp_trim_lie_symm_indicator MeasureTheory.lpMeasToLpTrimLie_symm_indicator
-
-theorem lpMeasToLpTrimLie_symm_toLp [one_le_p : Fact (1 ≤ p)] [NormedSpace ℝ F] (hm : m ≤ m0)
-    (f : α → F) (hf : Memℒp f p (μ.trim hm)) :
-    ((lpMeasToLpTrimLie F ℝ p μ hm).symm (hf.toLp f) : Lp F p μ) =
-      (memℒp_of_memℒp_trim hm hf).toLp f :=
-  by
-  ext1
-  rw [← Lp_meas_coe]
-  refine' (Lp_trim_to_Lp_meas_ae_eq hm _).trans _
-  exact (ae_eq_of_ae_eq_trim (mem_ℒp.coe_fn_to_Lp hf)).trans (mem_ℒp.coe_fn_to_Lp _).symm
-#align measure_theory.Lp_meas_to_Lp_trim_lie_symm_to_Lp MeasureTheory.lpMeasToLpTrimLie_symm_toLp
-
-end StronglyMeasurable
-
-end LpMeas
-
-section Induction
-
-variable {m m0 : MeasurableSpace α} {μ : Measure α} [Fact (1 ≤ p)] [NormedSpace ℝ F]
-
-/-- Auxiliary lemma for `Lp.induction_strongly_measurable`. -/
-@[elab_as_elim]
-theorem Lp.induction_strongly_measurable_aux (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : Lp F p μ → Prop)
-    (h_ind :
-      ∀ (c : F) {s : Set α} (hs : measurable_set[m] s) (hμs : μ s < ∞),
-        P (Lp.simpleFunc.indicatorConst p (hm s hs) hμs.Ne c))
-    (h_add :
-      ∀ ⦃f g⦄,
-        ∀ hf : Memℒp f p μ,
-          ∀ hg : Memℒp g p μ,
-            ∀ hfm : AeStronglyMeasurable' m f μ,
-              ∀ hgm : AeStronglyMeasurable' m g μ,
-                Disjoint (Function.support f) (Function.support g) →
-                  P (hf.toLp f) → P (hg.toLp g) → P (hf.toLp f + hg.toLp g))
-    (h_closed : IsClosed {f : lpMeas F ℝ m p μ | P f}) :
-    ∀ f : Lp F p μ, AeStronglyMeasurable' m f μ → P f :=
-  by
-  intro f hf
-  let f' := (⟨f, hf⟩ : Lp_meas F ℝ m p μ)
-  let g := Lp_meas_to_Lp_trim_lie F ℝ p μ hm f'
-  have hfg : f' = (Lp_meas_to_Lp_trim_lie F ℝ p μ hm).symm g := by
-    simp only [LinearIsometryEquiv.symm_apply_apply]
-  change P ↑f'
-  rw [hfg]
-  refine'
-    @Lp.induction α F m _ p (μ.trim hm) _ hp_ne_top
-      (fun g => P ((Lp_meas_to_Lp_trim_lie F ℝ p μ hm).symm g)) _ _ _ g
-  · intro b t ht hμt
-    rw [Lp.simple_func.coe_indicator_const, Lp_meas_to_Lp_trim_lie_symm_indicator ht hμt.ne b]
-    have hμt' : μ t < ∞ := (le_trim hm).trans_lt hμt
-    specialize h_ind b ht hμt'
-    rwa [Lp.simple_func.coe_indicator_const] at h_ind 
-  · intro f g hf hg h_disj hfP hgP
-    rw [LinearIsometryEquiv.map_add]
-    push_cast
-    have h_eq :
-      ∀ (f : α → F) (hf : mem_ℒp f p (μ.trim hm)),
-        ((Lp_meas_to_Lp_trim_lie F ℝ p μ hm).symm (mem_ℒp.to_Lp f hf) : Lp F p μ) =
-          (mem_ℒp_of_mem_ℒp_trim hm hf).toLp f :=
-      Lp_meas_to_Lp_trim_lie_symm_to_Lp hm
-    rw [h_eq f hf] at hfP ⊢
-    rw [h_eq g hg] at hgP ⊢
-    exact
-      h_add (mem_ℒp_of_mem_ℒp_trim hm hf) (mem_ℒp_of_mem_ℒp_trim hm hg)
-        (ae_strongly_measurable'_of_ae_strongly_measurable'_trim hm hf.ae_strongly_measurable)
-        (ae_strongly_measurable'_of_ae_strongly_measurable'_trim hm hg.ae_strongly_measurable)
-        h_disj hfP hgP
-  · change IsClosed ((Lp_meas_to_Lp_trim_lie F ℝ p μ hm).symm ⁻¹' {g : Lp_meas F ℝ m p μ | P ↑g})
-    exact IsClosed.preimage (LinearIsometryEquiv.continuous _) h_closed
-#align measure_theory.Lp.induction_strongly_measurable_aux MeasureTheory.Lp.induction_strongly_measurable_aux
-
-/-- To prove something for an `Lp` function a.e. strongly measurable with respect to a
-sub-σ-algebra `m` in a normed space, it suffices to show that
-* the property holds for (multiples of) characteristic functions which are measurable w.r.t. `m`;
-* is closed under addition;
-* the set of functions in `Lp` strongly measurable w.r.t. `m` for which the property holds is
-  closed.
--/
-@[elab_as_elim]
-theorem Lp.induction_stronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : Lp F p μ → Prop)
-    (h_ind :
-      ∀ (c : F) {s : Set α} (hs : measurable_set[m] s) (hμs : μ s < ∞),
-        P (Lp.simpleFunc.indicatorConst p (hm s hs) hμs.Ne c))
-    (h_add :
-      ∀ ⦃f g⦄,
-        ∀ hf : Memℒp f p μ,
-          ∀ hg : Memℒp g p μ,
-            ∀ hfm : strongly_measurable[m] f,
-              ∀ hgm : strongly_measurable[m] g,
-                Disjoint (Function.support f) (Function.support g) →
-                  P (hf.toLp f) → P (hg.toLp g) → P (hf.toLp f + hg.toLp g))
-    (h_closed : IsClosed {f : lpMeas F ℝ m p μ | P f}) :
-    ∀ f : Lp F p μ, AeStronglyMeasurable' m f μ → P f :=
-  by
-  intro f hf
-  suffices h_add_ae :
-    ∀ ⦃f g⦄,
-      ∀ hf : mem_ℒp f p μ,
-        ∀ hg : mem_ℒp g p μ,
-          ∀ hfm : ae_strongly_measurable' m f μ,
-            ∀ hgm : ae_strongly_measurable' m g μ,
-              Disjoint (Function.support f) (Function.support g) →
-                P (hf.toLp f) → P (hg.toLp g) → P (hf.toLp f + hg.toLp g)
-  exact Lp.induction_strongly_measurable_aux hm hp_ne_top P h_ind h_add_ae h_closed f hf
-  intro f g hf hg hfm hgm h_disj hPf hPg
-  let s_f : Set α := Function.support (hfm.mk f)
-  have hs_f : measurable_set[m] s_f := hfm.strongly_measurable_mk.measurable_set_support
-  have hs_f_eq : s_f =ᵐ[μ] Function.support f := hfm.ae_eq_mk.symm.support
-  let s_g : Set α := Function.support (hgm.mk g)
-  have hs_g : measurable_set[m] s_g := hgm.strongly_measurable_mk.measurable_set_support
-  have hs_g_eq : s_g =ᵐ[μ] Function.support g := hgm.ae_eq_mk.symm.support
-  have h_inter_empty : (s_f ∩ s_g : Set α) =ᵐ[μ] (∅ : Set α) :=
-    by
-    refine' (hs_f_eq.inter hs_g_eq).trans _
-    suffices Function.support f ∩ Function.support g = ∅ by rw [this]
-    exact set.disjoint_iff_inter_eq_empty.mp h_disj
-  let f' := (s_f \ s_g).indicator (hfm.mk f)
-  have hff' : f =ᵐ[μ] f' :=
-    by
-    have : s_f \ s_g =ᵐ[μ] s_f :=
-      by
-      rw [← Set.diff_inter_self_eq_diff, Set.inter_comm]
-      refine' ((ae_eq_refl s_f).diffₓ h_inter_empty).trans _
-      rw [Set.diff_empty]
-    refine' ((indicator_ae_eq_of_ae_eq_set this).trans _).symm
-    rw [Set.indicator_support]
-    exact hfm.ae_eq_mk.symm
-  have hf'_meas : strongly_measurable[m] f' := hfm.strongly_measurable_mk.indicator (hs_f.diff hs_g)
-  have hf'_Lp : mem_ℒp f' p μ := hf.ae_eq hff'
-  let g' := (s_g \ s_f).indicator (hgm.mk g)
-  have hgg' : g =ᵐ[μ] g' :=
-    by
-    have : s_g \ s_f =ᵐ[μ] s_g := by
-      rw [← Set.diff_inter_self_eq_diff]
-      refine' ((ae_eq_refl s_g).diffₓ h_inter_empty).trans _
-      rw [Set.diff_empty]
-    refine' ((indicator_ae_eq_of_ae_eq_set this).trans _).symm
-    rw [Set.indicator_support]
-    exact hgm.ae_eq_mk.symm
-  have hg'_meas : strongly_measurable[m] g' := hgm.strongly_measurable_mk.indicator (hs_g.diff hs_f)
-  have hg'_Lp : mem_ℒp g' p μ := hg.ae_eq hgg'
-  have h_disj : Disjoint (Function.support f') (Function.support g') :=
-    haveI : Disjoint (s_f \ s_g) (s_g \ s_f) := disjoint_sdiff_sdiff
-    this.mono Set.support_indicator_subset Set.support_indicator_subset
-  rw [← mem_ℒp.to_Lp_congr hf'_Lp hf hff'.symm] at hPf ⊢
-  rw [← mem_ℒp.to_Lp_congr hg'_Lp hg hgg'.symm] at hPg ⊢
-  exact h_add hf'_Lp hg'_Lp hf'_meas hg'_meas h_disj hPf hPg
-#align measure_theory.Lp.induction_strongly_measurable MeasureTheory.Lp.induction_stronglyMeasurable
-
-/-- To prove something for an arbitrary `mem_ℒp` function a.e. strongly measurable with respect
-to a sub-σ-algebra `m` in a normed space, it suffices to show that
-* the property holds for (multiples of) characteristic functions which are measurable w.r.t. `m`;
-* is closed under addition;
-* the set of functions in the `Lᵖ` space strongly measurable w.r.t. `m` for which the property
-  holds is closed.
-* the property is closed under the almost-everywhere equal relation.
--/
-@[elab_as_elim]
-theorem Memℒp.induction_stronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : (α → F) → Prop)
-    (h_ind : ∀ (c : F) ⦃s⦄, measurable_set[m] s → μ s < ∞ → P (s.indicator fun _ => c))
-    (h_add :
-      ∀ ⦃f g : α → F⦄,
-        Disjoint (Function.support f) (Function.support g) →
-          Memℒp f p μ →
-            Memℒp g p μ →
-              strongly_measurable[m] f → strongly_measurable[m] g → P f → P g → P (f + g))
-    (h_closed : IsClosed {f : lpMeas F ℝ m p μ | P f})
-    (h_ae : ∀ ⦃f g⦄, f =ᵐ[μ] g → Memℒp f p μ → P f → P g) :
-    ∀ ⦃f : α → F⦄ (hf : Memℒp f p μ) (hfm : AeStronglyMeasurable' m f μ), P f :=
-  by
-  intro f hf hfm
-  let f_Lp := hf.to_Lp f
-  have hfm_Lp : ae_strongly_measurable' m f_Lp μ := hfm.congr hf.coe_fn_to_Lp.symm
-  refine' h_ae hf.coe_fn_to_Lp (Lp.mem_ℒp _) _
-  change P f_Lp
-  refine' Lp.induction_strongly_measurable hm hp_ne_top (fun f => P ⇑f) _ _ h_closed f_Lp hfm_Lp
-  · intro c s hs hμs
-    rw [Lp.simple_func.coe_indicator_const]
-    refine' h_ae indicator_const_Lp_coe_fn.symm _ (h_ind c hs hμs)
-    exact mem_ℒp_indicator_const p (hm s hs) c (Or.inr hμs.ne)
-  · intro f g hf_mem hg_mem hfm hgm h_disj hfP hgP
-    have hfP' : P f := h_ae hf_mem.coe_fn_to_Lp (Lp.mem_ℒp _) hfP
-    have hgP' : P g := h_ae hg_mem.coe_fn_to_Lp (Lp.mem_ℒp _) hgP
-    specialize h_add h_disj hf_mem hg_mem hfm hgm hfP' hgP'
-    refine' h_ae _ (hf_mem.add hg_mem) h_add
-    exact (hf_mem.coe_fn_to_Lp.symm.add hg_mem.coe_fn_to_Lp.symm).trans (Lp.coe_fn_add _ _).symm
-#align measure_theory.mem_ℒp.induction_strongly_measurable MeasureTheory.Memℒp.induction_stronglyMeasurable
-
-end Induction
-
-section UniquenessOfConditionalExpectation
-
-/-! ## Uniqueness of the conditional expectation -/
-
-
-variable {m m0 : MeasurableSpace α} {μ : Measure α}
-
-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)
-    (hf_zero : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0) : f =ᵐ[μ] 0 :=
-  by
-  obtain ⟨g, hg_sm, hfg⟩ := Lp_meas.ae_fin_strongly_measurable' hm f hp_ne_zero hp_ne_top
-  refine' hfg.trans _
-  refine' ae_eq_zero_of_forall_set_integral_eq_of_fin_strongly_measurable_trim hm _ _ hg_sm
-  · intro s hs hμs
-    have hfg_restrict : f =ᵐ[μ.restrict s] g := ae_restrict_of_ae hfg
-    rw [integrable_on, integrable_congr hfg_restrict.symm]
-    exact hf_int_finite s hs hμs
-  · intro s hs hμs
-    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
-
-include 𝕜
-
-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, 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 :=
-  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]
-  refine' hf_f_meas.trans _
-  refine' Lp_meas.ae_eq_zero_of_forall_set_integral_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 [integrable_on, integrable_congr hfg_restrict.symm]
-    exact hf_int_finite s hs hμs
-  · intro s hs hμs
-    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'
-
-/-- **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)
-    (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 :=
-  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
-  have hfg' : ∀ s : Set α, measurable_set[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.coe_fn_sub f g))]
-    rw [integral_sub' (hf_int_finite s hs hμs) (hg_int_finite s hs hμs)]
-    exact sub_eq_zero.mpr (hfg s hs hμs)
-  have hfg_int : ∀ s, measurable_set[m] s → μ s < ∞ → integrable_on (⇑(f - g)) s μ :=
-    by
-    intro s hs hμs
-    rw [integrable_on, integrable_congr (ae_restrict_of_ae (Lp.coe_fn_sub f g))]
-    exact (hf_int_finite s hs hμs).sub (hg_int_finite s hs hμs)
-  have hfg_meas : ae_strongly_measurable' m (⇑(f - g)) μ :=
-    ae_strongly_measurable'.congr (hf_meas.sub hg_meas) (Lp.coe_fn_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'
-      hfg_meas
-#align measure_theory.Lp.ae_eq_of_forall_set_integral_eq' MeasureTheory.Lp.ae_eq_of_forall_set_integral_eq'
-
-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)
-    (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 :=
-  by
-  rw [← ae_eq_trim_iff_of_ae_strongly_measurable' hm hfm hgm]
-  have hf_mk_int_finite :
-    ∀ 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 [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)
-  have hg_mk_int_finite :
-    ∀ 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 [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)
-  have hfg_mk_eq :
-    ∀ s : Set α,
-      measurable_set[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
-    intro s hs 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),
-      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'
-
-end UniquenessOfConditionalExpectation
-
-section IntegralNormLe
-
-variable {m m0 : MeasurableSpace α} {μ : Measure α} {s : Set α}
-
-/-- 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. -/
-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 : strongly_measurable[m] g)
-    (hgi : IntegrableOn g s μ)
-    (hgf : ∀ t, measurable_set[m] t → μ t < ∞ → ∫ x in t, g x ∂μ = ∫ x in t, f x ∂μ)
-    (hs : measurable_set[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 : measurable_set[m] {x | 0 ≤ g x} :=
-    (@strongly_measurable_const _ _ m _ _).measurableSet_le hg
-  have h_meas_nonneg_f : MeasurableSet {x | 0 ≤ f x} :=
-    strongly_measurable_const.measurable_set_le hf
-  have h_meas_nonpos_g : measurable_set[m] {x | g x ≤ 0} :=
-    hg.measurable_set_le (@strongly_measurable_const _ _ m _ _)
-  have h_meas_nonpos_f : MeasurableSet {x | f x ≤ 0} :=
-    hf.measurable_set_le strongly_measurable_const
-  refine' sub_le_sub _ _
-  · rw [measure.restrict_restrict (hm _ h_meas_nonneg_g), measure.restrict_restrict h_meas_nonneg_f,
-      hgf _ (@MeasurableSet.inter α m _ _ h_meas_nonneg_g hs)
-        ((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
-  · 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
-#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
-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 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 : strongly_measurable[m] g)
-    (hgi : IntegrableOn g s μ)
-    (hgf : ∀ t, measurable_set[m] t → μ t < ∞ → ∫ x in t, g x ∂μ = ∫ x in t, f x ∂μ)
-    (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) : ∫⁻ x in s, ‖g x‖₊ ∂μ ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ :=
-  by
-  rw [← of_real_integral_norm_eq_lintegral_nnnorm hfi, ←
-    of_real_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 _
-#align measure_theory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq MeasureTheory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq
-
-end IntegralNormLe
-
-/-! ## Conditional expectation in L2
-
-We define a conditional expectation in `L2`: it is the orthogonal projection on the subspace
-`Lp_meas`. -/
-
-
-section CondexpL2
-
-variable [CompleteSpace E] {m m0 : MeasurableSpace α} {μ : Measure α} {s t : Set α}
-
--- mathport name: «expr⟪ , ⟫»
-local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
-
--- mathport name: «expr⟪ , ⟫₂»
-local notation "⟪" x ", " y "⟫₂" => @inner 𝕜 (α →₂[μ] E) _ x y
-
-variable (𝕜)
-
-/-- Conditional expectation of a function in L2 with respect to a sigma-algebra -/
-def condexpL2 (hm : m ≤ m0) : (α →₂[μ] E) →L[𝕜] lpMeas E 𝕜 m 2 μ :=
-  @orthogonalProjection 𝕜 (α →₂[μ] E) _ _ _ (lpMeas E 𝕜 m 2 μ)
-    haveI : Fact (m ≤ m0) := ⟨hm⟩
-    inferInstance
-#align measure_theory.condexp_L2 MeasureTheory.condexpL2
-
-variable {𝕜}
-
-theorem aeStronglyMeasurable'_condexpL2 (hm : m ≤ m0) (f : α →₂[μ] E) :
-    AeStronglyMeasurable' m (condexpL2 𝕜 hm f) μ :=
-  lpMeas.aeStronglyMeasurable' _
-#align measure_theory.ae_strongly_measurable'_condexp_L2 MeasureTheory.aeStronglyMeasurable'_condexpL2
-
-theorem integrableOn_condexpL2_of_measure_ne_top (hm : m ≤ m0) (hμs : μ s ≠ ∞) (f : α →₂[μ] E) :
-    IntegrableOn (condexpL2 𝕜 hm f) s μ :=
-  integrableOn_Lp_of_measure_ne_top (condexpL2 𝕜 hm f : α →₂[μ] E) fact_one_le_two_ennreal.elim hμs
-#align measure_theory.integrable_on_condexp_L2_of_measure_ne_top MeasureTheory.integrableOn_condexpL2_of_measure_ne_top
-
-theorem integrable_condexpL2_of_isFiniteMeasure (hm : m ≤ m0) [IsFiniteMeasure μ] {f : α →₂[μ] E} :
-    Integrable (condexpL2 𝕜 hm f) μ :=
-  integrableOn_univ.mp <| integrableOn_condexpL2_of_measure_ne_top hm (measure_ne_top _ _) f
-#align measure_theory.integrable_condexp_L2_of_is_finite_measure MeasureTheory.integrable_condexpL2_of_isFiniteMeasure
-
-theorem norm_condexpL2_le_one (hm : m ≤ m0) : ‖@condexpL2 α E 𝕜 _ _ _ _ _ _ μ hm‖ ≤ 1 :=
-  haveI : Fact (m ≤ m0) := ⟨hm⟩
-  orthogonalProjection_norm_le _
-#align measure_theory.norm_condexp_L2_le_one MeasureTheory.norm_condexpL2_le_one
-
-theorem norm_condexpL2_le (hm : m ≤ m0) (f : α →₂[μ] E) : ‖condexpL2 𝕜 hm f‖ ≤ ‖f‖ :=
-  ((@condexpL2 _ E 𝕜 _ _ _ _ _ _ μ hm).le_opNorm f).trans
-    (mul_le_of_le_one_left (norm_nonneg _) (norm_condexpL2_le_one hm))
-#align measure_theory.norm_condexp_L2_le MeasureTheory.norm_condexpL2_le
-
-theorem snorm_condexpL2_le (hm : m ≤ m0) (f : α →₂[μ] E) :
-    snorm (condexpL2 𝕜 hm f) 2 μ ≤ snorm f 2 μ :=
-  by
-  rw [Lp_meas_coe, ← ENNReal.toReal_le_toReal (Lp.snorm_ne_top _) (Lp.snorm_ne_top _), ←
-    Lp.norm_def, ← Lp.norm_def, Submodule.norm_coe]
-  exact norm_condexp_L2_le hm f
-#align measure_theory.snorm_condexp_L2_le MeasureTheory.snorm_condexpL2_le
-
-theorem norm_condexpL2_coe_le (hm : m ≤ m0) (f : α →₂[μ] E) :
-    ‖(condexpL2 𝕜 hm f : α →₂[μ] E)‖ ≤ ‖f‖ :=
-  by
-  rw [Lp.norm_def, Lp.norm_def, ← Lp_meas_coe]
-  refine' (ENNReal.toReal_le_toReal _ (Lp.snorm_ne_top _)).mpr (snorm_condexp_L2_le hm f)
-  exact Lp.snorm_ne_top _
-#align measure_theory.norm_condexp_L2_coe_le MeasureTheory.norm_condexpL2_coe_le
-
-theorem inner_condexpL2_left_eq_right (hm : m ≤ m0) {f g : α →₂[μ] E} :
-    ⟪(condexpL2 𝕜 hm f : α →₂[μ] E), g⟫₂ = ⟪f, (condexpL2 𝕜 hm g : α →₂[μ] E)⟫₂ :=
-  haveI : Fact (m ≤ m0) := ⟨hm⟩
-  inner_orthogonalProjection_left_eq_right _ f g
-#align measure_theory.inner_condexp_L2_left_eq_right MeasureTheory.inner_condexpL2_left_eq_right
-
-theorem condexpL2_indicator_of_measurable (hm : m ≤ m0) (hs : measurable_set[m] s) (hμs : μ s ≠ ∞)
-    (c : E) :
-    (condexpL2 𝕜 hm (indicatorConstLp 2 (hm s hs) hμs c) : α →₂[μ] E) =
-      indicatorConstLp 2 (hm s hs) hμs c :=
-  by
-  rw [condexp_L2]
-  haveI : Fact (m ≤ m0) := ⟨hm⟩
-  have h_mem : indicator_const_Lp 2 (hm s hs) hμs c ∈ Lp_meas E 𝕜 m 2 μ :=
-    mem_Lp_meas_indicator_const_Lp hm hs hμs
-  let ind := (⟨indicator_const_Lp 2 (hm s hs) hμs c, h_mem⟩ : Lp_meas E 𝕜 m 2 μ)
-  have h_coe_ind : (ind : α →₂[μ] E) = indicator_const_Lp 2 (hm s hs) hμs c := by rfl
-  have h_orth_mem := orthogonalProjection_mem_subspace_eq_self ind
-  rw [← h_coe_ind, h_orth_mem]
-#align measure_theory.condexp_L2_indicator_of_measurable MeasureTheory.condexpL2_indicator_of_measurable
-
-theorem inner_condexpL2_eq_inner_fun (hm : m ≤ m0) (f g : α →₂[μ] E)
-    (hg : AeStronglyMeasurable' m g μ) : ⟪(condexpL2 𝕜 hm f : α →₂[μ] E), g⟫₂ = ⟪f, g⟫₂ :=
-  by
-  symm
-  rw [← sub_eq_zero, ← inner_sub_left, condexp_L2]
-  simp only [mem_Lp_meas_iff_ae_strongly_measurable'.mpr hg, orthogonalProjection_inner_eq_zero]
-#align measure_theory.inner_condexp_L2_eq_inner_fun MeasureTheory.inner_condexpL2_eq_inner_fun
-
-section Real
-
-variable {hm : m ≤ m0}
-
-theorem integral_condexpL2_eq_of_fin_meas_real (f : Lp 𝕜 2 μ) (hs : measurable_set[m] s)
-    (hμs : μ s ≠ ∞) : ∫ x in s, condexpL2 𝕜 hm f x ∂μ = ∫ x in s, f x ∂μ :=
-  by
-  rw [← L2.inner_indicator_const_Lp_one (hm s hs) hμs]
-  have h_eq_inner :
-    ∫ x in s, condexp_L2 𝕜 hm f x ∂μ =
-      inner (indicator_const_Lp 2 (hm s hs) hμs (1 : 𝕜)) (condexp_L2 𝕜 hm f) :=
-    by
-    rw [L2.inner_indicator_const_Lp_one (hm s hs) hμs]
-    congr
-  rw [h_eq_inner, ← inner_condexp_L2_left_eq_right, condexp_L2_indicator_of_measurable hm hs hμs]
-#align measure_theory.integral_condexp_L2_eq_of_fin_meas_real MeasureTheory.integral_condexpL2_eq_of_fin_meas_real
-
-theorem lintegral_nnnorm_condexpL2_le (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) (f : Lp ℝ 2 μ) :
-    ∫⁻ x in s, ‖condexpL2 ℝ hm f x‖₊ ∂μ ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ :=
-  by
-  let h_meas := Lp_meas.ae_strongly_measurable' (condexp_L2 ℝ hm f)
-  let g := h_meas.some
-  have hg_meas : strongly_measurable[m] g := h_meas.some_spec.1
-  have hg_eq : g =ᵐ[μ] condexp_L2 ℝ hm f := h_meas.some_spec.2.symm
-  have hg_eq_restrict : g =ᵐ[μ.restrict s] condexp_L2 ℝ hm f := ae_restrict_of_ae hg_eq
-  have hg_nnnorm_eq :
-    (fun x => (‖g x‖₊ : ℝ≥0∞)) =ᵐ[μ.restrict s] fun x => (‖condexp_L2 ℝ hm f x‖₊ : ℝ≥0∞) :=
-    by
-    refine' hg_eq_restrict.mono fun x hx => _
-    dsimp only
-    rw [hx]
-  rw [lintegral_congr_ae hg_nnnorm_eq.symm]
-  refine'
-    lintegral_nnnorm_le_of_forall_fin_meas_integral_eq hm (Lp.strongly_measurable f) _ _ _ _ hs hμs
-  · exact integrable_on_Lp_of_measure_ne_top f fact_one_le_two_ennreal.elim hμs
-  · exact hg_meas
-  · rw [integrable_on, integrable_congr hg_eq_restrict]
-    exact integrable_on_condexp_L2_of_measure_ne_top hm hμs f
-  · intro t ht hμt
-    rw [← integral_condexp_L2_eq_of_fin_meas_real f ht hμt.ne]
-    exact set_integral_congr_ae (hm t ht) (hg_eq.mono fun x hx _ => hx)
-#align measure_theory.lintegral_nnnorm_condexp_L2_le MeasureTheory.lintegral_nnnorm_condexpL2_le
-
-theorem condexpL2_ae_eq_zero_of_ae_eq_zero (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) {f : Lp ℝ 2 μ}
-    (hf : f =ᵐ[μ.restrict s] 0) : condexpL2 ℝ hm f =ᵐ[μ.restrict s] 0 :=
-  by
-  suffices h_nnnorm_eq_zero : ∫⁻ x in s, ‖condexp_L2 ℝ hm f x‖₊ ∂μ = 0
-  · rw [lintegral_eq_zero_iff] at h_nnnorm_eq_zero 
-    refine' h_nnnorm_eq_zero.mono fun x hx => _
-    dsimp only at hx 
-    rw [Pi.zero_apply] at hx ⊢
-    · rwa [ENNReal.coe_eq_zero, nnnorm_eq_zero] at hx 
-    · refine' Measurable.coe_nnreal_ennreal (Measurable.nnnorm _)
-      rw [Lp_meas_coe]
-      exact (Lp.strongly_measurable _).Measurable
-  refine' le_antisymm _ (zero_le _)
-  refine' (lintegral_nnnorm_condexp_L2_le hs hμs f).trans (le_of_eq _)
-  rw [lintegral_eq_zero_iff]
-  · refine' hf.mono fun x hx => _
-    dsimp only
-    rw [hx]
-    simp
-  · exact (Lp.strongly_measurable _).ennnorm
-#align measure_theory.condexp_L2_ae_eq_zero_of_ae_eq_zero MeasureTheory.condexpL2_ae_eq_zero_of_ae_eq_zero
-
-theorem lintegral_nnnorm_condexpL2_indicator_le_real (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
-    (ht : measurable_set[m] t) (hμt : μ t ≠ ∞) :
-    ∫⁻ a in t, ‖condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a‖₊ ∂μ ≤ μ (s ∩ t) :=
-  by
-  refine' (lintegral_nnnorm_condexp_L2_le ht hμt _).trans (le_of_eq _)
-  have h_eq :
-    ∫⁻ x in t, ‖(indicator_const_Lp 2 hs hμs (1 : ℝ)) x‖₊ ∂μ =
-      ∫⁻ x in t, s.indicator (fun x => (1 : ℝ≥0∞)) x ∂μ :=
-    by
-    refine' lintegral_congr_ae (ae_restrict_of_ae _)
-    refine' (@indicator_const_Lp_coe_fn _ _ _ 2 _ _ _ hs hμs (1 : ℝ)).mono fun x hx => _
-    rw [hx]
-    classical
-    simp_rw [Set.indicator_apply]
-    split_ifs <;> simp
-  rw [h_eq, lintegral_indicator _ hs, lintegral_const, measure.restrict_restrict hs]
-  simp only [one_mul, Set.univ_inter, MeasurableSet.univ, measure.restrict_apply]
-#align measure_theory.lintegral_nnnorm_condexp_L2_indicator_le_real MeasureTheory.lintegral_nnnorm_condexpL2_indicator_le_real
-
-end Real
-
-/-- `condexp_L2` commutes with taking inner products with constants. See the lemma
-`condexp_L2_comp_continuous_linear_map` for a more general result about commuting with continuous
-linear maps. -/
-theorem condexpL2_const_inner (hm : m ≤ m0) (f : Lp E 2 μ) (c : E) :
-    condexpL2 𝕜 hm (((Lp.memℒp f).const_inner c).toLp fun a => ⟪c, f a⟫) =ᵐ[μ] fun a =>
-      ⟪c, condexpL2 𝕜 hm f a⟫ :=
-  by
-  rw [Lp_meas_coe]
-  have h_mem_Lp : mem_ℒp (fun a => ⟪c, condexp_L2 𝕜 hm f a⟫) 2 μ := by
-    refine' mem_ℒp.const_inner _ _; rw [Lp_meas_coe]; exact Lp.mem_ℒp _
-  have h_eq : h_mem_Lp.to_Lp _ =ᵐ[μ] fun a => ⟪c, condexp_L2 𝕜 hm f a⟫ := h_mem_Lp.coe_fn_to_Lp
-  refine' eventually_eq.trans _ h_eq
-  refine'
-    Lp.ae_eq_of_forall_set_integral_eq' 𝕜 hm _ _ two_ne_zero ENNReal.coe_ne_top
-      (fun s hs hμs => integrable_on_condexp_L2_of_measure_ne_top hm hμs.Ne _) _ _ _ _
-  · intro s hs hμs
-    rw [integrable_on, integrable_congr (ae_restrict_of_ae h_eq)]
-    exact (integrable_on_condexp_L2_of_measure_ne_top hm hμs.ne _).const_inner _
-  · intro s hs hμs
-    rw [← Lp_meas_coe, integral_condexp_L2_eq_of_fin_meas_real _ hs hμs.ne,
-      integral_congr_ae (ae_restrict_of_ae h_eq), Lp_meas_coe, ←
-      L2.inner_indicator_const_Lp_eq_set_integral_inner 𝕜 (↑(condexp_L2 𝕜 hm f)) (hm s hs) c hμs.ne,
-      ← inner_condexp_L2_left_eq_right, condexp_L2_indicator_of_measurable,
-      L2.inner_indicator_const_Lp_eq_set_integral_inner 𝕜 f (hm s hs) c hμs.ne,
-      set_integral_congr_ae (hm s hs)
-        ((mem_ℒp.coe_fn_to_Lp ((Lp.mem_ℒp f).const_inner c)).mono fun x hx hxs => hx)]
-  · rw [← Lp_meas_coe]; exact Lp_meas.ae_strongly_measurable' _
-  · refine' ae_strongly_measurable'.congr _ h_eq.symm
-    exact (Lp_meas.ae_strongly_measurable' _).const_inner _
-#align measure_theory.condexp_L2_const_inner MeasureTheory.condexpL2_const_inner
-
-/-- `condexp_L2` verifies the equality of integrals defining the conditional expectation. -/
-theorem integral_condexpL2_eq (hm : m ≤ m0) (f : Lp E' 2 μ) (hs : measurable_set[m] s)
-    (hμs : μ s ≠ ∞) : ∫ x in s, condexpL2 𝕜 hm f x ∂μ = ∫ x in s, f x ∂μ :=
-  by
-  rw [← sub_eq_zero, Lp_meas_coe, ←
-    integral_sub' (integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs)
-      (integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs)]
-  refine' integral_eq_zero_of_forall_integral_inner_eq_zero 𝕜 _ _ _
-  · rw [integrable_congr (ae_restrict_of_ae (Lp.coe_fn_sub (↑(condexp_L2 𝕜 hm f)) f).symm)]
-    exact integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs
-  intro c
-  simp_rw [Pi.sub_apply, inner_sub_right]
-  rw [integral_sub
-      ((integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs).const_inner c)
-      ((integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs).const_inner c)]
-  have h_ae_eq_f := mem_ℒp.coe_fn_to_Lp ((Lp.mem_ℒp f).const_inner c)
-  rw [← Lp_meas_coe, sub_eq_zero, ←
-    set_integral_congr_ae (hm s hs) ((condexp_L2_const_inner hm f c).mono fun x hx _ => hx), ←
-    set_integral_congr_ae (hm s hs) (h_ae_eq_f.mono fun x hx _ => hx)]
-  exact integral_condexp_L2_eq_of_fin_meas_real _ hs hμs
-#align measure_theory.integral_condexp_L2_eq MeasureTheory.integral_condexpL2_eq
-
-variable {E'' 𝕜' : Type _} [IsROrC 𝕜'] [NormedAddCommGroup E''] [InnerProductSpace 𝕜' E'']
-  [CompleteSpace E''] [NormedSpace ℝ E'']
-
-variable (𝕜 𝕜')
-
-theorem condexpL2_comp_continuousLinearMap (hm : m ≤ m0) (T : E' →L[ℝ] E'') (f : α →₂[μ] E') :
-    (condexpL2 𝕜' hm (T.compLp f) : α →₂[μ] E'') =ᵐ[μ] T.compLp (condexpL2 𝕜 hm f : α →₂[μ] E') :=
-  by
-  refine'
-    Lp.ae_eq_of_forall_set_integral_eq' 𝕜' hm _ _ two_ne_zero ENNReal.coe_ne_top
-      (fun s hs hμs => integrable_on_condexp_L2_of_measure_ne_top hm hμs.Ne _)
-      (fun s hs hμs => integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs.Ne) _ _
-      _
-  · intro s hs hμs
-    rw [T.set_integral_comp_Lp _ (hm s hs),
-      T.integral_comp_comm
-        (integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs.ne),
-      ← Lp_meas_coe, ← Lp_meas_coe, integral_condexp_L2_eq hm f hs hμs.ne,
-      integral_condexp_L2_eq hm (T.comp_Lp f) hs hμs.ne, T.set_integral_comp_Lp _ (hm s hs),
-      T.integral_comp_comm
-        (integrable_on_Lp_of_measure_ne_top f fact_one_le_two_ennreal.elim hμs.ne)]
-  · rw [← Lp_meas_coe]; exact Lp_meas.ae_strongly_measurable' _
-  · have h_coe := T.coe_fn_comp_Lp (condexp_L2 𝕜 hm f : α →₂[μ] E')
-    rw [← eventually_eq] at h_coe 
-    refine' ae_strongly_measurable'.congr _ h_coe.symm
-    exact (Lp_meas.ae_strongly_measurable' (condexp_L2 𝕜 hm f)).continuous_comp T.continuous
-#align measure_theory.condexp_L2_comp_continuous_linear_map MeasureTheory.condexpL2_comp_continuousLinearMap
-
-variable {𝕜 𝕜'}
-
-section CondexpL2Indicator
-
-variable (𝕜)
-
-theorem condexpL2_indicator_ae_eq_smul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
-    (x : E') :
-    condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x) =ᵐ[μ] fun a =>
-      condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a • x :=
-  by
-  rw [indicator_const_Lp_eq_to_span_singleton_comp_Lp hs hμs x]
-  have h_comp :=
-    condexp_L2_comp_continuous_linear_map ℝ 𝕜 hm (to_span_singleton ℝ x)
-      (indicator_const_Lp 2 hs hμs (1 : ℝ))
-  rw [← Lp_meas_coe] at h_comp 
-  refine' h_comp.trans _
-  exact (to_span_singleton ℝ x).coeFn_compLp _
-#align measure_theory.condexp_L2_indicator_ae_eq_smul MeasureTheory.condexpL2_indicator_ae_eq_smul
-
-theorem condexpL2_indicator_eq_toSpanSingleton_comp (hm : m ≤ m0) (hs : MeasurableSet s)
-    (hμs : μ s ≠ ∞) (x : E') :
-    (condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x) : α →₂[μ] E') =
-      (toSpanSingleton ℝ x).compLp (condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ))) :=
-  by
-  ext1
-  rw [← Lp_meas_coe]
-  refine' (condexp_L2_indicator_ae_eq_smul 𝕜 hm hs hμs x).trans _
-  have h_comp :=
-    (to_span_singleton ℝ x).coeFn_compLp
-      (condexp_L2 ℝ hm (indicator_const_Lp 2 hs hμs (1 : ℝ)) : α →₂[μ] ℝ)
-  rw [← eventually_eq] at h_comp 
-  refine' eventually_eq.trans _ h_comp.symm
-  refine' eventually_of_forall fun y => _
-  rfl
-#align measure_theory.condexp_L2_indicator_eq_to_span_singleton_comp MeasureTheory.condexpL2_indicator_eq_toSpanSingleton_comp
-
-variable {𝕜}
-
-theorem set_lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : MeasurableSet s)
-    (hμs : μ s ≠ ∞) (x : E') {t : Set α} (ht : measurable_set[m] t) (hμt : μ t ≠ ∞) :
-    ∫⁻ a in t, ‖condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x) a‖₊ ∂μ ≤ μ (s ∩ t) * ‖x‖₊ :=
-  calc
-    ∫⁻ a in t, ‖condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x) a‖₊ ∂μ =
-        ∫⁻ a in t, ‖condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a • x‖₊ ∂μ :=
-      set_lintegral_congr_fun (hm t ht)
-        ((condexpL2_indicator_ae_eq_smul 𝕜 hm hs hμs x).mono fun a ha hat => by rw [ha])
-    _ = (∫⁻ a in t, ‖condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a‖₊ ∂μ) * ‖x‖₊ :=
-      by
-      simp_rw [nnnorm_smul, ENNReal.coe_mul]
-      rw [lintegral_mul_const, Lp_meas_coe]
-      exact (Lp.strongly_measurable _).ennnorm
-    _ ≤ μ (s ∩ t) * ‖x‖₊ :=
-      mul_le_mul_right' (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) _
-#align measure_theory.set_lintegral_nnnorm_condexp_L2_indicator_le MeasureTheory.set_lintegral_nnnorm_condexpL2_indicator_le
-
-theorem lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
-    (x : E') [SigmaFinite (μ.trim hm)] :
-    ∫⁻ a, ‖condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x) a‖₊ ∂μ ≤ μ s * ‖x‖₊ :=
-  by
-  refine' lintegral_le_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) _ fun t ht hμt => _
-  · rw [Lp_meas_coe]
-    exact (Lp.ae_strongly_measurable _).ennnorm
-  refine' (set_lintegral_nnnorm_condexp_L2_indicator_le hm hs hμs x ht hμt).trans _
-  exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
-#align measure_theory.lintegral_nnnorm_condexp_L2_indicator_le MeasureTheory.lintegral_nnnorm_condexpL2_indicator_le
-
-/-- If the measure `μ.trim hm` is sigma-finite, then the conditional expectation of a measurable set
-with finite measure is integrable. -/
-theorem integrable_condexpL2_indicator (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
-    (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : E') :
-    Integrable (condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x)) μ :=
-  by
-  refine'
-    integrable_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) (ENNReal.mul_lt_top hμs ENNReal.coe_ne_top) _
-      _
-  · rw [Lp_meas_coe]; exact Lp.ae_strongly_measurable _
-  · refine' fun t ht hμt =>
-      (set_lintegral_nnnorm_condexp_L2_indicator_le hm hs hμs x ht hμt).trans _
-    exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
-#align measure_theory.integrable_condexp_L2_indicator MeasureTheory.integrable_condexpL2_indicator
-
-end CondexpL2Indicator
-
-section CondexpIndSmul
-
-variable [NormedSpace ℝ G] {hm : m ≤ m0}
-
-/-- Conditional expectation of the indicator of a measurable set with finite measure, in L2. -/
-def condexpIndSmul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) : Lp G 2 μ :=
-  (toSpanSingleton ℝ x).compLpL 2 μ (condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)))
-#align measure_theory.condexp_ind_smul MeasureTheory.condexpIndSmul
-
-theorem aeStronglyMeasurable'_condexpIndSmul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
-    (x : G) : AeStronglyMeasurable' m (condexpIndSmul hm hs hμs x) μ :=
-  by
-  have h : ae_strongly_measurable' m (condexp_L2 ℝ hm (indicator_const_Lp 2 hs hμs (1 : ℝ))) μ :=
-    ae_strongly_measurable'_condexp_L2 _ _
-  rw [condexp_ind_smul]
-  suffices
-    ae_strongly_measurable' m
-      (to_span_singleton ℝ x ∘ condexp_L2 ℝ hm (indicator_const_Lp 2 hs hμs (1 : ℝ))) μ
-    by
-    refine' ae_strongly_measurable'.congr this _
-    refine' eventually_eq.trans _ (coe_fn_comp_LpL _ _).symm
-    rw [Lp_meas_coe]
-  exact ae_strongly_measurable'.continuous_comp (to_span_singleton ℝ x).Continuous h
-#align measure_theory.ae_strongly_measurable'_condexp_ind_smul MeasureTheory.aeStronglyMeasurable'_condexpIndSmul
-
-theorem condexpIndSmul_add (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x y : G) :
-    condexpIndSmul hm hs hμs (x + y) = condexpIndSmul hm hs hμs x + condexpIndSmul hm hs hμs y := by
-  simp_rw [condexp_ind_smul]; rw [to_span_singleton_add, add_comp_LpL, add_apply]
-#align measure_theory.condexp_ind_smul_add MeasureTheory.condexpIndSmul_add
-
-theorem condexpIndSmul_smul (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (c : ℝ) (x : G) :
-    condexpIndSmul hm hs hμs (c • x) = c • condexpIndSmul hm hs hμs x := by
-  simp_rw [condexp_ind_smul]; rw [to_span_singleton_smul, smul_comp_LpL, smul_apply]
-#align measure_theory.condexp_ind_smul_smul MeasureTheory.condexpIndSmul_smul
-
-theorem condexpIndSmul_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (hs : MeasurableSet s)
-    (hμs : μ s ≠ ∞) (c : 𝕜) (x : F) :
-    condexpIndSmul hm hs hμs (c • x) = c • condexpIndSmul hm hs hμs x := by
-  rw [condexp_ind_smul, condexp_ind_smul, to_span_singleton_smul',
-    (to_span_singleton ℝ x).smul_compLpL c, smul_apply]
-#align measure_theory.condexp_ind_smul_smul' MeasureTheory.condexpIndSmul_smul'
-
-theorem condexpIndSmul_ae_eq_smul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :
-    condexpIndSmul hm hs hμs x =ᵐ[μ] fun a =>
-      condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a • x :=
-  (toSpanSingleton ℝ x).coeFn_compLpL _
-#align measure_theory.condexp_ind_smul_ae_eq_smul MeasureTheory.condexpIndSmul_ae_eq_smul
-
-theorem set_lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
-    (x : G) {t : Set α} (ht : measurable_set[m] t) (hμt : μ t ≠ ∞) :
-    ∫⁻ a in t, ‖condexpIndSmul hm hs hμs x a‖₊ ∂μ ≤ μ (s ∩ t) * ‖x‖₊ :=
-  calc
-    ∫⁻ a in t, ‖condexpIndSmul hm hs hμs x a‖₊ ∂μ =
-        ∫⁻ a in t, ‖condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a • x‖₊ ∂μ :=
-      set_lintegral_congr_fun (hm t ht)
-        ((condexpIndSmul_ae_eq_smul hm hs hμs x).mono fun a ha hat => by rw [ha])
-    _ = (∫⁻ a in t, ‖condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a‖₊ ∂μ) * ‖x‖₊ :=
-      by
-      simp_rw [nnnorm_smul, ENNReal.coe_mul]
-      rw [lintegral_mul_const, Lp_meas_coe]
-      exact (Lp.strongly_measurable _).ennnorm
-    _ ≤ μ (s ∩ t) * ‖x‖₊ :=
-      mul_le_mul_right' (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) _
-#align measure_theory.set_lintegral_nnnorm_condexp_ind_smul_le MeasureTheory.set_lintegral_nnnorm_condexpIndSmul_le
-
-theorem lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
-    (x : G) [SigmaFinite (μ.trim hm)] : ∫⁻ a, ‖condexpIndSmul hm hs hμs x a‖₊ ∂μ ≤ μ s * ‖x‖₊ :=
-  by
-  refine' lintegral_le_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) _ fun t ht hμt => _
-  · exact (Lp.ae_strongly_measurable _).ennnorm
-  refine' (set_lintegral_nnnorm_condexp_ind_smul_le hm hs hμs x ht hμt).trans _
-  exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
-#align measure_theory.lintegral_nnnorm_condexp_ind_smul_le MeasureTheory.lintegral_nnnorm_condexpIndSmul_le
-
-/-- If the measure `μ.trim hm` is sigma-finite, then the conditional expectation of a measurable set
-with finite measure is integrable. -/
-theorem integrable_condexpIndSmul (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hs : MeasurableSet s)
-    (hμs : μ s ≠ ∞) (x : G) : Integrable (condexpIndSmul hm hs hμs x) μ :=
-  by
-  refine'
-    integrable_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) (ENNReal.mul_lt_top hμs ENNReal.coe_ne_top) _
-      _
-  · exact Lp.ae_strongly_measurable _
-  · refine' fun t ht hμt => (set_lintegral_nnnorm_condexp_ind_smul_le hm hs hμs x ht hμt).trans _
-    exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
-#align measure_theory.integrable_condexp_ind_smul MeasureTheory.integrable_condexpIndSmul
-
-theorem condexpIndSmul_empty {x : G} :
-    condexpIndSmul hm MeasurableSet.empty ((@measure_empty _ _ μ).le.trans_lt ENNReal.coe_lt_top).Ne
-        x =
-      0 :=
-  by
-  rw [condexp_ind_smul, indicator_const_empty]
-  simp only [coeFn_coeBase, Submodule.coe_zero, ContinuousLinearMap.map_zero]
-#align measure_theory.condexp_ind_smul_empty MeasureTheory.condexpIndSmul_empty
-
-theorem set_integral_condexpL2_indicator (hs : measurable_set[m] s) (ht : MeasurableSet t)
-    (hμs : μ s ≠ ∞) (hμt : μ t ≠ ∞) :
-    ∫ x in s, (condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ))) x ∂μ = (μ (t ∩ s)).toReal :=
-  calc
-    ∫ x in s, (condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ))) x ∂μ =
-        ∫ x in s, indicatorConstLp 2 ht hμt (1 : ℝ) x ∂μ :=
-      @integral_condexpL2_eq α _ ℝ _ _ _ _ _ _ _ _ _ hm (indicatorConstLp 2 ht hμt (1 : ℝ)) hs hμs
-    _ = (μ (t ∩ s)).toReal • 1 := (set_integral_indicatorConstLp (hm s hs) ht hμt (1 : ℝ))
-    _ = (μ (t ∩ s)).toReal := by rw [smul_eq_mul, mul_one]
-#align measure_theory.set_integral_condexp_L2_indicator MeasureTheory.set_integral_condexpL2_indicator
-
-theorem set_integral_condexpIndSmul (hs : measurable_set[m] s) (ht : MeasurableSet t)
-    (hμs : μ s ≠ ∞) (hμt : μ t ≠ ∞) (x : G') :
-    ∫ a in s, (condexpIndSmul hm ht hμt x) a ∂μ = (μ (t ∩ s)).toReal • x :=
-  calc
-    ∫ a in s, (condexpIndSmul hm ht hμt x) a ∂μ =
-        ∫ a in s, condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ)) a • x ∂μ :=
-      set_integral_congr_ae (hm s hs)
-        ((condexpIndSmul_ae_eq_smul hm ht hμt x).mono fun x hx hxs => hx)
-    _ = (∫ a in s, condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ)) a ∂μ) • x :=
-      (integral_smul_const _ x)
-    _ = (μ (t ∩ s)).toReal • x := by rw [set_integral_condexp_L2_indicator hs ht hμs hμt]
-#align measure_theory.set_integral_condexp_ind_smul MeasureTheory.set_integral_condexpIndSmul
-
-theorem condexpL2_indicator_nonneg (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
-    [SigmaFinite (μ.trim hm)] : 0 ≤ᵐ[μ] condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) :=
-  by
-  have h : ae_strongly_measurable' m (condexp_L2 ℝ hm (indicator_const_Lp 2 hs hμs (1 : ℝ))) μ :=
-    ae_strongly_measurable'_condexp_L2 _ _
-  refine' eventually_le.trans_eq _ h.ae_eq_mk.symm
-  refine' @ae_le_of_ae_le_trim _ _ _ _ _ _ hm _ _ _
-  refine' ae_nonneg_of_forall_set_integral_nonneg_of_sigma_finite _ _
-  · intro t ht hμt
-    refine' @integrable.integrable_on _ _ m _ _ _ _ _
-    refine' integrable.trim hm _ _
-    · rw [integrable_congr h.ae_eq_mk.symm]
-      exact integrable_condexp_L2_indicator hm hs hμs _
-    · exact h.strongly_measurable_mk
-  · intro t ht hμt
-    rw [← set_integral_trim hm h.strongly_measurable_mk ht]
-    have h_ae :
-      ∀ᵐ x ∂μ, x ∈ t → h.mk _ x = condexp_L2 ℝ hm (indicator_const_Lp 2 hs hμs (1 : ℝ)) x :=
-      by
-      filter_upwards [h.ae_eq_mk] with x hx
-      exact fun _ => hx.symm
-    rw [set_integral_congr_ae (hm t ht) h_ae,
-      set_integral_condexp_L2_indicator ht hs ((le_trim hm).trans_lt hμt).Ne hμs]
-    exact ENNReal.toReal_nonneg
-#align measure_theory.condexp_L2_indicator_nonneg MeasureTheory.condexpL2_indicator_nonneg
-
-theorem condexpIndSmul_nonneg {E} [NormedLatticeAddCommGroup E] [NormedSpace ℝ E] [OrderedSMul ℝ E]
-    [SigmaFinite (μ.trim hm)] (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : E) (hx : 0 ≤ x) :
-    0 ≤ᵐ[μ] condexpIndSmul hm hs hμs x :=
-  by
-  refine' eventually_le.trans_eq _ (condexp_ind_smul_ae_eq_smul hm hs hμs x).symm
-  filter_upwards [condexp_L2_indicator_nonneg hm hs hμs] with a ha
-  exact smul_nonneg ha hx
-#align measure_theory.condexp_ind_smul_nonneg MeasureTheory.condexpIndSmul_nonneg
-
-end CondexpIndSmul
-
-end CondexpL2
-
-section CondexpInd
-
-/-! ## Conditional expectation of an indicator as a continuous linear map.
-
-The goal of this section is to build
-`condexp_ind (hm : m ≤ m0) (μ : measure α) (s : set s) : G →L[ℝ] α →₁[μ] G`, which
-takes `x : G` to the conditional expectation of the indicator of the set `s` with value `x`,
-seen as an element of `α →₁[μ] G`.
--/
-
-
-variable {m m0 : MeasurableSpace α} {μ : Measure α} {s t : Set α} [NormedSpace ℝ G]
-
-section CondexpIndL1Fin
-
-/-- Conditional expectation of the indicator of a measurable set with finite measure,
-as a function in L1. -/
-def condexpIndL1Fin (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
-    (x : G) : α →₁[μ] G :=
-  (integrable_condexpIndSmul hm hs hμs x).toL1 _
-#align measure_theory.condexp_ind_L1_fin MeasureTheory.condexpIndL1Fin
-
-theorem condexpIndL1Fin_ae_eq_condexpIndSmul (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
-    (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :
-    condexpIndL1Fin hm hs hμs x =ᵐ[μ] condexpIndSmul hm hs hμs x :=
-  (integrable_condexpIndSmul hm hs hμs x).coeFn_toL1
-#align measure_theory.condexp_ind_L1_fin_ae_eq_condexp_ind_smul MeasureTheory.condexpIndL1Fin_ae_eq_condexpIndSmul
-
-variable {hm : m ≤ m0} [SigmaFinite (μ.trim hm)]
-
-theorem condexpIndL1Fin_add (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x y : G) :
-    condexpIndL1Fin hm hs hμs (x + y) = condexpIndL1Fin hm hs hμs x + condexpIndL1Fin hm hs hμs y :=
-  by
-  ext1
-  refine' (mem_ℒp.coe_fn_to_Lp _).trans _
-  refine' eventually_eq.trans _ (Lp.coe_fn_add _ _).symm
-  refine'
-    eventually_eq.trans _
-      (eventually_eq.add (mem_ℒp.coe_fn_to_Lp _).symm (mem_ℒp.coe_fn_to_Lp _).symm)
-  rw [condexp_ind_smul_add]
-  refine' (Lp.coe_fn_add _ _).trans (eventually_of_forall fun a => _)
-  rfl
-#align measure_theory.condexp_ind_L1_fin_add MeasureTheory.condexpIndL1Fin_add
-
-theorem condexpIndL1Fin_smul (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (c : ℝ) (x : G) :
-    condexpIndL1Fin hm hs hμs (c • x) = c • condexpIndL1Fin hm hs hμs x :=
-  by
-  ext1
-  refine' (mem_ℒp.coe_fn_to_Lp _).trans _
-  refine' eventually_eq.trans _ (Lp.coe_fn_smul _ _).symm
-  rw [condexp_ind_smul_smul hs hμs c x]
-  refine' (Lp.coe_fn_smul _ _).trans _
-  refine' (condexp_ind_L1_fin_ae_eq_condexp_ind_smul hm hs hμs x).mono fun y hy => _
-  rw [Pi.smul_apply, Pi.smul_apply, hy]
-#align measure_theory.condexp_ind_L1_fin_smul MeasureTheory.condexpIndL1Fin_smul
-
-theorem condexpIndL1Fin_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (hs : MeasurableSet s)
-    (hμs : μ s ≠ ∞) (c : 𝕜) (x : F) :
-    condexpIndL1Fin hm hs hμs (c • x) = c • condexpIndL1Fin hm hs hμs x :=
-  by
-  ext1
-  refine' (mem_ℒp.coe_fn_to_Lp _).trans _
-  refine' eventually_eq.trans _ (Lp.coe_fn_smul _ _).symm
-  rw [condexp_ind_smul_smul' hs hμs c x]
-  refine' (Lp.coe_fn_smul _ _).trans _
-  refine' (condexp_ind_L1_fin_ae_eq_condexp_ind_smul hm hs hμs x).mono fun y hy => _
-  rw [Pi.smul_apply, Pi.smul_apply, hy]
-#align measure_theory.condexp_ind_L1_fin_smul' MeasureTheory.condexpIndL1Fin_smul'
-
-theorem norm_condexpIndL1Fin_le (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :
-    ‖condexpIndL1Fin hm hs hμs x‖ ≤ (μ s).toReal * ‖x‖ :=
-  by
-  have : 0 ≤ ∫ a : α, ‖condexp_ind_L1_fin hm hs hμs x a‖ ∂μ :=
-    integral_nonneg fun a => norm_nonneg _
-  rw [L1.norm_eq_integral_norm, ← ENNReal.toReal_ofReal (norm_nonneg x), ← ENNReal.toReal_mul, ←
-    ENNReal.toReal_ofReal this,
-    ENNReal.toReal_le_toReal ENNReal.ofReal_ne_top (ENNReal.mul_ne_top hμs ENNReal.ofReal_ne_top),
-    of_real_integral_norm_eq_lintegral_nnnorm]
-  swap; · rw [← mem_ℒp_one_iff_integrable]; exact Lp.mem_ℒp _
-  have h_eq :
-    ∫⁻ a, ‖condexp_ind_L1_fin hm hs hμs x a‖₊ ∂μ = ∫⁻ a, ‖condexp_ind_smul hm hs hμs x a‖₊ ∂μ :=
-    by
-    refine' lintegral_congr_ae _
-    refine' (condexp_ind_L1_fin_ae_eq_condexp_ind_smul hm hs hμs x).mono fun z hz => _
-    dsimp only
-    rw [hz]
-  rw [h_eq, ofReal_norm_eq_coe_nnnorm]
-  exact lintegral_nnnorm_condexp_ind_smul_le hm hs hμs x
-#align measure_theory.norm_condexp_ind_L1_fin_le MeasureTheory.norm_condexpIndL1Fin_le
-
-theorem condexpIndL1Fin_disjoint_union (hs : MeasurableSet s) (ht : MeasurableSet t) (hμs : μ s ≠ ∞)
-    (hμt : μ t ≠ ∞) (hst : s ∩ t = ∅) (x : G) :
-    condexpIndL1Fin hm (hs.union ht)
-        ((measure_union_le s t).trans_lt
-            (lt_top_iff_ne_top.mpr (ENNReal.add_ne_top.mpr ⟨hμs, hμt⟩))).Ne
-        x =
-      condexpIndL1Fin hm hs hμs x + condexpIndL1Fin hm ht hμt x :=
-  by
-  ext1
-  have hμst :=
-    ((measure_union_le s t).trans_lt (lt_top_iff_ne_top.mpr (ennreal.add_ne_top.mpr ⟨hμs, hμt⟩))).Ne
-  refine' (condexp_ind_L1_fin_ae_eq_condexp_ind_smul hm (hs.union ht) hμst x).trans _
-  refine' eventually_eq.trans _ (Lp.coe_fn_add _ _).symm
-  have hs_eq := condexp_ind_L1_fin_ae_eq_condexp_ind_smul hm hs hμs x
-  have ht_eq := condexp_ind_L1_fin_ae_eq_condexp_ind_smul hm ht hμt x
-  refine' eventually_eq.trans _ (eventually_eq.add hs_eq.symm ht_eq.symm)
-  rw [condexp_ind_smul]
-  rw [indicator_const_Lp_disjoint_union hs ht hμs hμt hst (1 : ℝ)]
-  rw [(condexp_L2 ℝ hm).map_add]
-  push_cast
-  rw [((to_span_singleton ℝ x).compLpL 2 μ).map_add]
-  refine' (Lp.coe_fn_add _ _).trans _
-  refine' eventually_of_forall fun y => _
-  rfl
-#align measure_theory.condexp_ind_L1_fin_disjoint_union MeasureTheory.condexpIndL1Fin_disjoint_union
-
-end CondexpIndL1Fin
-
-open scoped Classical
-
-section CondexpIndL1
-
-/-- Conditional expectation of the indicator of a set, as a function in L1. Its value for sets
-which are not both measurable and of finite measure is not used: we set it to 0. -/
-def condexpIndL1 {m m0 : MeasurableSpace α} (hm : m ≤ m0) (μ : Measure α) (s : Set α)
-    [SigmaFinite (μ.trim hm)] (x : G) : α →₁[μ] G :=
-  if hs : MeasurableSet s ∧ μ s ≠ ∞ then condexpIndL1Fin hm hs.1 hs.2 x else 0
-#align measure_theory.condexp_ind_L1 MeasureTheory.condexpIndL1
-
-variable {hm : m ≤ m0} [SigmaFinite (μ.trim hm)]
-
-theorem condexpIndL1_of_measurableSet_of_measure_ne_top (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
-    (x : G) : condexpIndL1 hm μ s x = condexpIndL1Fin hm hs hμs x := by
-  simp only [condexp_ind_L1, And.intro hs hμs, dif_pos, Ne.def, not_false_iff, and_self_iff]
-#align measure_theory.condexp_ind_L1_of_measurable_set_of_measure_ne_top MeasureTheory.condexpIndL1_of_measurableSet_of_measure_ne_top
-
-theorem condexpIndL1_of_measure_eq_top (hμs : μ s = ∞) (x : G) : condexpIndL1 hm μ s x = 0 := by
-  simp only [condexp_ind_L1, hμs, eq_self_iff_true, not_true, Ne.def, dif_neg, not_false_iff,
-    and_false_iff]
-#align measure_theory.condexp_ind_L1_of_measure_eq_top MeasureTheory.condexpIndL1_of_measure_eq_top
-
-theorem condexpIndL1_of_not_measurableSet (hs : ¬MeasurableSet s) (x : G) :
-    condexpIndL1 hm μ s x = 0 := by
-  simp only [condexp_ind_L1, hs, dif_neg, not_false_iff, false_and_iff]
-#align measure_theory.condexp_ind_L1_of_not_measurable_set MeasureTheory.condexpIndL1_of_not_measurableSet
-
-theorem condexpIndL1_add (x y : G) :
-    condexpIndL1 hm μ s (x + y) = condexpIndL1 hm μ s x + condexpIndL1 hm μ s y :=
-  by
-  by_cases hs : MeasurableSet s
-  swap; · simp_rw [condexp_ind_L1_of_not_measurable_set hs]; rw [zero_add]
-  by_cases hμs : μ s = ∞
-  · simp_rw [condexp_ind_L1_of_measure_eq_top hμs]; rw [zero_add]
-  · simp_rw [condexp_ind_L1_of_measurable_set_of_measure_ne_top hs hμs]
-    exact condexp_ind_L1_fin_add hs hμs x y
-#align measure_theory.condexp_ind_L1_add MeasureTheory.condexpIndL1_add
-
-theorem condexpIndL1_smul (c : ℝ) (x : G) :
-    condexpIndL1 hm μ s (c • x) = c • condexpIndL1 hm μ s x :=
-  by
-  by_cases hs : MeasurableSet s
-  swap; · simp_rw [condexp_ind_L1_of_not_measurable_set hs]; rw [smul_zero]
-  by_cases hμs : μ s = ∞
-  · simp_rw [condexp_ind_L1_of_measure_eq_top hμs]; rw [smul_zero]
-  · simp_rw [condexp_ind_L1_of_measurable_set_of_measure_ne_top hs hμs]
-    exact condexp_ind_L1_fin_smul hs hμs c x
-#align measure_theory.condexp_ind_L1_smul MeasureTheory.condexpIndL1_smul
-
-theorem condexpIndL1_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (c : 𝕜) (x : F) :
-    condexpIndL1 hm μ s (c • x) = c • condexpIndL1 hm μ s x :=
-  by
-  by_cases hs : MeasurableSet s
-  swap; · simp_rw [condexp_ind_L1_of_not_measurable_set hs]; rw [smul_zero]
-  by_cases hμs : μ s = ∞
-  · simp_rw [condexp_ind_L1_of_measure_eq_top hμs]; rw [smul_zero]
-  · simp_rw [condexp_ind_L1_of_measurable_set_of_measure_ne_top hs hμs]
-    exact condexp_ind_L1_fin_smul' hs hμs c x
-#align measure_theory.condexp_ind_L1_smul' MeasureTheory.condexpIndL1_smul'
-
-theorem norm_condexpIndL1_le (x : G) : ‖condexpIndL1 hm μ s x‖ ≤ (μ s).toReal * ‖x‖ :=
-  by
-  by_cases hs : MeasurableSet s
-  swap;
-  · simp_rw [condexp_ind_L1_of_not_measurable_set hs]; rw [Lp.norm_zero]
-    exact mul_nonneg ENNReal.toReal_nonneg (norm_nonneg _)
-  by_cases hμs : μ s = ∞
-  · rw [condexp_ind_L1_of_measure_eq_top hμs x, Lp.norm_zero]
-    exact mul_nonneg ENNReal.toReal_nonneg (norm_nonneg _)
-  · rw [condexp_ind_L1_of_measurable_set_of_measure_ne_top hs hμs x]
-    exact norm_condexp_ind_L1_fin_le hs hμs x
-#align measure_theory.norm_condexp_ind_L1_le MeasureTheory.norm_condexpIndL1_le
-
-theorem continuous_condexpIndL1 : Continuous fun x : G => condexpIndL1 hm μ s x :=
-  continuous_of_linear_of_bound condexpIndL1_add condexpIndL1_smul norm_condexpIndL1_le
-#align measure_theory.continuous_condexp_ind_L1 MeasureTheory.continuous_condexpIndL1
-
-theorem condexpIndL1_disjoint_union (hs : MeasurableSet s) (ht : MeasurableSet t) (hμs : μ s ≠ ∞)
-    (hμt : μ t ≠ ∞) (hst : s ∩ t = ∅) (x : G) :
-    condexpIndL1 hm μ (s ∪ t) x = condexpIndL1 hm μ s x + condexpIndL1 hm μ t x :=
-  by
-  have hμst : μ (s ∪ t) ≠ ∞ :=
-    ((measure_union_le s t).trans_lt (lt_top_iff_ne_top.mpr (ennreal.add_ne_top.mpr ⟨hμs, hμt⟩))).Ne
-  rw [condexp_ind_L1_of_measurable_set_of_measure_ne_top hs hμs x,
-    condexp_ind_L1_of_measurable_set_of_measure_ne_top ht hμt x,
-    condexp_ind_L1_of_measurable_set_of_measure_ne_top (hs.union ht) hμst x]
-  exact condexp_ind_L1_fin_disjoint_union hs ht hμs hμt hst x
-#align measure_theory.condexp_ind_L1_disjoint_union MeasureTheory.condexpIndL1_disjoint_union
-
-end CondexpIndL1
-
-/-- Conditional expectation of the indicator of a set, as a linear map from `G` to L1. -/
-def condexpInd {m m0 : MeasurableSpace α} (hm : m ≤ m0) (μ : Measure α) [SigmaFinite (μ.trim hm)]
-    (s : Set α) : G →L[ℝ] α →₁[μ] G
-    where
-  toFun := condexpIndL1 hm μ s
-  map_add' := condexpIndL1_add
-  map_smul' := condexpIndL1_smul
-  cont := continuous_condexpIndL1
-#align measure_theory.condexp_ind MeasureTheory.condexpInd
-
-theorem condexpInd_ae_eq_condexpIndSmul (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
-    (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :
-    condexpInd hm μ s x =ᵐ[μ] condexpIndSmul hm hs hμs x :=
-  by
-  refine' eventually_eq.trans _ (condexp_ind_L1_fin_ae_eq_condexp_ind_smul hm hs hμs x)
-  simp [condexp_ind, condexp_ind_L1, hs, hμs]
-#align measure_theory.condexp_ind_ae_eq_condexp_ind_smul MeasureTheory.condexpInd_ae_eq_condexpIndSmul
-
-variable {hm : m ≤ m0} [SigmaFinite (μ.trim hm)]
-
-theorem aeStronglyMeasurable'_condexpInd (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :
-    AeStronglyMeasurable' m (condexpInd hm μ s x) μ :=
-  AeStronglyMeasurable'.congr (aeStronglyMeasurable'_condexpIndSmul hm hs hμs x)
-    (condexpInd_ae_eq_condexpIndSmul hm hs hμs x).symm
-#align measure_theory.ae_strongly_measurable'_condexp_ind MeasureTheory.aeStronglyMeasurable'_condexpInd
-
-@[simp]
-theorem condexpInd_empty : condexpInd hm μ ∅ = (0 : G →L[ℝ] α →₁[μ] G) :=
-  by
-  ext1
-  ext1
-  refine' (condexp_ind_ae_eq_condexp_ind_smul hm MeasurableSet.empty (by simp) x).trans _
-  rw [condexp_ind_smul_empty]
-  refine' (Lp.coe_fn_zero G 2 μ).trans _
-  refine' eventually_eq.trans _ (Lp.coe_fn_zero G 1 μ).symm
-  rfl
-#align measure_theory.condexp_ind_empty MeasureTheory.condexpInd_empty
-
-theorem condexpInd_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (c : 𝕜) (x : F) :
-    condexpInd hm μ s (c • x) = c • condexpInd hm μ s x :=
-  condexpIndL1_smul' c x
-#align measure_theory.condexp_ind_smul' MeasureTheory.condexpInd_smul'
-
-theorem norm_condexpInd_apply_le (x : G) : ‖condexpInd hm μ s x‖ ≤ (μ s).toReal * ‖x‖ :=
-  norm_condexpIndL1_le x
-#align measure_theory.norm_condexp_ind_apply_le MeasureTheory.norm_condexpInd_apply_le
-
-theorem norm_condexpInd_le : ‖(condexpInd hm μ s : G →L[ℝ] α →₁[μ] G)‖ ≤ (μ s).toReal :=
-  ContinuousLinearMap.op_norm_le_bound _ ENNReal.toReal_nonneg norm_condexpInd_apply_le
-#align measure_theory.norm_condexp_ind_le MeasureTheory.norm_condexpInd_le
-
-theorem condexpInd_disjoint_union_apply (hs : MeasurableSet s) (ht : MeasurableSet t)
-    (hμs : μ s ≠ ∞) (hμt : μ t ≠ ∞) (hst : s ∩ t = ∅) (x : G) :
-    condexpInd hm μ (s ∪ t) x = condexpInd hm μ s x + condexpInd hm μ t x :=
-  condexpIndL1_disjoint_union hs ht hμs hμt hst x
-#align measure_theory.condexp_ind_disjoint_union_apply MeasureTheory.condexpInd_disjoint_union_apply
-
-theorem condexpInd_disjoint_union (hs : MeasurableSet s) (ht : MeasurableSet t) (hμs : μ s ≠ ∞)
-    (hμt : μ t ≠ ∞) (hst : s ∩ t = ∅) :
-    (condexpInd hm μ (s ∪ t) : G →L[ℝ] α →₁[μ] G) = condexpInd hm μ s + condexpInd hm μ t := by
-  ext1; push_cast ; exact condexp_ind_disjoint_union_apply hs ht hμs hμt hst x
-#align measure_theory.condexp_ind_disjoint_union MeasureTheory.condexpInd_disjoint_union
-
-variable (G)
-
-theorem dominatedFinMeasAdditive_condexpInd (hm : m ≤ m0) (μ : Measure α)
-    [SigmaFinite (μ.trim hm)] :
-    DominatedFinMeasAdditive μ (condexpInd hm μ : Set α → G →L[ℝ] α →₁[μ] G) 1 :=
-  ⟨fun s t => condexpInd_disjoint_union, fun s _ _ => norm_condexpInd_le.trans (one_mul _).symm.le⟩
-#align measure_theory.dominated_fin_meas_additive_condexp_ind MeasureTheory.dominatedFinMeasAdditive_condexpInd
-
-variable {G}
-
-theorem set_integral_condexpInd (hs : measurable_set[m] s) (ht : MeasurableSet t) (hμs : μ s ≠ ∞)
-    (hμt : μ t ≠ ∞) (x : G') : ∫ a in s, condexpInd hm μ t x a ∂μ = (μ (t ∩ s)).toReal • x :=
-  calc
-    ∫ a in s, condexpInd hm μ t x a ∂μ = ∫ a in s, condexpIndSmul hm ht hμt x a ∂μ :=
-      set_integral_congr_ae (hm s hs)
-        ((condexpInd_ae_eq_condexpIndSmul hm ht hμt x).mono fun x hx hxs => hx)
-    _ = (μ (t ∩ s)).toReal • x := set_integral_condexpIndSmul hs ht hμs hμt x
-#align measure_theory.set_integral_condexp_ind MeasureTheory.set_integral_condexpInd
-
-theorem condexpInd_of_measurable (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) (c : G) :
-    condexpInd hm μ s c = indicatorConstLp 1 (hm s hs) hμs c :=
-  by
-  ext1
-  refine' eventually_eq.trans _ indicator_const_Lp_coe_fn.symm
-  refine' (condexp_ind_ae_eq_condexp_ind_smul hm (hm s hs) hμs c).trans _
-  refine' (condexp_ind_smul_ae_eq_smul hm (hm s hs) hμs c).trans _
-  rw [Lp_meas_coe, condexp_L2_indicator_of_measurable hm hs hμs (1 : ℝ)]
-  refine' (@indicator_const_Lp_coe_fn α _ _ 2 μ _ s (hm s hs) hμs (1 : ℝ)).mono fun x hx => _
-  dsimp only
-  rw [hx]
-  by_cases hx_mem : x ∈ s <;> simp [hx_mem]
-#align measure_theory.condexp_ind_of_measurable MeasureTheory.condexpInd_of_measurable
-
-theorem condexpInd_nonneg {E} [NormedLatticeAddCommGroup E] [NormedSpace ℝ E] [OrderedSMul ℝ E]
-    (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : E) (hx : 0 ≤ x) : 0 ≤ condexpInd hm μ s x :=
-  by
-  rw [← coe_fn_le]
-  refine' eventually_le.trans_eq _ (condexp_ind_ae_eq_condexp_ind_smul hm hs hμs x).symm
-  exact (coe_fn_zero E 1 μ).trans_le (condexp_ind_smul_nonneg hs hμs x hx)
-#align measure_theory.condexp_ind_nonneg MeasureTheory.condexpInd_nonneg
-
-end CondexpInd
-
-section CondexpL1
-
-variable {m m0 : MeasurableSpace α} {μ : Measure α} {hm : m ≤ m0} [SigmaFinite (μ.trim hm)]
-  {f g : α → F'} {s : Set α}
-
-/-- Conditional expectation of a function as a linear map from `α →₁[μ] F'` to itself. -/
-def condexpL1Clm (hm : m ≤ m0) (μ : Measure α) [SigmaFinite (μ.trim hm)] :
-    (α →₁[μ] F') →L[ℝ] α →₁[μ] F' :=
-  L1.setToL1 (dominatedFinMeasAdditive_condexpInd F' hm μ)
-#align measure_theory.condexp_L1_clm MeasureTheory.condexpL1Clm
-
-theorem condexpL1Clm_smul (c : 𝕜) (f : α →₁[μ] F') :
-    condexpL1Clm hm μ (c • f) = c • condexpL1Clm hm μ f :=
-  L1.setToL1_smul (dominatedFinMeasAdditive_condexpInd F' hm μ) (fun c s x => condexpInd_smul' c x)
-    c f
-#align measure_theory.condexp_L1_clm_smul MeasureTheory.condexpL1Clm_smul
-
-theorem condexpL1Clm_indicatorConstLp (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : F') :
-    (condexpL1Clm hm μ) (indicatorConstLp 1 hs hμs x) = condexpInd hm μ s x :=
-  L1.setToL1_indicatorConstLp (dominatedFinMeasAdditive_condexpInd F' hm μ) hs hμs x
-#align measure_theory.condexp_L1_clm_indicator_const_Lp MeasureTheory.condexpL1Clm_indicatorConstLp
-
-theorem condexpL1Clm_indicatorConst (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : F') :
-    (condexpL1Clm hm μ) ↑(simpleFunc.indicatorConst 1 hs hμs x) = condexpInd hm μ s x := by
-  rw [Lp.simple_func.coe_indicator_const]; exact condexp_L1_clm_indicator_const_Lp hs hμs x
-#align measure_theory.condexp_L1_clm_indicator_const MeasureTheory.condexpL1Clm_indicatorConst
-
-/-- Auxiliary lemma used in the proof of `set_integral_condexp_L1_clm`. -/
-theorem set_integral_condexpL1Clm_of_measure_ne_top (f : α →₁[μ] F') (hs : measurable_set[m] s)
-    (hμs : μ s ≠ ∞) : ∫ x in s, condexpL1Clm hm μ f x ∂μ = ∫ x in s, f x ∂μ :=
-  by
-  refine'
-    Lp.induction ENNReal.one_ne_top
-      (fun f : α →₁[μ] F' => ∫ x in s, condexp_L1_clm hm μ f x ∂μ = ∫ x in s, f x ∂μ) _ _
-      (isClosed_eq _ _) f
-  · intro x t ht hμt
-    simp_rw [condexp_L1_clm_indicator_const ht hμt.ne x]
-    rw [Lp.simple_func.coe_indicator_const, set_integral_indicator_const_Lp (hm _ hs)]
-    exact set_integral_condexp_ind hs ht hμs hμt.ne x
-  · intro f g hf_Lp hg_Lp hfg_disj hf hg
-    simp_rw [(condexp_L1_clm hm μ).map_add]
-    rw [set_integral_congr_ae (hm s hs)
-        ((Lp.coe_fn_add (condexp_L1_clm hm μ (hf_Lp.to_Lp f))
-              (condexp_L1_clm hm μ (hg_Lp.to_Lp g))).mono
-          fun x hx hxs => hx)]
-    rw [set_integral_congr_ae (hm s hs)
-        ((Lp.coe_fn_add (hf_Lp.to_Lp f) (hg_Lp.to_Lp g)).mono fun x hx hxs => hx)]
-    simp_rw [Pi.add_apply]
-    rw [integral_add (L1.integrable_coe_fn _).IntegrableOn (L1.integrable_coe_fn _).IntegrableOn,
-      integral_add (L1.integrable_coe_fn _).IntegrableOn (L1.integrable_coe_fn _).IntegrableOn, hf,
-      hg]
-  · exact (continuous_set_integral s).comp (condexp_L1_clm hm μ).Continuous
-  · exact continuous_set_integral s
-#align measure_theory.set_integral_condexp_L1_clm_of_measure_ne_top MeasureTheory.set_integral_condexpL1Clm_of_measure_ne_top
-
-/-- The integral of the conditional expectation `condexp_L1_clm` over an `m`-measurable set is equal
-to the integral of `f` on that set. See also `set_integral_condexp`, the similar statement for
-`condexp`. -/
-theorem set_integral_condexpL1Clm (f : α →₁[μ] F') (hs : measurable_set[m] s) :
-    ∫ x in s, condexpL1Clm hm μ f x ∂μ = ∫ x in s, f x ∂μ :=
-  by
-  let S := spanning_sets (μ.trim hm)
-  have hS_meas : ∀ i, measurable_set[m] (S i) := measurable_spanning_sets (μ.trim hm)
-  have hS_meas0 : ∀ i, MeasurableSet (S i) := fun i => hm _ (hS_meas i)
-  have hs_eq : s = ⋃ i, S i ∩ s := by
-    simp_rw [Set.inter_comm]
-    rw [← Set.inter_iUnion, Union_spanning_sets (μ.trim hm), Set.inter_univ]
-  have hS_finite : ∀ i, μ (S i ∩ s) < ∞ :=
-    by
-    refine' fun i => (measure_mono (Set.inter_subset_left _ _)).trans_lt _
-    have hS_finite_trim := measure_spanning_sets_lt_top (μ.trim hm) i
-    rwa [trim_measurable_set_eq hm (hS_meas i)] at hS_finite_trim 
-  have h_mono : Monotone fun i => S i ∩ s :=
-    by
-    intro i j hij x
-    simp_rw [Set.mem_inter_iff]
-    exact fun h => ⟨monotone_spanning_sets (μ.trim hm) hij h.1, h.2⟩
-  have h_eq_forall :
-    (fun i => ∫ x in S i ∩ s, condexp_L1_clm hm μ f x ∂μ) = fun i => ∫ x in S i ∩ s, f x ∂μ :=
-    funext fun i =>
-      set_integral_condexp_L1_clm_of_measure_ne_top f (@MeasurableSet.inter α m _ _ (hS_meas i) hs)
-        (hS_finite i).Ne
-  have h_right : tendsto (fun i => ∫ x in S i ∩ s, f x ∂μ) at_top (𝓝 (∫ x in s, f x ∂μ)) :=
-    by
-    have h :=
-      tendsto_set_integral_of_monotone (fun i => (hS_meas0 i).inter (hm s hs)) h_mono
-        (L1.integrable_coe_fn f).IntegrableOn
-    rwa [← hs_eq] at h 
-  have h_left :
-    tendsto (fun i => ∫ x in S i ∩ s, condexp_L1_clm hm μ f x ∂μ) at_top
-      (𝓝 (∫ x in s, condexp_L1_clm hm μ f x ∂μ)) :=
-    by
-    have h :=
-      tendsto_set_integral_of_monotone (fun i => (hS_meas0 i).inter (hm s hs)) h_mono
-        (L1.integrable_coe_fn (condexp_L1_clm hm μ f)).IntegrableOn
-    rwa [← hs_eq] at h 
-  rw [h_eq_forall] at h_left 
-  exact tendsto_nhds_unique h_left h_right
-#align measure_theory.set_integral_condexp_L1_clm MeasureTheory.set_integral_condexpL1Clm
-
-theorem aeStronglyMeasurable'_condexpL1Clm (f : α →₁[μ] F') :
-    AeStronglyMeasurable' m (condexpL1Clm hm μ f) μ :=
-  by
-  refine'
-    Lp.induction ENNReal.one_ne_top
-      (fun f : α →₁[μ] F' => ae_strongly_measurable' m (condexp_L1_clm hm μ f) μ) _ _ _ f
-  · intro c s hs hμs
-    rw [condexp_L1_clm_indicator_const hs hμs.ne c]
-    exact ae_strongly_measurable'_condexp_ind hs hμs.ne c
-  · intro f g hf hg h_disj hfm hgm
-    rw [(condexp_L1_clm hm μ).map_add]
-    refine' ae_strongly_measurable'.congr _ (coe_fn_add _ _).symm
-    exact ae_strongly_measurable'.add hfm hgm
-  · have :
-      {f : Lp F' 1 μ | ae_strongly_measurable' m (condexp_L1_clm hm μ f) μ} =
-        condexp_L1_clm hm μ ⁻¹' {f | ae_strongly_measurable' m f μ} :=
-      by rfl
-    rw [this]
-    refine' IsClosed.preimage (condexp_L1_clm hm μ).Continuous _
-    exact is_closed_ae_strongly_measurable' hm
-#align measure_theory.ae_strongly_measurable'_condexp_L1_clm MeasureTheory.aeStronglyMeasurable'_condexpL1Clm
-
-theorem condexpL1Clm_lpMeas (f : lpMeas F' ℝ m 1 μ) : condexpL1Clm hm μ (f : α →₁[μ] F') = ↑f :=
-  by
-  let g := Lp_meas_to_Lp_trim_lie F' ℝ 1 μ hm f
-  have hfg : f = (Lp_meas_to_Lp_trim_lie F' ℝ 1 μ hm).symm g := by
-    simp only [LinearIsometryEquiv.symm_apply_apply]
-  rw [hfg]
-  refine'
-    @Lp.induction α F' m _ 1 (μ.trim hm) _ ENNReal.coe_ne_top
-      (fun g : α →₁[μ.trim hm] F' =>
-        condexp_L1_clm hm μ ((Lp_meas_to_Lp_trim_lie F' ℝ 1 μ hm).symm g : α →₁[μ] F') =
-          ↑((Lp_meas_to_Lp_trim_lie F' ℝ 1 μ hm).symm g))
-      _ _ _ g
-  · intro c s hs hμs
-    rw [Lp.simple_func.coe_indicator_const, Lp_meas_to_Lp_trim_lie_symm_indicator hs hμs.ne c,
-      condexp_L1_clm_indicator_const_Lp]
-    exact condexp_ind_of_measurable hs ((le_trim hm).trans_lt hμs).Ne c
-  · intro f g hf hg hfg_disj hf_eq hg_eq
-    rw [LinearIsometryEquiv.map_add]
-    push_cast
-    rw [map_add, hf_eq, hg_eq]
-  · refine' isClosed_eq _ _
-    · refine' (condexp_L1_clm hm μ).Continuous.comp (continuous_induced_dom.comp _)
-      exact LinearIsometryEquiv.continuous _
-    · refine' continuous_induced_dom.comp _
-      exact LinearIsometryEquiv.continuous _
-#align measure_theory.condexp_L1_clm_Lp_meas MeasureTheory.condexpL1Clm_lpMeas
-
-theorem condexpL1Clm_of_aeStronglyMeasurable' (f : α →₁[μ] F') (hfm : AeStronglyMeasurable' m f μ) :
-    condexpL1Clm hm μ f = f :=
-  condexpL1Clm_lpMeas (⟨f, hfm⟩ : lpMeas F' ℝ m 1 μ)
-#align measure_theory.condexp_L1_clm_of_ae_strongly_measurable' MeasureTheory.condexpL1Clm_of_aeStronglyMeasurable'
-
-/-- Conditional expectation of a function, in L1. Its value is 0 if the function is not
-integrable. The function-valued `condexp` should be used instead in most cases. -/
-def condexpL1 (hm : m ≤ m0) (μ : Measure α) [SigmaFinite (μ.trim hm)] (f : α → F') : α →₁[μ] F' :=
-  setToFun μ (condexpInd hm μ) (dominatedFinMeasAdditive_condexpInd F' hm μ) f
-#align measure_theory.condexp_L1 MeasureTheory.condexpL1
-
-theorem condexpL1_undef (hf : ¬Integrable f μ) : condexpL1 hm μ f = 0 :=
-  setToFun_undef (dominatedFinMeasAdditive_condexpInd F' hm μ) hf
-#align measure_theory.condexp_L1_undef MeasureTheory.condexpL1_undef
-
-theorem condexpL1_eq (hf : Integrable f μ) : condexpL1 hm μ f = condexpL1Clm hm μ (hf.toL1 f) :=
-  setToFun_eq (dominatedFinMeasAdditive_condexpInd F' hm μ) hf
-#align measure_theory.condexp_L1_eq MeasureTheory.condexpL1_eq
-
-@[simp]
-theorem condexpL1_zero : condexpL1 hm μ (0 : α → F') = 0 :=
-  setToFun_zero _
-#align measure_theory.condexp_L1_zero MeasureTheory.condexpL1_zero
-
-@[simp]
-theorem condexpL1_measure_zero (hm : m ≤ m0) : condexpL1 hm (0 : Measure α) f = 0 :=
-  setToFun_measure_zero _ rfl
-#align measure_theory.condexp_L1_measure_zero MeasureTheory.condexpL1_measure_zero
-
-theorem aeStronglyMeasurable'_condexpL1 {f : α → F'} :
-    AeStronglyMeasurable' m (condexpL1 hm μ f) μ :=
-  by
-  by_cases hf : integrable f μ
-  · rw [condexp_L1_eq hf]
-    exact ae_strongly_measurable'_condexp_L1_clm _
-  · rw [condexp_L1_undef hf]
-    refine' ae_strongly_measurable'.congr _ (coe_fn_zero _ _ _).symm
-    exact strongly_measurable.ae_strongly_measurable' (@strongly_measurable_zero _ _ m _ _)
-#align measure_theory.ae_strongly_measurable'_condexp_L1 MeasureTheory.aeStronglyMeasurable'_condexpL1
-
-theorem condexpL1_congr_ae (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (h : f =ᵐ[μ] g) :
-    condexpL1 hm μ f = condexpL1 hm μ g :=
-  setToFun_congr_ae _ h
-#align measure_theory.condexp_L1_congr_ae MeasureTheory.condexpL1_congr_ae
-
-theorem integrable_condexpL1 (f : α → F') : Integrable (condexpL1 hm μ f) μ :=
-  L1.integrable_coeFn _
-#align measure_theory.integrable_condexp_L1 MeasureTheory.integrable_condexpL1
-
-/-- The integral of the conditional expectation `condexp_L1` over an `m`-measurable set is equal to
-the integral of `f` on that set. See also `set_integral_condexp`, the similar statement for
-`condexp`. -/
-theorem set_integral_condexpL1 (hf : Integrable f μ) (hs : measurable_set[m] s) :
-    ∫ x in s, condexpL1 hm μ f x ∂μ = ∫ x in s, f x ∂μ :=
-  by
-  simp_rw [condexp_L1_eq hf]
-  rw [set_integral_condexp_L1_clm (hf.to_L1 f) hs]
-  exact set_integral_congr_ae (hm s hs) (hf.coe_fn_to_L1.mono fun x hx hxs => hx)
-#align measure_theory.set_integral_condexp_L1 MeasureTheory.set_integral_condexpL1
-
-theorem condexpL1_add (hf : Integrable f μ) (hg : Integrable g μ) :
-    condexpL1 hm μ (f + g) = condexpL1 hm μ f + condexpL1 hm μ g :=
-  setToFun_add _ hf hg
-#align measure_theory.condexp_L1_add MeasureTheory.condexpL1_add
-
-theorem condexpL1_neg (f : α → F') : condexpL1 hm μ (-f) = -condexpL1 hm μ f :=
-  setToFun_neg _ f
-#align measure_theory.condexp_L1_neg MeasureTheory.condexpL1_neg
-
-theorem condexpL1_smul (c : 𝕜) (f : α → F') : condexpL1 hm μ (c • f) = c • condexpL1 hm μ f :=
-  setToFun_smul _ (fun c _ x => condexpInd_smul' c x) c f
-#align measure_theory.condexp_L1_smul MeasureTheory.condexpL1_smul
-
-theorem condexpL1_sub (hf : Integrable f μ) (hg : Integrable g μ) :
-    condexpL1 hm μ (f - g) = condexpL1 hm μ f - condexpL1 hm μ g :=
-  setToFun_sub _ hf hg
-#align measure_theory.condexp_L1_sub MeasureTheory.condexpL1_sub
-
-theorem condexpL1_of_aeStronglyMeasurable' (hfm : AeStronglyMeasurable' m f μ)
-    (hfi : Integrable f μ) : condexpL1 hm μ f =ᵐ[μ] f :=
-  by
-  rw [condexp_L1_eq hfi]
-  refine' eventually_eq.trans _ (integrable.coe_fn_to_L1 hfi)
-  rw [condexp_L1_clm_of_ae_strongly_measurable']
-  exact ae_strongly_measurable'.congr hfm (integrable.coe_fn_to_L1 hfi).symm
-#align measure_theory.condexp_L1_of_ae_strongly_measurable' MeasureTheory.condexpL1_of_aeStronglyMeasurable'
-
-theorem condexpL1_mono {E} [NormedLatticeAddCommGroup E] [CompleteSpace E] [NormedSpace ℝ E]
-    [OrderedSMul ℝ E] {f g : α → E} (hf : Integrable f μ) (hg : Integrable g μ) (hfg : f ≤ᵐ[μ] g) :
-    condexpL1 hm μ f ≤ᵐ[μ] condexpL1 hm μ g :=
-  by
-  rw [coe_fn_le]
-  have h_nonneg : ∀ s, MeasurableSet s → μ s < ∞ → ∀ x : E, 0 ≤ x → 0 ≤ condexp_ind hm μ s x :=
-    fun s hs hμs x hx => condexp_ind_nonneg hs hμs.Ne x hx
-  exact set_to_fun_mono (dominated_fin_meas_additive_condexp_ind E hm μ) h_nonneg hf hg hfg
-#align measure_theory.condexp_L1_mono MeasureTheory.condexpL1_mono
-
-end CondexpL1
-
-section Condexp
-
-/-! ### Conditional expectation of a function -/
-
 
 open scoped Classical
 
@@ -2059,8 +92,8 @@ is true:
 - `m` is not a sub-σ-algebra of `m0`,
 - `μ` is not σ-finite with respect to `m`,
 - `f` is not integrable. -/
-irreducible_def condexp (m : MeasurableSpace α) {m0 : MeasurableSpace α} (μ : Measure α)
-    (f : α → F') : α → F' :=
+noncomputable irreducible_def condexp (m : MeasurableSpace α) {m0 : MeasurableSpace α}
+    (μ : Measure α) (f : α → F') : α → F' :=
   if hm : m ≤ m0 then
     if h : SigmaFinite (μ.trim hm) ∧ Integrable f μ then
       if strongly_measurable[m] f then f
@@ -2420,7 +453,5 @@ theorem tendsto_condexp_unique (fs gs : ℕ → α → F') (f g : α → F')
   exact tendsto_nhds_unique_of_eventuallyEq hcond_gs hcond_fs (eventually_of_forall hn_eq)
 #align measure_theory.tendsto_condexp_unique MeasureTheory.tendsto_condexp_unique
 
-end Condexp
-
 end MeasureTheory
 

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

@@ -809,7 +809,7 @@ variable {m m0 : MeasurableSpace α} {μ : Measure α}
 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)
-    (hf_zero : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → (∫ x in s, f x ∂μ) = 0) : f =ᵐ[μ] 0 :=
+    (hf_zero : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, f x ∂μ = 0) : f =ᵐ[μ] 0 :=
   by
   obtain ⟨g, hg_sm, hfg⟩ := Lp_meas.ae_fin_strongly_measurable' hm f hp_ne_zero hp_ne_top
   refine' hfg.trans _
@@ -831,7 +831,7 @@ 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, 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_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 :=
   by
   let f_meas : Lp_meas E' 𝕜 m p μ := ⟨f, hf_meas⟩
@@ -852,12 +852,12 @@ 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, 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)
+    (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 :=
   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
-  have hfg' : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → (∫ x in s, (f - g) x ∂μ) = 0 :=
+  have hfg' : ∀ s : Set α, measurable_set[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.coe_fn_sub f g))]
@@ -882,7 +882,7 @@ 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)
-    (hfg_eq : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → (∫ x in s, f x ∂μ) = ∫ x in s, g x ∂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 :=
   by
   rw [← ae_eq_trim_iff_of_ae_strongly_measurable' hm hfm hgm]
@@ -905,7 +905,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaF
   have hfg_mk_eq :
     ∀ s : Set α,
       measurable_set[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 :=
+        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 
@@ -929,8 +929,8 @@ 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 : strongly_measurable[m] g)
     (hgi : IntegrableOn g s μ)
-    (hgf : ∀ t, measurable_set[m] t → μ t < ∞ → (∫ x in t, g x ∂μ) = ∫ x in t, f x ∂μ)
-    (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) : (∫ x in s, ‖g x‖ ∂μ) ≤ ∫ x in s, ‖f x‖ ∂μ :=
+    (hgf : ∀ t, measurable_set[m] t → μ t < ∞ → ∫ x in t, g x ∂μ = ∫ x in t, f x ∂μ)
+    (hs : measurable_set[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 : measurable_set[m] {x | 0 ≤ g x} :=
@@ -963,8 +963,8 @@ 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 : strongly_measurable[m] g)
     (hgi : IntegrableOn g s μ)
-    (hgf : ∀ t, measurable_set[m] t → μ t < ∞ → (∫ x in t, g x ∂μ) = ∫ x in t, f x ∂μ)
-    (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) : (∫⁻ x in s, ‖g x‖₊ ∂μ) ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ :=
+    (hgf : ∀ t, measurable_set[m] t → μ t < ∞ → ∫ x in t, g x ∂μ = ∫ x in t, f x ∂μ)
+    (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) : ∫⁻ x in s, ‖g x‖₊ ∂μ ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ :=
   by
   rw [← of_real_integral_norm_eq_lintegral_nnnorm hfi, ←
     of_real_integral_norm_eq_lintegral_nnnorm hgi, ENNReal.ofReal_le_ofReal_iff]
@@ -1076,11 +1076,11 @@ section Real
 variable {hm : m ≤ m0}
 
 theorem integral_condexpL2_eq_of_fin_meas_real (f : Lp 𝕜 2 μ) (hs : measurable_set[m] s)
-    (hμs : μ s ≠ ∞) : (∫ x in s, condexpL2 𝕜 hm f x ∂μ) = ∫ x in s, f x ∂μ :=
+    (hμs : μ s ≠ ∞) : ∫ x in s, condexpL2 𝕜 hm f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   rw [← L2.inner_indicator_const_Lp_one (hm s hs) hμs]
   have h_eq_inner :
-    (∫ x in s, condexp_L2 𝕜 hm f x ∂μ) =
+    ∫ x in s, condexp_L2 𝕜 hm f x ∂μ =
       inner (indicator_const_Lp 2 (hm s hs) hμs (1 : 𝕜)) (condexp_L2 𝕜 hm f) :=
     by
     rw [L2.inner_indicator_const_Lp_one (hm s hs) hμs]
@@ -1089,7 +1089,7 @@ theorem integral_condexpL2_eq_of_fin_meas_real (f : Lp 𝕜 2 μ) (hs : measurab
 #align measure_theory.integral_condexp_L2_eq_of_fin_meas_real MeasureTheory.integral_condexpL2_eq_of_fin_meas_real
 
 theorem lintegral_nnnorm_condexpL2_le (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) (f : Lp ℝ 2 μ) :
-    (∫⁻ x in s, ‖condexpL2 ℝ hm f x‖₊ ∂μ) ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ :=
+    ∫⁻ x in s, ‖condexpL2 ℝ hm f x‖₊ ∂μ ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ :=
   by
   let h_meas := Lp_meas.ae_strongly_measurable' (condexp_L2 ℝ hm f)
   let g := h_meas.some
@@ -1117,7 +1117,7 @@ theorem lintegral_nnnorm_condexpL2_le (hs : measurable_set[m] s) (hμs : μ s 
 theorem condexpL2_ae_eq_zero_of_ae_eq_zero (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) {f : Lp ℝ 2 μ}
     (hf : f =ᵐ[μ.restrict s] 0) : condexpL2 ℝ hm f =ᵐ[μ.restrict s] 0 :=
   by
-  suffices h_nnnorm_eq_zero : (∫⁻ x in s, ‖condexp_L2 ℝ hm f x‖₊ ∂μ) = 0
+  suffices h_nnnorm_eq_zero : ∫⁻ x in s, ‖condexp_L2 ℝ hm f x‖₊ ∂μ = 0
   · rw [lintegral_eq_zero_iff] at h_nnnorm_eq_zero 
     refine' h_nnnorm_eq_zero.mono fun x hx => _
     dsimp only at hx 
@@ -1138,11 +1138,11 @@ theorem condexpL2_ae_eq_zero_of_ae_eq_zero (hs : measurable_set[m] s) (hμs : μ
 
 theorem lintegral_nnnorm_condexpL2_indicator_le_real (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
     (ht : measurable_set[m] t) (hμt : μ t ≠ ∞) :
-    (∫⁻ a in t, ‖condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a‖₊ ∂μ) ≤ μ (s ∩ t) :=
+    ∫⁻ a in t, ‖condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a‖₊ ∂μ ≤ μ (s ∩ t) :=
   by
   refine' (lintegral_nnnorm_condexp_L2_le ht hμt _).trans (le_of_eq _)
   have h_eq :
-    (∫⁻ x in t, ‖(indicator_const_Lp 2 hs hμs (1 : ℝ)) x‖₊ ∂μ) =
+    ∫⁻ x in t, ‖(indicator_const_Lp 2 hs hμs (1 : ℝ)) x‖₊ ∂μ =
       ∫⁻ x in t, s.indicator (fun x => (1 : ℝ≥0∞)) x ∂μ :=
     by
     refine' lintegral_congr_ae (ae_restrict_of_ae _)
@@ -1190,7 +1190,7 @@ theorem condexpL2_const_inner (hm : m ≤ m0) (f : Lp E 2 μ) (c : E) :
 
 /-- `condexp_L2` verifies the equality of integrals defining the conditional expectation. -/
 theorem integral_condexpL2_eq (hm : m ≤ m0) (f : Lp E' 2 μ) (hs : measurable_set[m] s)
-    (hμs : μ s ≠ ∞) : (∫ x in s, condexpL2 𝕜 hm f x ∂μ) = ∫ x in s, f x ∂μ :=
+    (hμs : μ s ≠ ∞) : ∫ x in s, condexpL2 𝕜 hm f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   rw [← sub_eq_zero, Lp_meas_coe, ←
     integral_sub' (integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs)
@@ -1279,9 +1279,9 @@ variable {𝕜}
 
 theorem set_lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : MeasurableSet s)
     (hμs : μ s ≠ ∞) (x : E') {t : Set α} (ht : measurable_set[m] t) (hμt : μ t ≠ ∞) :
-    (∫⁻ a in t, ‖condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x) a‖₊ ∂μ) ≤ μ (s ∩ t) * ‖x‖₊ :=
+    ∫⁻ a in t, ‖condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x) a‖₊ ∂μ ≤ μ (s ∩ t) * ‖x‖₊ :=
   calc
-    (∫⁻ a in t, ‖condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x) a‖₊ ∂μ) =
+    ∫⁻ a in t, ‖condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x) a‖₊ ∂μ =
         ∫⁻ a in t, ‖condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a • x‖₊ ∂μ :=
       set_lintegral_congr_fun (hm t ht)
         ((condexpL2_indicator_ae_eq_smul 𝕜 hm hs hμs x).mono fun a ha hat => by rw [ha])
@@ -1296,7 +1296,7 @@ theorem set_lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : Measur
 
 theorem lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
     (x : E') [SigmaFinite (μ.trim hm)] :
-    (∫⁻ a, ‖condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x) a‖₊ ∂μ) ≤ μ s * ‖x‖₊ :=
+    ∫⁻ a, ‖condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x) a‖₊ ∂μ ≤ μ s * ‖x‖₊ :=
   by
   refine' lintegral_le_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) _ fun t ht hμt => _
   · rw [Lp_meas_coe]
@@ -1372,9 +1372,9 @@ theorem condexpIndSmul_ae_eq_smul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs :
 
 theorem set_lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
     (x : G) {t : Set α} (ht : measurable_set[m] t) (hμt : μ t ≠ ∞) :
-    (∫⁻ a in t, ‖condexpIndSmul hm hs hμs x a‖₊ ∂μ) ≤ μ (s ∩ t) * ‖x‖₊ :=
+    ∫⁻ a in t, ‖condexpIndSmul hm hs hμs x a‖₊ ∂μ ≤ μ (s ∩ t) * ‖x‖₊ :=
   calc
-    (∫⁻ a in t, ‖condexpIndSmul hm hs hμs x a‖₊ ∂μ) =
+    ∫⁻ a in t, ‖condexpIndSmul hm hs hμs x a‖₊ ∂μ =
         ∫⁻ a in t, ‖condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a • x‖₊ ∂μ :=
       set_lintegral_congr_fun (hm t ht)
         ((condexpIndSmul_ae_eq_smul hm hs hμs x).mono fun a ha hat => by rw [ha])
@@ -1388,7 +1388,7 @@ theorem set_lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableS
 #align measure_theory.set_lintegral_nnnorm_condexp_ind_smul_le MeasureTheory.set_lintegral_nnnorm_condexpIndSmul_le
 
 theorem lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
-    (x : G) [SigmaFinite (μ.trim hm)] : (∫⁻ a, ‖condexpIndSmul hm hs hμs x a‖₊ ∂μ) ≤ μ s * ‖x‖₊ :=
+    (x : G) [SigmaFinite (μ.trim hm)] : ∫⁻ a, ‖condexpIndSmul hm hs hμs x a‖₊ ∂μ ≤ μ s * ‖x‖₊ :=
   by
   refine' lintegral_le_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) _ fun t ht hμt => _
   · exact (Lp.ae_strongly_measurable _).ennnorm
@@ -1420,9 +1420,9 @@ theorem condexpIndSmul_empty {x : G} :
 
 theorem set_integral_condexpL2_indicator (hs : measurable_set[m] s) (ht : MeasurableSet t)
     (hμs : μ s ≠ ∞) (hμt : μ t ≠ ∞) :
-    (∫ x in s, (condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ))) x ∂μ) = (μ (t ∩ s)).toReal :=
+    ∫ x in s, (condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ))) x ∂μ = (μ (t ∩ s)).toReal :=
   calc
-    (∫ x in s, (condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ))) x ∂μ) =
+    ∫ x in s, (condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ))) x ∂μ =
         ∫ x in s, indicatorConstLp 2 ht hμt (1 : ℝ) x ∂μ :=
       @integral_condexpL2_eq α _ ℝ _ _ _ _ _ _ _ _ _ hm (indicatorConstLp 2 ht hμt (1 : ℝ)) hs hμs
     _ = (μ (t ∩ s)).toReal • 1 := (set_integral_indicatorConstLp (hm s hs) ht hμt (1 : ℝ))
@@ -1431,9 +1431,9 @@ theorem set_integral_condexpL2_indicator (hs : measurable_set[m] s) (ht : Measur
 
 theorem set_integral_condexpIndSmul (hs : measurable_set[m] s) (ht : MeasurableSet t)
     (hμs : μ s ≠ ∞) (hμt : μ t ≠ ∞) (x : G') :
-    (∫ a in s, (condexpIndSmul hm ht hμt x) a ∂μ) = (μ (t ∩ s)).toReal • x :=
+    ∫ a in s, (condexpIndSmul hm ht hμt x) a ∂μ = (μ (t ∩ s)).toReal • x :=
   calc
-    (∫ a in s, (condexpIndSmul hm ht hμt x) a ∂μ) =
+    ∫ a in s, (condexpIndSmul hm ht hμt x) a ∂μ =
         ∫ a in s, condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ)) a • x ∂μ :=
       set_integral_congr_ae (hm s hs)
         ((condexpIndSmul_ae_eq_smul hm ht hμt x).mono fun x hx hxs => hx)
@@ -1561,7 +1561,7 @@ theorem norm_condexpIndL1Fin_le (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x
     of_real_integral_norm_eq_lintegral_nnnorm]
   swap; · rw [← mem_ℒp_one_iff_integrable]; exact Lp.mem_ℒp _
   have h_eq :
-    (∫⁻ a, ‖condexp_ind_L1_fin hm hs hμs x a‖₊ ∂μ) = ∫⁻ a, ‖condexp_ind_smul hm hs hμs x a‖₊ ∂μ :=
+    ∫⁻ a, ‖condexp_ind_L1_fin hm hs hμs x a‖₊ ∂μ = ∫⁻ a, ‖condexp_ind_smul hm hs hμs x a‖₊ ∂μ :=
     by
     refine' lintegral_congr_ae _
     refine' (condexp_ind_L1_fin_ae_eq_condexp_ind_smul hm hs hμs x).mono fun z hz => _
@@ -1765,9 +1765,9 @@ theorem dominatedFinMeasAdditive_condexpInd (hm : m ≤ m0) (μ : Measure α)
 variable {G}
 
 theorem set_integral_condexpInd (hs : measurable_set[m] s) (ht : MeasurableSet t) (hμs : μ s ≠ ∞)
-    (hμt : μ t ≠ ∞) (x : G') : (∫ a in s, condexpInd hm μ t x a ∂μ) = (μ (t ∩ s)).toReal • x :=
+    (hμt : μ t ≠ ∞) (x : G') : ∫ a in s, condexpInd hm μ t x a ∂μ = (μ (t ∩ s)).toReal • x :=
   calc
-    (∫ a in s, condexpInd hm μ t x a ∂μ) = ∫ a in s, condexpIndSmul hm ht hμt x a ∂μ :=
+    ∫ a in s, condexpInd hm μ t x a ∂μ = ∫ a in s, condexpIndSmul hm ht hμt x a ∂μ :=
       set_integral_congr_ae (hm s hs)
         ((condexpInd_ae_eq_condexpIndSmul hm ht hμt x).mono fun x hx hxs => hx)
     _ = (μ (t ∩ s)).toReal • x := set_integral_condexpIndSmul hs ht hμs hμt x
@@ -1826,11 +1826,11 @@ theorem condexpL1Clm_indicatorConst (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
 
 /-- Auxiliary lemma used in the proof of `set_integral_condexp_L1_clm`. -/
 theorem set_integral_condexpL1Clm_of_measure_ne_top (f : α →₁[μ] F') (hs : measurable_set[m] s)
-    (hμs : μ s ≠ ∞) : (∫ x in s, condexpL1Clm hm μ f x ∂μ) = ∫ x in s, f x ∂μ :=
+    (hμs : μ s ≠ ∞) : ∫ x in s, condexpL1Clm hm μ f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   refine'
     Lp.induction ENNReal.one_ne_top
-      (fun f : α →₁[μ] F' => (∫ x in s, condexp_L1_clm hm μ f x ∂μ) = ∫ x in s, f x ∂μ) _ _
+      (fun f : α →₁[μ] F' => ∫ x in s, condexp_L1_clm hm μ f x ∂μ = ∫ x in s, f x ∂μ) _ _
       (isClosed_eq _ _) f
   · intro x t ht hμt
     simp_rw [condexp_L1_clm_indicator_const ht hμt.ne x]
@@ -1856,7 +1856,7 @@ theorem set_integral_condexpL1Clm_of_measure_ne_top (f : α →₁[μ] F') (hs :
 to the integral of `f` on that set. See also `set_integral_condexp`, the similar statement for
 `condexp`. -/
 theorem set_integral_condexpL1Clm (f : α →₁[μ] F') (hs : measurable_set[m] s) :
-    (∫ x in s, condexpL1Clm hm μ f x ∂μ) = ∫ x in s, f x ∂μ :=
+    ∫ x in s, condexpL1Clm hm μ f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   let S := spanning_sets (μ.trim hm)
   have hS_meas : ∀ i, measurable_set[m] (S i) := measurable_spanning_sets (μ.trim hm)
@@ -1999,7 +1999,7 @@ theorem integrable_condexpL1 (f : α → F') : Integrable (condexpL1 hm μ f) μ
 the integral of `f` on that set. See also `set_integral_condexp`, the similar statement for
 `condexp`. -/
 theorem set_integral_condexpL1 (hf : Integrable f μ) (hs : measurable_set[m] s) :
-    (∫ x in s, condexpL1 hm μ f x ∂μ) = ∫ x in s, f x ∂μ :=
+    ∫ x in s, condexpL1 hm μ f x ∂μ = ∫ x in s, f x ∂μ :=
   by
   simp_rw [condexp_L1_eq hf]
   rw [set_integral_condexp_L1_clm (hf.to_L1 f) hs]
@@ -2201,16 +2201,16 @@ theorem integrable_condexp : Integrable (μ[f|m]) μ :=
 /-- The integral of the conditional expectation `μ[f|hm]` over an `m`-measurable set is equal to
 the integral of `f` on that set. -/
 theorem set_integral_condexp (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : Integrable f μ)
-    (hs : measurable_set[m] s) : (∫ x in s, (μ[f|m]) x ∂μ) = ∫ x in s, f x ∂μ :=
+    (hs : measurable_set[m] s) : ∫ x in s, (μ[f|m]) x ∂μ = ∫ x in s, f x ∂μ :=
   by
   rw [set_integral_congr_ae (hm s hs) ((condexp_ae_eq_condexp_L1 hm f).mono fun x hx _ => hx)]
   exact set_integral_condexp_L1 hf hs
 #align measure_theory.set_integral_condexp MeasureTheory.set_integral_condexp
 
 theorem integral_condexp (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] (hf : Integrable f μ) :
-    (∫ x, (μ[f|m]) x ∂μ) = ∫ x, f x ∂μ :=
+    ∫ x, (μ[f|m]) x ∂μ = ∫ x, f x ∂μ :=
   by
-  suffices (∫ x in Set.univ, (μ[f|m]) x ∂μ) = ∫ x in Set.univ, f x ∂μ by
+  suffices ∫ x in Set.univ, (μ[f|m]) x ∂μ = ∫ x in Set.univ, f x ∂μ by
     simp_rw [integral_univ] at this ; exact this
   exact set_integral_condexp hm hf (@MeasurableSet.univ _ m)
 #align measure_theory.integral_condexp MeasureTheory.integral_condexp
@@ -2221,7 +2221,7 @@ as `f` on all `m`-measurable sets, then it is a.e. equal to `μ[f|hm]`. -/
 theorem ae_eq_condexp_of_forall_set_integral_eq (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     {f g : α → F'} (hf : Integrable f μ)
     (hg_int_finite : ∀ s, measurable_set[m] s → μ s < ∞ → IntegrableOn g s μ)
-    (hg_eq : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → (∫ x in s, g x ∂μ) = ∫ x in s, f x ∂μ)
+    (hg_eq : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → ∫ x in s, g x ∂μ = ∫ x in s, f x ∂μ)
     (hgm : AeStronglyMeasurable' m g μ) : g =ᵐ[μ] μ[f|m] :=
   by
   refine'
@@ -2247,7 +2247,7 @@ theorem condexp_bot' [hμ : μ.ae.ne_bot] (f : α → F') :
   have h_meas : strongly_measurable[⊥] (μ[f|⊥]) := strongly_measurable_condexp
   obtain ⟨c, h_eq⟩ := strongly_measurable_bot_iff.mp h_meas
   rw [h_eq]
-  have h_integral : (∫ x, (μ[f|⊥]) x ∂μ) = ∫ x, f x ∂μ := integral_condexp bot_le hf
+  have h_integral : ∫ x, (μ[f|⊥]) x ∂μ = ∫ x, f x ∂μ := integral_condexp bot_le hf
   simp_rw [h_eq, integral_const] at h_integral 
   rw [← h_integral, ← smul_assoc, smul_eq_mul, inv_mul_cancel, one_smul]
   rw [Ne.def, ENNReal.toReal_eq_zero_iff, Auto.not_or_eq, measure.measure_univ_eq_zero, ← ae_eq_bot,

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

@@ -1292,7 +1292,6 @@ theorem set_lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : Measur
       exact (Lp.strongly_measurable _).ennnorm
     _ ≤ μ (s ∩ t) * ‖x‖₊ :=
       mul_le_mul_right' (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) _
-    
 #align measure_theory.set_lintegral_nnnorm_condexp_L2_indicator_le MeasureTheory.set_lintegral_nnnorm_condexpL2_indicator_le
 
 theorem lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
@@ -1386,7 +1385,6 @@ theorem set_lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableS
       exact (Lp.strongly_measurable _).ennnorm
     _ ≤ μ (s ∩ t) * ‖x‖₊ :=
       mul_le_mul_right' (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) _
-    
 #align measure_theory.set_lintegral_nnnorm_condexp_ind_smul_le MeasureTheory.set_lintegral_nnnorm_condexpIndSmul_le
 
 theorem lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
@@ -1429,7 +1427,6 @@ theorem set_integral_condexpL2_indicator (hs : measurable_set[m] s) (ht : Measur
       @integral_condexpL2_eq α _ ℝ _ _ _ _ _ _ _ _ _ hm (indicatorConstLp 2 ht hμt (1 : ℝ)) hs hμs
     _ = (μ (t ∩ s)).toReal • 1 := (set_integral_indicatorConstLp (hm s hs) ht hμt (1 : ℝ))
     _ = (μ (t ∩ s)).toReal := by rw [smul_eq_mul, mul_one]
-    
 #align measure_theory.set_integral_condexp_L2_indicator MeasureTheory.set_integral_condexpL2_indicator
 
 theorem set_integral_condexpIndSmul (hs : measurable_set[m] s) (ht : MeasurableSet t)
@@ -1443,7 +1440,6 @@ theorem set_integral_condexpIndSmul (hs : measurable_set[m] s) (ht : MeasurableS
     _ = (∫ a in s, condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ)) a ∂μ) • x :=
       (integral_smul_const _ x)
     _ = (μ (t ∩ s)).toReal • x := by rw [set_integral_condexp_L2_indicator hs ht hμs hμt]
-    
 #align measure_theory.set_integral_condexp_ind_smul MeasureTheory.set_integral_condexpIndSmul
 
 theorem condexpL2_indicator_nonneg (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
@@ -1775,7 +1771,6 @@ theorem set_integral_condexpInd (hs : measurable_set[m] s) (ht : MeasurableSet t
       set_integral_congr_ae (hm s hs)
         ((condexpInd_ae_eq_condexpIndSmul hm ht hμt x).mono fun x hx hxs => hx)
     _ = (μ (t ∩ s)).toReal • x := set_integral_condexpIndSmul hs ht hμs hμt x
-    
 #align measure_theory.set_integral_condexp_ind MeasureTheory.set_integral_condexpInd
 
 theorem condexpInd_of_measurable (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) (c : G) :
@@ -2322,7 +2317,6 @@ theorem condexp_neg (f : α → F') : μ[-f|m] =ᵐ[μ] -μ[f|m] := by
       μ[-f|m] = μ[(-1 : ℝ) • f|m] := by rw [neg_one_smul ℝ f]
       _ =ᵐ[μ] (-1 : ℝ) • μ[f|m] := (condexp_smul (-1) f)
       _ = -μ[f|m] := neg_one_smul ℝ (μ[f|m])
-      
 #align measure_theory.condexp_neg MeasureTheory.condexp_neg
 
 theorem condexp_sub (hf : Integrable f μ) (hg : Integrable g μ) :

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

@@ -219,7 +219,7 @@ theorem AeStronglyMeasurable'.aeStronglyMeasurable'_of_measurableSpace_le_on {α
     by
     refine'
       Filter.EventuallyEq.trans _ (indicator_ae_eq_of_restrict_compl_ae_eq_zero (hm _ hs_m) hf_zero)
-    filter_upwards [hf.ae_eq_mk]with x hx
+    filter_upwards [hf.ae_eq_mk] with x hx
     by_cases hxs : x ∈ s
     · simp [hxs, hx]
     · simp [hxs]
@@ -269,7 +269,7 @@ an `m`-strongly measurable function. -/
 def lpMeasSubgroup (m : MeasurableSpace α) [MeasurableSpace α] (p : ℝ≥0∞) (μ : Measure α) :
     AddSubgroup (Lp F p μ)
     where
-  carrier := { f : Lp F p μ | AeStronglyMeasurable' m f μ }
+  carrier := {f : Lp F p μ | AeStronglyMeasurable' m f μ}
   zero_mem' := ⟨(0 : α → F), @stronglyMeasurable_zero _ _ m _ _, Lp.coeFn_zero _ _ _⟩
   add_mem' f g hf hg := (hf.add hg).congr (Lp.coeFn_add f g).symm
   neg_mem' f hf := AeStronglyMeasurable'.congr hf.neg (Lp.coeFn_neg f).symm
@@ -283,7 +283,7 @@ an `m`-strongly measurable function. -/
 def lpMeas (m : MeasurableSpace α) [MeasurableSpace α] (p : ℝ≥0∞) (μ : Measure α) :
     Submodule 𝕜 (Lp F p μ)
     where
-  carrier := { f : Lp F p μ | AeStronglyMeasurable' m f μ }
+  carrier := {f : Lp F p μ | AeStronglyMeasurable' m f μ}
   zero_mem' := ⟨(0 : α → F), @stronglyMeasurable_zero _ _ m _ _, Lp.coeFn_zero _ _ _⟩
   add_mem' f g hf hg := (hf.add hg).congr (Lp.coeFn_add f g).symm
   smul_mem' c f hf := (hf.const_smul c).congr (Lp.coeFn_smul c f).symm
@@ -565,7 +565,7 @@ instance [hm : Fact (m ≤ m0)] [CompleteSpace F] [hp : Fact (1 ≤ p)] :
   rw [(Lp_meas_subgroup_to_Lp_meas_iso F 𝕜 p μ).symm.completeSpace_iff]; infer_instance
 
 theorem isComplete_aeStronglyMeasurable' [hp : Fact (1 ≤ p)] [CompleteSpace F] (hm : m ≤ m0) :
-    IsComplete { f : Lp F p μ | AeStronglyMeasurable' m f μ } :=
+    IsComplete {f : Lp F p μ | AeStronglyMeasurable' m f μ} :=
   by
   rw [← completeSpace_coe_iff_isComplete]
   haveI : Fact (m ≤ m0) := ⟨hm⟩
@@ -574,7 +574,7 @@ theorem isComplete_aeStronglyMeasurable' [hp : Fact (1 ≤ p)] [CompleteSpace F]
 #align measure_theory.is_complete_ae_strongly_measurable' MeasureTheory.isComplete_aeStronglyMeasurable'
 
 theorem isClosed_aeStronglyMeasurable' [hp : Fact (1 ≤ p)] [CompleteSpace F] (hm : m ≤ m0) :
-    IsClosed { f : Lp F p μ | AeStronglyMeasurable' m f μ } :=
+    IsClosed {f : Lp F p μ | AeStronglyMeasurable' m f μ} :=
   IsComplete.isClosed (isComplete_aeStronglyMeasurable' hm)
 #align measure_theory.is_closed_ae_strongly_measurable' MeasureTheory.isClosed_aeStronglyMeasurable'
 
@@ -643,7 +643,7 @@ theorem Lp.induction_strongly_measurable_aux (hm : m ≤ m0) (hp_ne_top : p ≠
               ∀ hgm : AeStronglyMeasurable' m g μ,
                 Disjoint (Function.support f) (Function.support g) →
                   P (hf.toLp f) → P (hg.toLp g) → P (hf.toLp f + hg.toLp g))
-    (h_closed : IsClosed { f : lpMeas F ℝ m p μ | P f }) :
+    (h_closed : IsClosed {f : lpMeas F ℝ m p μ | P f}) :
     ∀ f : Lp F p μ, AeStronglyMeasurable' m f μ → P f :=
   by
   intro f hf
@@ -676,7 +676,7 @@ theorem Lp.induction_strongly_measurable_aux (hm : m ≤ m0) (hp_ne_top : p ≠
         (ae_strongly_measurable'_of_ae_strongly_measurable'_trim hm hf.ae_strongly_measurable)
         (ae_strongly_measurable'_of_ae_strongly_measurable'_trim hm hg.ae_strongly_measurable)
         h_disj hfP hgP
-  · change IsClosed ((Lp_meas_to_Lp_trim_lie F ℝ p μ hm).symm ⁻¹' { g : Lp_meas F ℝ m p μ | P ↑g })
+  · change IsClosed ((Lp_meas_to_Lp_trim_lie F ℝ p μ hm).symm ⁻¹' {g : Lp_meas F ℝ m p μ | P ↑g})
     exact IsClosed.preimage (LinearIsometryEquiv.continuous _) h_closed
 #align measure_theory.Lp.induction_strongly_measurable_aux MeasureTheory.Lp.induction_strongly_measurable_aux
 
@@ -700,7 +700,7 @@ theorem Lp.induction_stronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞)
               ∀ hgm : strongly_measurable[m] g,
                 Disjoint (Function.support f) (Function.support g) →
                   P (hf.toLp f) → P (hg.toLp g) → P (hf.toLp f + hg.toLp g))
-    (h_closed : IsClosed { f : lpMeas F ℝ m p μ | P f }) :
+    (h_closed : IsClosed {f : lpMeas F ℝ m p μ | P f}) :
     ∀ f : Lp F p μ, AeStronglyMeasurable' m f μ → P f :=
   by
   intro f hf
@@ -775,7 +775,7 @@ theorem Memℒp.induction_stronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠
           Memℒp f p μ →
             Memℒp g p μ →
               strongly_measurable[m] f → strongly_measurable[m] g → P f → P g → P (f + g))
-    (h_closed : IsClosed { f : lpMeas F ℝ m p μ | P f })
+    (h_closed : IsClosed {f : lpMeas F ℝ m p μ | P f})
     (h_ae : ∀ ⦃f g⦄, f =ᵐ[μ] g → Memℒp f p μ → P f → P g) :
     ∀ ⦃f : α → F⦄ (hf : Memℒp f p μ) (hfm : AeStronglyMeasurable' m f μ), P f :=
   by
@@ -933,13 +933,13 @@ theorem integral_norm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g : 
     (hs : measurable_set[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 : measurable_set[m] { x | 0 ≤ g x } :=
+  have h_meas_nonneg_g : measurable_set[m] {x | 0 ≤ g x} :=
     (@strongly_measurable_const _ _ m _ _).measurableSet_le hg
-  have h_meas_nonneg_f : MeasurableSet { x | 0 ≤ f x } :=
+  have h_meas_nonneg_f : MeasurableSet {x | 0 ≤ f x} :=
     strongly_measurable_const.measurable_set_le hf
-  have h_meas_nonpos_g : measurable_set[m] { x | g x ≤ 0 } :=
+  have h_meas_nonpos_g : measurable_set[m] {x | g x ≤ 0} :=
     hg.measurable_set_le (@strongly_measurable_const _ _ m _ _)
-  have h_meas_nonpos_f : MeasurableSet { x | f x ≤ 0 } :=
+  have h_meas_nonpos_f : MeasurableSet {x | f x ≤ 0} :=
     hf.measurable_set_le strongly_measurable_const
   refine' sub_le_sub _ _
   · rw [measure.restrict_restrict (hm _ h_meas_nonneg_g), measure.restrict_restrict h_meas_nonneg_f,
@@ -1011,10 +1011,10 @@ theorem integrableOn_condexpL2_of_measure_ne_top (hm : m ≤ m0) (hμs : μ s 
   integrableOn_Lp_of_measure_ne_top (condexpL2 𝕜 hm f : α →₂[μ] E) fact_one_le_two_ennreal.elim hμs
 #align measure_theory.integrable_on_condexp_L2_of_measure_ne_top MeasureTheory.integrableOn_condexpL2_of_measure_ne_top
 
-theorem integrable_condexpL2_of_finiteMeasure (hm : m ≤ m0) [FiniteMeasure μ] {f : α →₂[μ] E} :
+theorem integrable_condexpL2_of_isFiniteMeasure (hm : m ≤ m0) [IsFiniteMeasure μ] {f : α →₂[μ] E} :
     Integrable (condexpL2 𝕜 hm f) μ :=
   integrableOn_univ.mp <| integrableOn_condexpL2_of_measure_ne_top hm (measure_ne_top _ _) f
-#align measure_theory.integrable_condexp_L2_of_is_finite_measure MeasureTheory.integrable_condexpL2_of_finiteMeasure
+#align measure_theory.integrable_condexp_L2_of_is_finite_measure MeasureTheory.integrable_condexpL2_of_isFiniteMeasure
 
 theorem norm_condexpL2_le_one (hm : m ≤ m0) : ‖@condexpL2 α E 𝕜 _ _ _ _ _ _ μ hm‖ ≤ 1 :=
   haveI : Fact (m ≤ m0) := ⟨hm⟩
@@ -1149,8 +1149,8 @@ theorem lintegral_nnnorm_condexpL2_indicator_le_real (hs : MeasurableSet s) (hμ
     refine' (@indicator_const_Lp_coe_fn _ _ _ 2 _ _ _ hs hμs (1 : ℝ)).mono fun x hx => _
     rw [hx]
     classical
-      simp_rw [Set.indicator_apply]
-      split_ifs <;> simp
+    simp_rw [Set.indicator_apply]
+    split_ifs <;> simp
   rw [h_eq, lintegral_indicator _ hs, lintegral_const, measure.restrict_restrict hs]
   simp only [one_mul, Set.univ_inter, MeasurableSet.univ, measure.restrict_apply]
 #align measure_theory.lintegral_nnnorm_condexp_L2_indicator_le_real MeasureTheory.lintegral_nnnorm_condexpL2_indicator_le_real
@@ -1465,7 +1465,7 @@ theorem condexpL2_indicator_nonneg (hm : m ≤ m0) (hs : MeasurableSet s) (hμs
     have h_ae :
       ∀ᵐ x ∂μ, x ∈ t → h.mk _ x = condexp_L2 ℝ hm (indicator_const_Lp 2 hs hμs (1 : ℝ)) x :=
       by
-      filter_upwards [h.ae_eq_mk]with x hx
+      filter_upwards [h.ae_eq_mk] with x hx
       exact fun _ => hx.symm
     rw [set_integral_congr_ae (hm t ht) h_ae,
       set_integral_condexp_L2_indicator ht hs ((le_trim hm).trans_lt hμt).Ne hμs]
@@ -1477,7 +1477,7 @@ theorem condexpIndSmul_nonneg {E} [NormedLatticeAddCommGroup E] [NormedSpace ℝ
     0 ≤ᵐ[μ] condexpIndSmul hm hs hμs x :=
   by
   refine' eventually_le.trans_eq _ (condexp_ind_smul_ae_eq_smul hm hs hμs x).symm
-  filter_upwards [condexp_L2_indicator_nonneg hm hs hμs]with a ha
+  filter_upwards [condexp_L2_indicator_nonneg hm hs hμs] with a ha
   exact smul_nonneg ha hx
 #align measure_theory.condexp_ind_smul_nonneg MeasureTheory.condexpIndSmul_nonneg
 
@@ -1916,8 +1916,8 @@ theorem aeStronglyMeasurable'_condexpL1Clm (f : α →₁[μ] F') :
     refine' ae_strongly_measurable'.congr _ (coe_fn_add _ _).symm
     exact ae_strongly_measurable'.add hfm hgm
   · have :
-      { f : Lp F' 1 μ | ae_strongly_measurable' m (condexp_L1_clm hm μ f) μ } =
-        condexp_L1_clm hm μ ⁻¹' { f | ae_strongly_measurable' m f μ } :=
+      {f : Lp F' 1 μ | ae_strongly_measurable' m (condexp_L1_clm hm μ f) μ} =
+        condexp_L1_clm hm μ ⁻¹' {f | ae_strongly_measurable' m f μ} :=
       by rfl
     rw [this]
     refine' IsClosed.preimage (condexp_L1_clm hm μ).Continuous _
@@ -2065,7 +2065,7 @@ is true:
 - `μ` is not σ-finite with respect to `m`,
 - `f` is not integrable. -/
 irreducible_def condexp (m : MeasurableSpace α) {m0 : MeasurableSpace α} (μ : Measure α)
-  (f : α → F') : α → F' :=
+    (f : α → F') : α → F' :=
   if hm : m ≤ m0 then
     if h : SigmaFinite (μ.trim hm) ∧ Integrable f μ then
       if strongly_measurable[m] f then f
@@ -2106,7 +2106,8 @@ theorem condexp_of_stronglyMeasurable (hm : m ≤ m0) [hμm : SigmaFinite (μ.tr
   rw [condexp_of_sigma_finite hm, if_pos hfi, if_pos hf]; infer_instance
 #align measure_theory.condexp_of_strongly_measurable MeasureTheory.condexp_of_stronglyMeasurable
 
-theorem condexp_const (hm : m ≤ m0) (c : F') [FiniteMeasure μ] : μ[fun x : α => c|m] = fun _ => c :=
+theorem condexp_const (hm : m ≤ m0) (c : F') [IsFiniteMeasure μ] :
+    μ[fun x : α => c|m] = fun _ => c :=
   condexp_of_stronglyMeasurable hm (@stronglyMeasurable_const _ _ m _ _) (integrable_const c)
 #align measure_theory.condexp_const MeasureTheory.condexp_const
 
@@ -2270,7 +2271,7 @@ theorem condexp_bot_ae_eq (f : α → F') :
     simp only [h, ae_zero]
 #align measure_theory.condexp_bot_ae_eq MeasureTheory.condexp_bot_ae_eq
 
-theorem condexp_bot [ProbabilityMeasure μ] (f : α → F') : μ[f|⊥] = fun _ => ∫ x, f x ∂μ := by
+theorem condexp_bot [IsProbabilityMeasure μ] (f : α → F') : μ[f|⊥] = fun _ => ∫ x, f x ∂μ := by
   refine' (condexp_bot' f).trans _; rw [measure_univ, ENNReal.one_toReal, inv_one, one_smul]
 #align measure_theory.condexp_bot MeasureTheory.condexp_bot
 

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

@@ -660,7 +660,7 @@ theorem Lp.induction_strongly_measurable_aux (hm : m ≤ m0) (hp_ne_top : p ≠
     rw [Lp.simple_func.coe_indicator_const, Lp_meas_to_Lp_trim_lie_symm_indicator ht hμt.ne b]
     have hμt' : μ t < ∞ := (le_trim hm).trans_lt hμt
     specialize h_ind b ht hμt'
-    rwa [Lp.simple_func.coe_indicator_const] at h_ind
+    rwa [Lp.simple_func.coe_indicator_const] at h_ind 
   · intro f g hf hg h_disj hfP hgP
     rw [LinearIsometryEquiv.map_add]
     push_cast
@@ -669,8 +669,8 @@ theorem Lp.induction_strongly_measurable_aux (hm : m ≤ m0) (hp_ne_top : p ≠
         ((Lp_meas_to_Lp_trim_lie F ℝ p μ hm).symm (mem_ℒp.to_Lp f hf) : Lp F p μ) =
           (mem_ℒp_of_mem_ℒp_trim hm hf).toLp f :=
       Lp_meas_to_Lp_trim_lie_symm_to_Lp hm
-    rw [h_eq f hf] at hfP⊢
-    rw [h_eq g hg] at hgP⊢
+    rw [h_eq f hf] at hfP ⊢
+    rw [h_eq g hg] at hgP ⊢
     exact
       h_add (mem_ℒp_of_mem_ℒp_trim hm hf) (mem_ℒp_of_mem_ℒp_trim hm hg)
         (ae_strongly_measurable'_of_ae_strongly_measurable'_trim hm hf.ae_strongly_measurable)
@@ -753,8 +753,8 @@ theorem Lp.induction_stronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞)
   have h_disj : Disjoint (Function.support f') (Function.support g') :=
     haveI : Disjoint (s_f \ s_g) (s_g \ s_f) := disjoint_sdiff_sdiff
     this.mono Set.support_indicator_subset Set.support_indicator_subset
-  rw [← mem_ℒp.to_Lp_congr hf'_Lp hf hff'.symm] at hPf⊢
-  rw [← mem_ℒp.to_Lp_congr hg'_Lp hg hgg'.symm] at hPg⊢
+  rw [← mem_ℒp.to_Lp_congr hf'_Lp hf hff'.symm] at hPf ⊢
+  rw [← mem_ℒp.to_Lp_congr hg'_Lp hg hgg'.symm] at hPg ⊢
   exact h_add hf'_Lp hg'_Lp hf'_meas hg'_meas h_disj hPf hPg
 #align measure_theory.Lp.induction_strongly_measurable MeasureTheory.Lp.induction_stronglyMeasurable
 
@@ -890,7 +890,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaF
     ∀ 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)
@@ -898,7 +898,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaF
     ∀ 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)
@@ -908,7 +908,7 @@ theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaF
         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),
@@ -1118,11 +1118,11 @@ theorem condexpL2_ae_eq_zero_of_ae_eq_zero (hs : measurable_set[m] s) (hμs : μ
     (hf : f =ᵐ[μ.restrict s] 0) : condexpL2 ℝ hm f =ᵐ[μ.restrict s] 0 :=
   by
   suffices h_nnnorm_eq_zero : (∫⁻ x in s, ‖condexp_L2 ℝ hm f x‖₊ ∂μ) = 0
-  · rw [lintegral_eq_zero_iff] at h_nnnorm_eq_zero
+  · rw [lintegral_eq_zero_iff] at h_nnnorm_eq_zero 
     refine' h_nnnorm_eq_zero.mono fun x hx => _
-    dsimp only at hx
-    rw [Pi.zero_apply] at hx⊢
-    · rwa [ENNReal.coe_eq_zero, nnnorm_eq_zero] at hx
+    dsimp only at hx 
+    rw [Pi.zero_apply] at hx ⊢
+    · rwa [ENNReal.coe_eq_zero, nnnorm_eq_zero] at hx 
     · refine' Measurable.coe_nnreal_ennreal (Measurable.nnnorm _)
       rw [Lp_meas_coe]
       exact (Lp.strongly_measurable _).Measurable
@@ -1233,7 +1233,7 @@ theorem condexpL2_comp_continuousLinearMap (hm : m ≤ m0) (T : E' →L[ℝ] E''
         (integrable_on_Lp_of_measure_ne_top f fact_one_le_two_ennreal.elim hμs.ne)]
   · rw [← Lp_meas_coe]; exact Lp_meas.ae_strongly_measurable' _
   · have h_coe := T.coe_fn_comp_Lp (condexp_L2 𝕜 hm f : α →₂[μ] E')
-    rw [← eventually_eq] at h_coe
+    rw [← eventually_eq] at h_coe 
     refine' ae_strongly_measurable'.congr _ h_coe.symm
     exact (Lp_meas.ae_strongly_measurable' (condexp_L2 𝕜 hm f)).continuous_comp T.continuous
 #align measure_theory.condexp_L2_comp_continuous_linear_map MeasureTheory.condexpL2_comp_continuousLinearMap
@@ -1253,7 +1253,7 @@ theorem condexpL2_indicator_ae_eq_smul (hm : m ≤ m0) (hs : MeasurableSet s) (h
   have h_comp :=
     condexp_L2_comp_continuous_linear_map ℝ 𝕜 hm (to_span_singleton ℝ x)
       (indicator_const_Lp 2 hs hμs (1 : ℝ))
-  rw [← Lp_meas_coe] at h_comp
+  rw [← Lp_meas_coe] at h_comp 
   refine' h_comp.trans _
   exact (to_span_singleton ℝ x).coeFn_compLp _
 #align measure_theory.condexp_L2_indicator_ae_eq_smul MeasureTheory.condexpL2_indicator_ae_eq_smul
@@ -1269,7 +1269,7 @@ theorem condexpL2_indicator_eq_toSpanSingleton_comp (hm : m ≤ m0) (hs : Measur
   have h_comp :=
     (to_span_singleton ℝ x).coeFn_compLp
       (condexp_L2 ℝ hm (indicator_const_Lp 2 hs hμs (1 : ℝ)) : α →₂[μ] ℝ)
-  rw [← eventually_eq] at h_comp
+  rw [← eventually_eq] at h_comp 
   refine' eventually_eq.trans _ h_comp.symm
   refine' eventually_of_forall fun y => _
   rfl
@@ -1873,7 +1873,7 @@ theorem set_integral_condexpL1Clm (f : α →₁[μ] F') (hs : measurable_set[m]
     by
     refine' fun i => (measure_mono (Set.inter_subset_left _ _)).trans_lt _
     have hS_finite_trim := measure_spanning_sets_lt_top (μ.trim hm) i
-    rwa [trim_measurable_set_eq hm (hS_meas i)] at hS_finite_trim
+    rwa [trim_measurable_set_eq hm (hS_meas i)] at hS_finite_trim 
   have h_mono : Monotone fun i => S i ∩ s :=
     by
     intro i j hij x
@@ -1889,7 +1889,7 @@ theorem set_integral_condexpL1Clm (f : α →₁[μ] F') (hs : measurable_set[m]
     have h :=
       tendsto_set_integral_of_monotone (fun i => (hS_meas0 i).inter (hm s hs)) h_mono
         (L1.integrable_coe_fn f).IntegrableOn
-    rwa [← hs_eq] at h
+    rwa [← hs_eq] at h 
   have h_left :
     tendsto (fun i => ∫ x in S i ∩ s, condexp_L1_clm hm μ f x ∂μ) at_top
       (𝓝 (∫ x in s, condexp_L1_clm hm μ f x ∂μ)) :=
@@ -1897,8 +1897,8 @@ theorem set_integral_condexpL1Clm (f : α →₁[μ] F') (hs : measurable_set[m]
     have h :=
       tendsto_set_integral_of_monotone (fun i => (hS_meas0 i).inter (hm s hs)) h_mono
         (L1.integrable_coe_fn (condexp_L1_clm hm μ f)).IntegrableOn
-    rwa [← hs_eq] at h
-  rw [h_eq_forall] at h_left
+    rwa [← hs_eq] at h 
+  rw [h_eq_forall] at h_left 
   exact tendsto_nhds_unique h_left h_right
 #align measure_theory.set_integral_condexp_L1_clm MeasureTheory.set_integral_condexpL1Clm
 
@@ -2215,7 +2215,7 @@ theorem integral_condexp (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] (hf :
     (∫ x, (μ[f|m]) x ∂μ) = ∫ x, f x ∂μ :=
   by
   suffices (∫ x in Set.univ, (μ[f|m]) x ∂μ) = ∫ x in Set.univ, f x ∂μ by
-    simp_rw [integral_univ] at this; exact this
+    simp_rw [integral_univ] at this ; exact this
   exact set_integral_condexp hm hf (@MeasurableSet.univ _ m)
 #align measure_theory.integral_condexp MeasureTheory.integral_condexp
 
@@ -2241,7 +2241,7 @@ theorem condexp_bot' [hμ : μ.ae.ne_bot] (f : α → F') :
   by_cases hμ_finite : is_finite_measure μ
   swap
   · have h : ¬sigma_finite (μ.trim bot_le) := by rwa [sigma_finite_trim_bot_iff]
-    rw [not_is_finite_measure_iff] at hμ_finite
+    rw [not_is_finite_measure_iff] at hμ_finite 
     rw [condexp_of_not_sigma_finite bot_le h]
     simp only [hμ_finite, ENNReal.top_toReal, inv_zero, zero_smul]
     rfl
@@ -2252,7 +2252,7 @@ theorem condexp_bot' [hμ : μ.ae.ne_bot] (f : α → F') :
   obtain ⟨c, h_eq⟩ := strongly_measurable_bot_iff.mp h_meas
   rw [h_eq]
   have h_integral : (∫ x, (μ[f|⊥]) x ∂μ) = ∫ x, f x ∂μ := integral_condexp bot_le hf
-  simp_rw [h_eq, integral_const] at h_integral
+  simp_rw [h_eq, integral_const] at h_integral 
   rw [← h_integral, ← smul_assoc, smul_eq_mul, inv_mul_cancel, one_smul]
   rw [Ne.def, ENNReal.toReal_eq_zero_iff, Auto.not_or_eq, measure.measure_univ_eq_zero, ← ae_eq_bot,
     ← Ne.def, ← ne_bot_iff]
@@ -2266,7 +2266,7 @@ theorem condexp_bot_ae_eq (f : α → F') :
   · refine' eventually_of_forall fun x => _
     rw [condexp_bot' f]
     exact h
-  · rw [ne_bot_iff, Classical.not_not, ae_eq_bot] at h
+  · rw [ne_bot_iff, Classical.not_not, ae_eq_bot] at h 
     simp only [h, ae_zero]
 #align measure_theory.condexp_bot_ae_eq MeasureTheory.condexp_bot_ae_eq
 

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

@@ -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.basic
-! leanprover-community/mathlib commit e0736bb5b48bdadbca19dbd857e12bee38ccfbb8
+! leanprover-community/mathlib commit 00abe0695d8767201e6d008afa22393978bb324d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -81,7 +81,7 @@ conditional expectation, conditional expected value
 
 noncomputable section
 
-open TopologicalSpace MeasureTheory.lp Filter ContinuousLinearMap
+open TopologicalSpace MeasureTheory.Lp Filter ContinuousLinearMap
 
 open scoped NNReal ENNReal Topology BigOperators MeasureTheory
 
@@ -196,6 +196,14 @@ theorem ae_eq_trim_iff_of_aeStronglyMeasurable' {α β} [TopologicalSpace β] [M
       hfm.ae_eq_mk.symm.trans (h.trans hgm.ae_eq_mk)⟩
 #align measure_theory.ae_eq_trim_iff_of_ae_strongly_measurable' MeasureTheory.ae_eq_trim_iff_of_aeStronglyMeasurable'
 
+theorem AEStronglyMeasurable.comp_ae_measurable' {α β γ : Type _} [TopologicalSpace β]
+    {mα : MeasurableSpace α} {mγ : MeasurableSpace γ} {f : α → β} {μ : Measure γ} {g : γ → α}
+    (hf : AEStronglyMeasurable f (μ.map g)) (hg : AEMeasurable g μ) :
+    AeStronglyMeasurable' (mα.comap g) (f ∘ g) μ :=
+  ⟨hf.mk f ∘ g, hf.stronglyMeasurable_mk.comp_measurable (measurable_iff_comap_le.mpr le_rfl),
+    ae_eq_comp hg hf.ae_eq_mk⟩
+#align measure_theory.ae_strongly_measurable.comp_ae_measurable' MeasureTheory.AEStronglyMeasurable.comp_ae_measurable'
+
 /-- If the restriction to a set `s` of a σ-algebra `m` is included in the restriction to `s` of
 another σ-algebra `m₂` (hypothesis `hs`), the set `s` is `m` measurable and a function `f` almost
 everywhere supported on `s` is `m`-ae-strongly-measurable, then `f` is also
@@ -259,12 +267,12 @@ variable (F)
 `ae_strongly_measurable' m f μ`, i.e. functions which are `μ`-a.e. equal to
 an `m`-strongly measurable function. -/
 def lpMeasSubgroup (m : MeasurableSpace α) [MeasurableSpace α] (p : ℝ≥0∞) (μ : Measure α) :
-    AddSubgroup (lp F p μ)
+    AddSubgroup (Lp F p μ)
     where
-  carrier := { f : lp F p μ | AeStronglyMeasurable' m f μ }
-  zero_mem' := ⟨(0 : α → F), @stronglyMeasurable_zero _ _ m _ _, lp.coeFn_zero _ _ _⟩
-  add_mem' f g hf hg := (hf.add hg).congr (lp.coeFn_add f g).symm
-  neg_mem' f hf := AeStronglyMeasurable'.congr hf.neg (lp.coeFn_neg f).symm
+  carrier := { f : Lp F p μ | AeStronglyMeasurable' m f μ }
+  zero_mem' := ⟨(0 : α → F), @stronglyMeasurable_zero _ _ m _ _, Lp.coeFn_zero _ _ _⟩
+  add_mem' f g hf hg := (hf.add hg).congr (Lp.coeFn_add f g).symm
+  neg_mem' f hf := AeStronglyMeasurable'.congr hf.neg (Lp.coeFn_neg f).symm
 #align measure_theory.Lp_meas_subgroup MeasureTheory.lpMeasSubgroup
 
 variable (𝕜)
@@ -273,12 +281,12 @@ variable (𝕜)
 `ae_strongly_measurable' m f μ`, i.e. functions which are `μ`-a.e. equal to
 an `m`-strongly measurable function. -/
 def lpMeas (m : MeasurableSpace α) [MeasurableSpace α] (p : ℝ≥0∞) (μ : Measure α) :
-    Submodule 𝕜 (lp F p μ)
+    Submodule 𝕜 (Lp F p μ)
     where
-  carrier := { f : lp F p μ | AeStronglyMeasurable' m f μ }
-  zero_mem' := ⟨(0 : α → F), @stronglyMeasurable_zero _ _ m _ _, lp.coeFn_zero _ _ _⟩
-  add_mem' f g hf hg := (hf.add hg).congr (lp.coeFn_add f g).symm
-  smul_mem' c f hf := (hf.const_smul c).congr (lp.coeFn_smul c f).symm
+  carrier := { f : Lp F p μ | AeStronglyMeasurable' m f μ }
+  zero_mem' := ⟨(0 : α → F), @stronglyMeasurable_zero _ _ m _ _, Lp.coeFn_zero _ _ _⟩
+  add_mem' f g hf hg := (hf.add hg).congr (Lp.coeFn_add f g).symm
+  smul_mem' c f hf := (hf.const_smul c).congr (Lp.coeFn_smul c f).symm
 #align measure_theory.Lp_meas MeasureTheory.lpMeas
 
 variable {F 𝕜}
@@ -286,12 +294,12 @@ variable {F 𝕜}
 variable ()
 
 theorem mem_lpMeasSubgroup_iff_aeStronglyMeasurable' {m m0 : MeasurableSpace α} {μ : Measure α}
-    {f : lp F p μ} : f ∈ lpMeasSubgroup F m p μ ↔ AeStronglyMeasurable' m f μ := by
+    {f : Lp F p μ} : f ∈ lpMeasSubgroup F m p μ ↔ AeStronglyMeasurable' m f μ := by
   rw [← AddSubgroup.mem_carrier, Lp_meas_subgroup, Set.mem_setOf_eq]
 #align measure_theory.mem_Lp_meas_subgroup_iff_ae_strongly_measurable' MeasureTheory.mem_lpMeasSubgroup_iff_aeStronglyMeasurable'
 
 theorem mem_lpMeas_iff_aeStronglyMeasurable' {m m0 : MeasurableSpace α} {μ : Measure α}
-    {f : lp F p μ} : f ∈ lpMeas F 𝕜 m p μ ↔ AeStronglyMeasurable' m f μ := by
+    {f : Lp F p μ} : f ∈ lpMeas F 𝕜 m p μ ↔ AeStronglyMeasurable' m f μ := by
   rw [← SetLike.mem_coe, ← Submodule.mem_carrier, Lp_meas, Set.mem_setOf_eq]
 #align measure_theory.mem_Lp_meas_iff_ae_strongly_measurable' MeasureTheory.mem_lpMeas_iff_aeStronglyMeasurable'
 
@@ -300,18 +308,18 @@ theorem lpMeas.aeStronglyMeasurable' {m m0 : MeasurableSpace α} {μ : Measure 
   mem_lpMeas_iff_aeStronglyMeasurable'.mp f.Mem
 #align measure_theory.Lp_meas.ae_strongly_measurable' MeasureTheory.lpMeas.aeStronglyMeasurable'
 
-theorem mem_lpMeas_self {m0 : MeasurableSpace α} (μ : Measure α) (f : lp F p μ) :
+theorem mem_lpMeas_self {m0 : MeasurableSpace α} (μ : Measure α) (f : Lp F p μ) :
     f ∈ lpMeas F 𝕜 m0 p μ :=
-  mem_lpMeas_iff_aeStronglyMeasurable'.mpr (lp.aEStronglyMeasurable f)
+  mem_lpMeas_iff_aeStronglyMeasurable'.mpr (Lp.aestronglyMeasurable f)
 #align measure_theory.mem_Lp_meas_self MeasureTheory.mem_lpMeas_self
 
 theorem lpMeasSubgroup_coe {m m0 : MeasurableSpace α} {μ : Measure α} {f : lpMeasSubgroup F m p μ} :
-    ⇑f = (f : lp F p μ) :=
+    ⇑f = (f : Lp F p μ) :=
   coeFn_coeBase f
 #align measure_theory.Lp_meas_subgroup_coe MeasureTheory.lpMeasSubgroup_coe
 
 theorem lpMeas_coe {m m0 : MeasurableSpace α} {μ : Measure α} {f : lpMeas F 𝕜 m p μ} :
-    ⇑f = (f : lp F p μ) :=
+    ⇑f = (f : Lp F p μ) :=
   coeFn_coeBase f
 #align measure_theory.Lp_meas_coe MeasureTheory.lpMeas_coe
 
@@ -335,7 +343,7 @@ variable {ι : Type _} {m m0 : MeasurableSpace α} {μ : Measure α}
 
 /-- If `f` belongs to `Lp_meas_subgroup F m p μ`, then the measurable function it is almost
 everywhere equal to (given by `ae_measurable.mk`) belongs to `ℒp` for the measure `μ.trim hm`. -/
-theorem memℒp_trim_of_mem_lpMeasSubgroup (hm : m ≤ m0) (f : lp F p μ)
+theorem memℒp_trim_of_mem_lpMeasSubgroup (hm : m ≤ m0) (f : Lp F p μ)
     (hf_meas : f ∈ lpMeasSubgroup F m p μ) :
     Memℒp (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp hf_meas).some p (μ.trim hm) :=
   by
@@ -353,8 +361,8 @@ theorem memℒp_trim_of_mem_lpMeasSubgroup (hm : m ≤ m0) (f : lp F p μ)
 
 /-- If `f` belongs to `Lp` for the measure `μ.trim hm`, then it belongs to the subgroup
 `Lp_meas_subgroup F m p μ`. -/
-theorem mem_lpMeasSubgroup_toLp_of_trim (hm : m ≤ m0) (f : lp F p (μ.trim hm)) :
-    (memℒp_of_memℒp_trim hm (lp.memℒp f)).toLp f ∈ lpMeasSubgroup F m p μ :=
+theorem mem_lpMeasSubgroup_toLp_of_trim (hm : m ≤ m0) (f : Lp F p (μ.trim hm)) :
+    (memℒp_of_memℒp_trim hm (Lp.memℒp f)).toLp f ∈ lpMeasSubgroup F m p μ :=
   by
   let hf_mem_ℒp := mem_ℒp_of_mem_ℒp_trim hm (Lp.mem_ℒp f)
   rw [mem_Lp_meas_subgroup_iff_ae_strongly_measurable']
@@ -366,7 +374,7 @@ theorem mem_lpMeasSubgroup_toLp_of_trim (hm : m ≤ m0) (f : lp F p (μ.trim hm)
 variable (F p μ)
 
 /-- Map from `Lp_meas_subgroup` to `Lp F p (μ.trim hm)`. -/
-def lpMeasSubgroupToLpTrim (hm : m ≤ m0) (f : lpMeasSubgroup F m p μ) : lp F p (μ.trim hm) :=
+def lpMeasSubgroupToLpTrim (hm : m ≤ m0) (f : lpMeasSubgroup F m p μ) : Lp F p (μ.trim hm) :=
   Memℒp.toLp (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp f.Mem).some
     (memℒp_trim_of_mem_lpMeasSubgroup hm f f.Mem)
 #align measure_theory.Lp_meas_subgroup_to_Lp_trim MeasureTheory.lpMeasSubgroupToLpTrim
@@ -374,7 +382,7 @@ def lpMeasSubgroupToLpTrim (hm : m ≤ m0) (f : lpMeasSubgroup F m p μ) : lp F
 variable (𝕜)
 
 /-- Map from `Lp_meas` to `Lp F p (μ.trim hm)`. -/
-def lpMeasToLpTrim (hm : m ≤ m0) (f : lpMeas F 𝕜 m p μ) : lp F p (μ.trim hm) :=
+def lpMeasToLpTrim (hm : m ≤ m0) (f : lpMeas F 𝕜 m p μ) : Lp F p (μ.trim hm) :=
   Memℒp.toLp (mem_lpMeas_iff_aeStronglyMeasurable'.mp f.Mem).some
     (memℒp_trim_of_mem_lpMeasSubgroup hm f f.Mem)
 #align measure_theory.Lp_meas_to_Lp_trim MeasureTheory.lpMeasToLpTrim
@@ -383,15 +391,15 @@ variable {𝕜}
 
 /-- Map from `Lp F p (μ.trim hm)` to `Lp_meas_subgroup`, inverse of
 `Lp_meas_subgroup_to_Lp_trim`. -/
-def lpTrimToLpMeasSubgroup (hm : m ≤ m0) (f : lp F p (μ.trim hm)) : lpMeasSubgroup F m p μ :=
-  ⟨(memℒp_of_memℒp_trim hm (lp.memℒp f)).toLp f, mem_lpMeasSubgroup_toLp_of_trim hm f⟩
+def lpTrimToLpMeasSubgroup (hm : m ≤ m0) (f : Lp F p (μ.trim hm)) : lpMeasSubgroup F m p μ :=
+  ⟨(memℒp_of_memℒp_trim hm (Lp.memℒp f)).toLp f, mem_lpMeasSubgroup_toLp_of_trim hm f⟩
 #align measure_theory.Lp_trim_to_Lp_meas_subgroup MeasureTheory.lpTrimToLpMeasSubgroup
 
 variable (𝕜)
 
 /-- Map from `Lp F p (μ.trim hm)` to `Lp_meas`, inverse of `Lp_meas_to_Lp_trim`. -/
-def lpTrimToLpMeas (hm : m ≤ m0) (f : lp F p (μ.trim hm)) : lpMeas F 𝕜 m p μ :=
-  ⟨(memℒp_of_memℒp_trim hm (lp.memℒp f)).toLp f, mem_lpMeasSubgroup_toLp_of_trim hm f⟩
+def lpTrimToLpMeas (hm : m ≤ m0) (f : Lp F p (μ.trim hm)) : lpMeas F 𝕜 m p μ :=
+  ⟨(memℒp_of_memℒp_trim hm (Lp.memℒp f)).toLp f, mem_lpMeasSubgroup_toLp_of_trim hm f⟩
 #align measure_theory.Lp_trim_to_Lp_meas MeasureTheory.lpTrimToLpMeas
 
 variable {F 𝕜 p μ}
@@ -402,7 +410,7 @@ theorem lpMeasSubgroupToLpTrim_ae_eq (hm : m ≤ m0) (f : lpMeasSubgroup F m p 
     (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp f.Mem).choose_spec.2.symm
 #align measure_theory.Lp_meas_subgroup_to_Lp_trim_ae_eq MeasureTheory.lpMeasSubgroupToLpTrim_ae_eq
 
-theorem lpTrimToLpMeasSubgroup_ae_eq (hm : m ≤ m0) (f : lp F p (μ.trim hm)) :
+theorem lpTrimToLpMeasSubgroup_ae_eq (hm : m ≤ m0) (f : Lp F p (μ.trim hm)) :
     lpTrimToLpMeasSubgroup F p μ hm f =ᵐ[μ] f :=
   Memℒp.coeFn_toLp _
 #align measure_theory.Lp_trim_to_Lp_meas_subgroup_ae_eq MeasureTheory.lpTrimToLpMeasSubgroup_ae_eq
@@ -413,7 +421,7 @@ theorem lpMeasToLpTrim_ae_eq (hm : m ≤ m0) (f : lpMeas F 𝕜 m p μ) :
     (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp f.Mem).choose_spec.2.symm
 #align measure_theory.Lp_meas_to_Lp_trim_ae_eq MeasureTheory.lpMeasToLpTrim_ae_eq
 
-theorem lpTrimToLpMeas_ae_eq (hm : m ≤ m0) (f : lp F p (μ.trim hm)) :
+theorem lpTrimToLpMeas_ae_eq (hm : m ≤ m0) (f : Lp F p (μ.trim hm)) :
     lpTrimToLpMeas F 𝕜 p μ hm f =ᵐ[μ] f :=
   Memℒp.coeFn_toLp _
 #align measure_theory.Lp_trim_to_Lp_meas_ae_eq MeasureTheory.lpTrimToLpMeas_ae_eq
@@ -514,7 +522,7 @@ variable (F p μ)
 
 /-- `Lp_meas_subgroup` and `Lp F p (μ.trim hm)` are isometric. -/
 def lpMeasSubgroupToLpTrimIso [hp : Fact (1 ≤ p)] (hm : m ≤ m0) :
-    lpMeasSubgroup F m p μ ≃ᵢ lp F p (μ.trim hm)
+    lpMeasSubgroup F m p μ ≃ᵢ Lp F p (μ.trim hm)
     where
   toFun := lpMeasSubgroupToLpTrim F p μ hm
   invFun := lpTrimToLpMeasSubgroup F p μ hm
@@ -531,7 +539,7 @@ def lpMeasSubgroupToLpMeasIso [hp : Fact (1 ≤ p)] : lpMeasSubgroup F m p μ 
 #align measure_theory.Lp_meas_subgroup_to_Lp_meas_iso MeasureTheory.lpMeasSubgroupToLpMeasIso
 
 /-- `Lp_meas` and `Lp F p (μ.trim hm)` are isometric, with a linear equivalence. -/
-def lpMeasToLpTrimLie [hp : Fact (1 ≤ p)] (hm : m ≤ m0) : lpMeas F 𝕜 m p μ ≃ₗᵢ[𝕜] lp F p (μ.trim hm)
+def lpMeasToLpTrimLie [hp : Fact (1 ≤ p)] (hm : m ≤ m0) : lpMeas F 𝕜 m p μ ≃ₗᵢ[𝕜] Lp F p (μ.trim hm)
     where
   toFun := lpMeasToLpTrim F 𝕜 p μ hm
   invFun := lpTrimToLpMeas F 𝕜 p μ hm
@@ -557,7 +565,7 @@ instance [hm : Fact (m ≤ m0)] [CompleteSpace F] [hp : Fact (1 ≤ p)] :
   rw [(Lp_meas_subgroup_to_Lp_meas_iso F 𝕜 p μ).symm.completeSpace_iff]; infer_instance
 
 theorem isComplete_aeStronglyMeasurable' [hp : Fact (1 ≤ p)] [CompleteSpace F] (hm : m ≤ m0) :
-    IsComplete { f : lp F p μ | AeStronglyMeasurable' m f μ } :=
+    IsComplete { f : Lp F p μ | AeStronglyMeasurable' m f μ } :=
   by
   rw [← completeSpace_coe_iff_isComplete]
   haveI : Fact (m ≤ m0) := ⟨hm⟩
@@ -566,7 +574,7 @@ theorem isComplete_aeStronglyMeasurable' [hp : Fact (1 ≤ p)] [CompleteSpace F]
 #align measure_theory.is_complete_ae_strongly_measurable' MeasureTheory.isComplete_aeStronglyMeasurable'
 
 theorem isClosed_aeStronglyMeasurable' [hp : Fact (1 ≤ p)] [CompleteSpace F] (hm : m ≤ m0) :
-    IsClosed { f : lp F p μ | AeStronglyMeasurable' m f μ } :=
+    IsClosed { f : Lp F p μ | AeStronglyMeasurable' m f μ } :=
   IsComplete.isClosed (isComplete_aeStronglyMeasurable' hm)
 #align measure_theory.is_closed_ae_strongly_measurable' MeasureTheory.isClosed_aeStronglyMeasurable'
 
@@ -581,7 +589,7 @@ variable {m m0 : MeasurableSpace α} {μ : Measure α}
 `f =ᵐ[μ] Lp_meas_to_Lp_trim F 𝕜 p μ hm f`. -/
 theorem lpMeas.ae_fin_strongly_measurable' (hm : m ≤ m0) (f : lpMeas F 𝕜 m p μ) (hp_ne_zero : p ≠ 0)
     (hp_ne_top : p ≠ ∞) : ∃ g, FinStronglyMeasurable g (μ.trim hm) ∧ f =ᵐ[μ] g :=
-  ⟨lpMeasSubgroupToLpTrim F p μ hm f, lp.finStronglyMeasurable _ hp_ne_zero hp_ne_top,
+  ⟨lpMeasSubgroupToLpTrim F p μ hm f, Lp.finStronglyMeasurable _ hp_ne_zero hp_ne_top,
     (lpMeasSubgroupToLpTrim_ae_eq hm f).symm⟩
 #align measure_theory.Lp_meas.ae_fin_strongly_measurable' MeasureTheory.lpMeas.ae_fin_strongly_measurable'
 
@@ -590,7 +598,7 @@ the sub-sigma algebra and returns its version in the larger Lp space) to an indi
 sub-sigma-algebra, we obtain an indicator in the Lp space of the larger sigma-algebra. -/
 theorem lpMeasToLpTrimLie_symm_indicator [one_le_p : Fact (1 ≤ p)] [NormedSpace ℝ F] {hm : m ≤ m0}
     {s : Set α} {μ : Measure α} (hs : measurable_set[m] s) (hμs : μ.trim hm s ≠ ∞) (c : F) :
-    ((lpMeasToLpTrimLie F ℝ p μ hm).symm (indicatorConstLp p hs hμs c) : lp F p μ) =
+    ((lpMeasToLpTrimLie F ℝ p μ hm).symm (indicatorConstLp p hs hμs c) : Lp F p μ) =
       indicatorConstLp p (hm s hs) ((le_trim hm).trans_lt hμs.lt_top).Ne c :=
   by
   ext1
@@ -604,7 +612,7 @@ theorem lpMeasToLpTrimLie_symm_indicator [one_le_p : Fact (1 ≤ p)] [NormedSpac
 
 theorem lpMeasToLpTrimLie_symm_toLp [one_le_p : Fact (1 ≤ p)] [NormedSpace ℝ F] (hm : m ≤ m0)
     (f : α → F) (hf : Memℒp f p (μ.trim hm)) :
-    ((lpMeasToLpTrimLie F ℝ p μ hm).symm (hf.toLp f) : lp F p μ) =
+    ((lpMeasToLpTrimLie F ℝ p μ hm).symm (hf.toLp f) : Lp F p μ) =
       (memℒp_of_memℒp_trim hm hf).toLp f :=
   by
   ext1
@@ -623,10 +631,10 @@ variable {m m0 : MeasurableSpace α} {μ : Measure α} [Fact (1 ≤ p)] [NormedS
 
 /-- Auxiliary lemma for `Lp.induction_strongly_measurable`. -/
 @[elab_as_elim]
-theorem lp.induction_strongly_measurable_aux (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : lp F p μ → Prop)
+theorem Lp.induction_strongly_measurable_aux (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : Lp F p μ → Prop)
     (h_ind :
       ∀ (c : F) {s : Set α} (hs : measurable_set[m] s) (hμs : μ s < ∞),
-        P (lp.simpleFunc.indicatorConst p (hm s hs) hμs.Ne c))
+        P (Lp.simpleFunc.indicatorConst p (hm s hs) hμs.Ne c))
     (h_add :
       ∀ ⦃f g⦄,
         ∀ hf : Memℒp f p μ,
@@ -636,7 +644,7 @@ theorem lp.induction_strongly_measurable_aux (hm : m ≤ m0) (hp_ne_top : p ≠
                 Disjoint (Function.support f) (Function.support g) →
                   P (hf.toLp f) → P (hg.toLp g) → P (hf.toLp f + hg.toLp g))
     (h_closed : IsClosed { f : lpMeas F ℝ m p μ | P f }) :
-    ∀ f : lp F p μ, AeStronglyMeasurable' m f μ → P f :=
+    ∀ f : Lp F p μ, AeStronglyMeasurable' m f μ → P f :=
   by
   intro f hf
   let f' := (⟨f, hf⟩ : Lp_meas F ℝ m p μ)
@@ -670,7 +678,7 @@ theorem lp.induction_strongly_measurable_aux (hm : m ≤ m0) (hp_ne_top : p ≠
         h_disj hfP hgP
   · change IsClosed ((Lp_meas_to_Lp_trim_lie F ℝ p μ hm).symm ⁻¹' { g : Lp_meas F ℝ m p μ | P ↑g })
     exact IsClosed.preimage (LinearIsometryEquiv.continuous _) h_closed
-#align measure_theory.Lp.induction_strongly_measurable_aux MeasureTheory.lp.induction_strongly_measurable_aux
+#align measure_theory.Lp.induction_strongly_measurable_aux MeasureTheory.Lp.induction_strongly_measurable_aux
 
 /-- To prove something for an `Lp` function a.e. strongly measurable with respect to a
 sub-σ-algebra `m` in a normed space, it suffices to show that
@@ -680,10 +688,10 @@ sub-σ-algebra `m` in a normed space, it suffices to show that
   closed.
 -/
 @[elab_as_elim]
-theorem lp.induction_stronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : lp F p μ → Prop)
+theorem Lp.induction_stronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : Lp F p μ → Prop)
     (h_ind :
       ∀ (c : F) {s : Set α} (hs : measurable_set[m] s) (hμs : μ s < ∞),
-        P (lp.simpleFunc.indicatorConst p (hm s hs) hμs.Ne c))
+        P (Lp.simpleFunc.indicatorConst p (hm s hs) hμs.Ne c))
     (h_add :
       ∀ ⦃f g⦄,
         ∀ hf : Memℒp f p μ,
@@ -693,7 +701,7 @@ theorem lp.induction_stronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞)
                 Disjoint (Function.support f) (Function.support g) →
                   P (hf.toLp f) → P (hg.toLp g) → P (hf.toLp f + hg.toLp g))
     (h_closed : IsClosed { f : lpMeas F ℝ m p μ | P f }) :
-    ∀ f : lp F p μ, AeStronglyMeasurable' m f μ → P f :=
+    ∀ f : Lp F p μ, AeStronglyMeasurable' m f μ → P f :=
   by
   intro f hf
   suffices h_add_ae :
@@ -748,7 +756,7 @@ theorem lp.induction_stronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞)
   rw [← mem_ℒp.to_Lp_congr hf'_Lp hf hff'.symm] at hPf⊢
   rw [← mem_ℒp.to_Lp_congr hg'_Lp hg hgg'.symm] at hPg⊢
   exact h_add hf'_Lp hg'_Lp hf'_meas hg'_meas h_disj hPf hPg
-#align measure_theory.Lp.induction_strongly_measurable MeasureTheory.lp.induction_stronglyMeasurable
+#align measure_theory.Lp.induction_strongly_measurable MeasureTheory.Lp.induction_stronglyMeasurable
 
 /-- To prove something for an arbitrary `mem_ℒp` function a.e. strongly measurable with respect
 to a sub-σ-algebra `m` in a normed space, it suffices to show that
@@ -820,7 +828,7 @@ include 𝕜
 
 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_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)
     (hf_zero : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → (∫ x in s, f x ∂μ) = 0)
@@ -838,10 +846,10 @@ 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_set_integral_eq_zero'
 
 /-- **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_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)
     (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)
@@ -865,7 +873,7 @@ 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_set_integral_eq'
 
 variable {𝕜}
 
@@ -1000,7 +1008,7 @@ theorem aeStronglyMeasurable'_condexpL2 (hm : m ≤ m0) (f : α →₂[μ] E) :
 
 theorem integrableOn_condexpL2_of_measure_ne_top (hm : m ≤ m0) (hμs : μ s ≠ ∞) (f : α →₂[μ] E) :
     IntegrableOn (condexpL2 𝕜 hm f) s μ :=
-  integrableOn_lp_of_measure_ne_top (condexpL2 𝕜 hm f : α →₂[μ] E) fact_one_le_two_ennreal.elim hμs
+  integrableOn_Lp_of_measure_ne_top (condexpL2 𝕜 hm f : α →₂[μ] E) fact_one_le_two_ennreal.elim hμs
 #align measure_theory.integrable_on_condexp_L2_of_measure_ne_top MeasureTheory.integrableOn_condexpL2_of_measure_ne_top
 
 theorem integrable_condexpL2_of_finiteMeasure (hm : m ≤ m0) [FiniteMeasure μ] {f : α →₂[μ] E} :
@@ -1067,7 +1075,7 @@ section Real
 
 variable {hm : m ≤ m0}
 
-theorem integral_condexpL2_eq_of_fin_meas_real (f : lp 𝕜 2 μ) (hs : measurable_set[m] s)
+theorem integral_condexpL2_eq_of_fin_meas_real (f : Lp 𝕜 2 μ) (hs : measurable_set[m] s)
     (hμs : μ s ≠ ∞) : (∫ x in s, condexpL2 𝕜 hm f x ∂μ) = ∫ x in s, f x ∂μ :=
   by
   rw [← L2.inner_indicator_const_Lp_one (hm s hs) hμs]
@@ -1080,7 +1088,7 @@ theorem integral_condexpL2_eq_of_fin_meas_real (f : lp 𝕜 2 μ) (hs : measurab
   rw [h_eq_inner, ← inner_condexp_L2_left_eq_right, condexp_L2_indicator_of_measurable hm hs hμs]
 #align measure_theory.integral_condexp_L2_eq_of_fin_meas_real MeasureTheory.integral_condexpL2_eq_of_fin_meas_real
 
-theorem lintegral_nnnorm_condexpL2_le (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) (f : lp ℝ 2 μ) :
+theorem lintegral_nnnorm_condexpL2_le (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) (f : Lp ℝ 2 μ) :
     (∫⁻ x in s, ‖condexpL2 ℝ hm f x‖₊ ∂μ) ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ :=
   by
   let h_meas := Lp_meas.ae_strongly_measurable' (condexp_L2 ℝ hm f)
@@ -1106,7 +1114,7 @@ theorem lintegral_nnnorm_condexpL2_le (hs : measurable_set[m] s) (hμs : μ s 
     exact set_integral_congr_ae (hm t ht) (hg_eq.mono fun x hx _ => hx)
 #align measure_theory.lintegral_nnnorm_condexp_L2_le MeasureTheory.lintegral_nnnorm_condexpL2_le
 
-theorem condexpL2_ae_eq_zero_of_ae_eq_zero (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) {f : lp ℝ 2 μ}
+theorem condexpL2_ae_eq_zero_of_ae_eq_zero (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) {f : Lp ℝ 2 μ}
     (hf : f =ᵐ[μ.restrict s] 0) : condexpL2 ℝ hm f =ᵐ[μ.restrict s] 0 :=
   by
   suffices h_nnnorm_eq_zero : (∫⁻ x in s, ‖condexp_L2 ℝ hm f x‖₊ ∂μ) = 0
@@ -1152,8 +1160,8 @@ end Real
 /-- `condexp_L2` commutes with taking inner products with constants. See the lemma
 `condexp_L2_comp_continuous_linear_map` for a more general result about commuting with continuous
 linear maps. -/
-theorem condexpL2_const_inner (hm : m ≤ m0) (f : lp E 2 μ) (c : E) :
-    condexpL2 𝕜 hm (((lp.memℒp f).const_inner c).toLp fun a => ⟪c, f a⟫) =ᵐ[μ] fun a =>
+theorem condexpL2_const_inner (hm : m ≤ m0) (f : Lp E 2 μ) (c : E) :
+    condexpL2 𝕜 hm (((Lp.memℒp f).const_inner c).toLp fun a => ⟪c, f a⟫) =ᵐ[μ] fun a =>
       ⟪c, condexpL2 𝕜 hm f a⟫ :=
   by
   rw [Lp_meas_coe]
@@ -1181,7 +1189,7 @@ theorem condexpL2_const_inner (hm : m ≤ m0) (f : lp E 2 μ) (c : E) :
 #align measure_theory.condexp_L2_const_inner MeasureTheory.condexpL2_const_inner
 
 /-- `condexp_L2` verifies the equality of integrals defining the conditional expectation. -/
-theorem integral_condexpL2_eq (hm : m ≤ m0) (f : lp E' 2 μ) (hs : measurable_set[m] s)
+theorem integral_condexpL2_eq (hm : m ≤ m0) (f : Lp E' 2 μ) (hs : measurable_set[m] s)
     (hμs : μ s ≠ ∞) : (∫ x in s, condexpL2 𝕜 hm f x ∂μ) = ∫ x in s, f x ∂μ :=
   by
   rw [← sub_eq_zero, Lp_meas_coe, ←
@@ -1320,7 +1328,7 @@ section CondexpIndSmul
 variable [NormedSpace ℝ G] {hm : m ≤ m0}
 
 /-- Conditional expectation of the indicator of a measurable set with finite measure, in L2. -/
-def condexpIndSmul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) : lp G 2 μ :=
+def condexpIndSmul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) : Lp G 2 μ :=
   (toSpanSingleton ℝ x).compLpL 2 μ (condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)))
 #align measure_theory.condexp_ind_smul MeasureTheory.condexpIndSmul
 

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

@@ -83,7 +83,7 @@ noncomputable section
 
 open TopologicalSpace MeasureTheory.lp Filter ContinuousLinearMap
 
-open NNReal ENNReal Topology BigOperators MeasureTheory
+open scoped NNReal ENNReal Topology BigOperators MeasureTheory
 
 namespace MeasureTheory
 
@@ -1595,7 +1595,7 @@ theorem condexpIndL1Fin_disjoint_union (hs : MeasurableSet s) (ht : MeasurableSe
 
 end CondexpIndL1Fin
 
-open Classical
+open scoped Classical
 
 section CondexpIndL1
 
@@ -2047,7 +2047,7 @@ section Condexp
 /-! ### Conditional expectation of a function -/
 
 
-open Classical
+open scoped Classical
 
 variable {𝕜} {m m0 : MeasurableSpace α} {μ : Measure α} {f g : α → F'} {s : Set α}
 

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

@@ -102,9 +102,7 @@ variable {α β 𝕜 : Type _} {m m0 : MeasurableSpace α} {μ : Measure α} [To
   {f g : α → β}
 
 theorem congr (hf : AeStronglyMeasurable' m f μ) (hfg : f =ᵐ[μ] g) : AeStronglyMeasurable' m g μ :=
-  by
-  obtain ⟨f', hf'_meas, hff'⟩ := hf
-  exact ⟨f', hf'_meas, hfg.symm.trans hff'⟩
+  by obtain ⟨f', hf'_meas, hff'⟩ := hf; exact ⟨f', hf'_meas, hfg.symm.trans hff'⟩
 #align measure_theory.ae_strongly_measurable'.congr MeasureTheory.AeStronglyMeasurable'.congr
 
 theorem add [Add β] [ContinuousAdd β] (hf : AeStronglyMeasurable' m f μ)
@@ -179,10 +177,8 @@ end AeStronglyMeasurable'
 
 theorem aeStronglyMeasurable'_of_aeStronglyMeasurable'_trim {α β} {m m0 m0' : MeasurableSpace α}
     [TopologicalSpace β] (hm0 : m0 ≤ m0') {μ : Measure α} {f : α → β}
-    (hf : AeStronglyMeasurable' m f (μ.trim hm0)) : AeStronglyMeasurable' m f μ :=
-  by
-  obtain ⟨g, hg_meas, hfg⟩ := hf
-  exact ⟨g, hg_meas, ae_eq_of_ae_eq_trim hfg⟩
+    (hf : AeStronglyMeasurable' m f (μ.trim hm0)) : AeStronglyMeasurable' m f μ := by
+  obtain ⟨g, hg_meas, hfg⟩ := hf; exact ⟨g, hg_meas, ae_eq_of_ae_eq_trim hfg⟩
 #align measure_theory.ae_strongly_measurable'_of_ae_strongly_measurable'_trim MeasureTheory.aeStronglyMeasurable'_of_aeStronglyMeasurable'_trim
 
 theorem StronglyMeasurable.aeStronglyMeasurable' {α β} {m m0 : MeasurableSpace α}
@@ -349,9 +345,7 @@ theorem memℒp_trim_of_mem_lpMeasSubgroup (hm : m ≤ m0) (f : lp F p μ)
   obtain ⟨hg, hfg⟩ := hf.some_spec
   change mem_ℒp g p (μ.trim hm)
   refine' ⟨hg.ae_strongly_measurable, _⟩
-  have h_snorm_fg : snorm g p (μ.trim hm) = snorm f p μ :=
-    by
-    rw [snorm_trim hm hg]
+  have h_snorm_fg : snorm g p (μ.trim hm) = snorm f p μ := by rw [snorm_trim hm hg];
     exact snorm_congr_ae hfg.symm
   rw [h_snorm_fg]
   exact Lp.snorm_lt_top f
@@ -551,20 +545,16 @@ def lpMeasToLpTrimLie [hp : Fact (1 ≤ p)] (hm : m ≤ m0) : lpMeas F 𝕜 m p
 variable {F 𝕜 p μ}
 
 instance [hm : Fact (m ≤ m0)] [CompleteSpace F] [hp : Fact (1 ≤ p)] :
-    CompleteSpace (lpMeasSubgroup F m p μ) :=
-  by
-  rw [(Lp_meas_subgroup_to_Lp_trim_iso F p μ hm.elim).completeSpace_iff]
-  infer_instance
+    CompleteSpace (lpMeasSubgroup F m p μ) := by
+  rw [(Lp_meas_subgroup_to_Lp_trim_iso F p μ hm.elim).completeSpace_iff]; infer_instance
 
 -- For now just no-lint this; lean4's tree-based logging will make this easier to debug.
 -- One possible change might be to generalize `𝕜` from `is_R_or_C` to `normed_field`, as this
 -- result may well hold there.
 @[nolint fails_quickly]
 instance [hm : Fact (m ≤ m0)] [CompleteSpace F] [hp : Fact (1 ≤ p)] :
-    CompleteSpace (lpMeas F 𝕜 m p μ) :=
-  by
-  rw [(Lp_meas_subgroup_to_Lp_meas_iso F 𝕜 p μ).symm.completeSpace_iff]
-  infer_instance
+    CompleteSpace (lpMeas F 𝕜 m p μ) := by
+  rw [(Lp_meas_subgroup_to_Lp_meas_iso F 𝕜 p μ).symm.completeSpace_iff]; infer_instance
 
 theorem isComplete_aeStronglyMeasurable' [hp : Fact (1 ≤ p)] [CompleteSpace F] (hm : m ≤ m0) :
     IsComplete { f : lp F p μ | AeStronglyMeasurable' m f μ } :=
@@ -858,8 +848,7 @@ theorem lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : lp E' p 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.coe_fn_sub f g).symm.trans h_sub
+  · rw [← sub_ae_eq_zero]; exact (Lp.coe_fn_sub f g).symm.trans h_sub
   have hfg' : ∀ s : Set α, measurable_set[m] s → μ s < ∞ → (∫ x in s, (f - g) x ∂μ) = 0 :=
     by
     intro s hs hμs
@@ -1168,11 +1157,8 @@ theorem condexpL2_const_inner (hm : m ≤ m0) (f : lp E 2 μ) (c : E) :
       ⟪c, condexpL2 𝕜 hm f a⟫ :=
   by
   rw [Lp_meas_coe]
-  have h_mem_Lp : mem_ℒp (fun a => ⟪c, condexp_L2 𝕜 hm f a⟫) 2 μ :=
-    by
-    refine' mem_ℒp.const_inner _ _
-    rw [Lp_meas_coe]
-    exact Lp.mem_ℒp _
+  have h_mem_Lp : mem_ℒp (fun a => ⟪c, condexp_L2 𝕜 hm f a⟫) 2 μ := by
+    refine' mem_ℒp.const_inner _ _; rw [Lp_meas_coe]; exact Lp.mem_ℒp _
   have h_eq : h_mem_Lp.to_Lp _ =ᵐ[μ] fun a => ⟪c, condexp_L2 𝕜 hm f a⟫ := h_mem_Lp.coe_fn_to_Lp
   refine' eventually_eq.trans _ h_eq
   refine'
@@ -1189,8 +1175,7 @@ theorem condexpL2_const_inner (hm : m ≤ m0) (f : lp E 2 μ) (c : E) :
       L2.inner_indicator_const_Lp_eq_set_integral_inner 𝕜 f (hm s hs) c hμs.ne,
       set_integral_congr_ae (hm s hs)
         ((mem_ℒp.coe_fn_to_Lp ((Lp.mem_ℒp f).const_inner c)).mono fun x hx hxs => hx)]
-  · rw [← Lp_meas_coe]
-    exact Lp_meas.ae_strongly_measurable' _
+  · rw [← Lp_meas_coe]; exact Lp_meas.ae_strongly_measurable' _
   · refine' ae_strongly_measurable'.congr _ h_eq.symm
     exact (Lp_meas.ae_strongly_measurable' _).const_inner _
 #align measure_theory.condexp_L2_const_inner MeasureTheory.condexpL2_const_inner
@@ -1238,8 +1223,7 @@ theorem condexpL2_comp_continuousLinearMap (hm : m ≤ m0) (T : E' →L[ℝ] E''
       integral_condexp_L2_eq hm (T.comp_Lp f) hs hμs.ne, T.set_integral_comp_Lp _ (hm s hs),
       T.integral_comp_comm
         (integrable_on_Lp_of_measure_ne_top f fact_one_le_two_ennreal.elim hμs.ne)]
-  · rw [← Lp_meas_coe]
-    exact Lp_meas.ae_strongly_measurable' _
+  · rw [← Lp_meas_coe]; exact Lp_meas.ae_strongly_measurable' _
   · have h_coe := T.coe_fn_comp_Lp (condexp_L2 𝕜 hm f : α →₂[μ] E')
     rw [← eventually_eq] at h_coe
     refine' ae_strongly_measurable'.congr _ h_coe.symm
@@ -1323,8 +1307,7 @@ theorem integrable_condexpL2_indicator (hm : m ≤ m0) [SigmaFinite (μ.trim hm)
   refine'
     integrable_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) (ENNReal.mul_lt_top hμs ENNReal.coe_ne_top) _
       _
-  · rw [Lp_meas_coe]
-    exact Lp.ae_strongly_measurable _
+  · rw [Lp_meas_coe]; exact Lp.ae_strongly_measurable _
   · refine' fun t ht hμt =>
       (set_lintegral_nnnorm_condexp_L2_indicator_le hm hs hμs x ht hμt).trans _
     exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
@@ -1358,17 +1341,13 @@ theorem aeStronglyMeasurable'_condexpIndSmul (hm : m ≤ m0) (hs : MeasurableSet
 #align measure_theory.ae_strongly_measurable'_condexp_ind_smul MeasureTheory.aeStronglyMeasurable'_condexpIndSmul
 
 theorem condexpIndSmul_add (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x y : G) :
-    condexpIndSmul hm hs hμs (x + y) = condexpIndSmul hm hs hμs x + condexpIndSmul hm hs hμs y :=
-  by
-  simp_rw [condexp_ind_smul]
-  rw [to_span_singleton_add, add_comp_LpL, add_apply]
+    condexpIndSmul hm hs hμs (x + y) = condexpIndSmul hm hs hμs x + condexpIndSmul hm hs hμs y := by
+  simp_rw [condexp_ind_smul]; rw [to_span_singleton_add, add_comp_LpL, add_apply]
 #align measure_theory.condexp_ind_smul_add MeasureTheory.condexpIndSmul_add
 
 theorem condexpIndSmul_smul (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (c : ℝ) (x : G) :
-    condexpIndSmul hm hs hμs (c • x) = c • condexpIndSmul hm hs hμs x :=
-  by
-  simp_rw [condexp_ind_smul]
-  rw [to_span_singleton_smul, smul_comp_LpL, smul_apply]
+    condexpIndSmul hm hs hμs (c • x) = c • condexpIndSmul hm hs hμs x := by
+  simp_rw [condexp_ind_smul]; rw [to_span_singleton_smul, smul_comp_LpL, smul_apply]
 #align measure_theory.condexp_ind_smul_smul MeasureTheory.condexpIndSmul_smul
 
 theorem condexpIndSmul_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (hs : MeasurableSet s)
@@ -1576,9 +1555,7 @@ theorem norm_condexpIndL1Fin_le (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x
     ENNReal.toReal_ofReal this,
     ENNReal.toReal_le_toReal ENNReal.ofReal_ne_top (ENNReal.mul_ne_top hμs ENNReal.ofReal_ne_top),
     of_real_integral_norm_eq_lintegral_nnnorm]
-  swap
-  · rw [← mem_ℒp_one_iff_integrable]
-    exact Lp.mem_ℒp _
+  swap; · rw [← mem_ℒp_one_iff_integrable]; exact Lp.mem_ℒp _
   have h_eq :
     (∫⁻ a, ‖condexp_ind_L1_fin hm hs hμs x a‖₊ ∂μ) = ∫⁻ a, ‖condexp_ind_smul hm hs hμs x a‖₊ ∂μ :=
     by
@@ -1650,12 +1627,9 @@ theorem condexpIndL1_add (x y : G) :
     condexpIndL1 hm μ s (x + y) = condexpIndL1 hm μ s x + condexpIndL1 hm μ s y :=
   by
   by_cases hs : MeasurableSet s
-  swap;
-  · simp_rw [condexp_ind_L1_of_not_measurable_set hs]
-    rw [zero_add]
+  swap; · simp_rw [condexp_ind_L1_of_not_measurable_set hs]; rw [zero_add]
   by_cases hμs : μ s = ∞
-  · simp_rw [condexp_ind_L1_of_measure_eq_top hμs]
-    rw [zero_add]
+  · simp_rw [condexp_ind_L1_of_measure_eq_top hμs]; rw [zero_add]
   · simp_rw [condexp_ind_L1_of_measurable_set_of_measure_ne_top hs hμs]
     exact condexp_ind_L1_fin_add hs hμs x y
 #align measure_theory.condexp_ind_L1_add MeasureTheory.condexpIndL1_add
@@ -1664,12 +1638,9 @@ theorem condexpIndL1_smul (c : ℝ) (x : G) :
     condexpIndL1 hm μ s (c • x) = c • condexpIndL1 hm μ s x :=
   by
   by_cases hs : MeasurableSet s
-  swap;
-  · simp_rw [condexp_ind_L1_of_not_measurable_set hs]
-    rw [smul_zero]
+  swap; · simp_rw [condexp_ind_L1_of_not_measurable_set hs]; rw [smul_zero]
   by_cases hμs : μ s = ∞
-  · simp_rw [condexp_ind_L1_of_measure_eq_top hμs]
-    rw [smul_zero]
+  · simp_rw [condexp_ind_L1_of_measure_eq_top hμs]; rw [smul_zero]
   · simp_rw [condexp_ind_L1_of_measurable_set_of_measure_ne_top hs hμs]
     exact condexp_ind_L1_fin_smul hs hμs c x
 #align measure_theory.condexp_ind_L1_smul MeasureTheory.condexpIndL1_smul
@@ -1678,12 +1649,9 @@ theorem condexpIndL1_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (c : 
     condexpIndL1 hm μ s (c • x) = c • condexpIndL1 hm μ s x :=
   by
   by_cases hs : MeasurableSet s
-  swap;
-  · simp_rw [condexp_ind_L1_of_not_measurable_set hs]
-    rw [smul_zero]
+  swap; · simp_rw [condexp_ind_L1_of_not_measurable_set hs]; rw [smul_zero]
   by_cases hμs : μ s = ∞
-  · simp_rw [condexp_ind_L1_of_measure_eq_top hμs]
-    rw [smul_zero]
+  · simp_rw [condexp_ind_L1_of_measure_eq_top hμs]; rw [smul_zero]
   · simp_rw [condexp_ind_L1_of_measurable_set_of_measure_ne_top hs hμs]
     exact condexp_ind_L1_fin_smul' hs hμs c x
 #align measure_theory.condexp_ind_L1_smul' MeasureTheory.condexpIndL1_smul'
@@ -1692,8 +1660,7 @@ theorem norm_condexpIndL1_le (x : G) : ‖condexpIndL1 hm μ s x‖ ≤ (μ s).t
   by
   by_cases hs : MeasurableSet s
   swap;
-  · simp_rw [condexp_ind_L1_of_not_measurable_set hs]
-    rw [Lp.norm_zero]
+  · simp_rw [condexp_ind_L1_of_not_measurable_set hs]; rw [Lp.norm_zero]
     exact mul_nonneg ENNReal.toReal_nonneg (norm_nonneg _)
   by_cases hμs : μ s = ∞
   · rw [condexp_ind_L1_of_measure_eq_top hμs x, Lp.norm_zero]
@@ -1779,11 +1746,8 @@ theorem condexpInd_disjoint_union_apply (hs : MeasurableSet s) (ht : MeasurableS
 
 theorem condexpInd_disjoint_union (hs : MeasurableSet s) (ht : MeasurableSet t) (hμs : μ s ≠ ∞)
     (hμt : μ t ≠ ∞) (hst : s ∩ t = ∅) :
-    (condexpInd hm μ (s ∪ t) : G →L[ℝ] α →₁[μ] G) = condexpInd hm μ s + condexpInd hm μ t :=
-  by
-  ext1
-  push_cast
-  exact condexp_ind_disjoint_union_apply hs ht hμs hμt hst x
+    (condexpInd hm μ (s ∪ t) : G →L[ℝ] α →₁[μ] G) = condexpInd hm μ s + condexpInd hm μ t := by
+  ext1; push_cast ; exact condexp_ind_disjoint_union_apply hs ht hμs hμt hst x
 #align measure_theory.condexp_ind_disjoint_union MeasureTheory.condexpInd_disjoint_union
 
 variable (G)
@@ -1853,10 +1817,8 @@ theorem condexpL1Clm_indicatorConstLp (hs : MeasurableSet s) (hμs : μ s ≠ 
 #align measure_theory.condexp_L1_clm_indicator_const_Lp MeasureTheory.condexpL1Clm_indicatorConstLp
 
 theorem condexpL1Clm_indicatorConst (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : F') :
-    (condexpL1Clm hm μ) ↑(simpleFunc.indicatorConst 1 hs hμs x) = condexpInd hm μ s x :=
-  by
-  rw [Lp.simple_func.coe_indicator_const]
-  exact condexp_L1_clm_indicator_const_Lp hs hμs x
+    (condexpL1Clm hm μ) ↑(simpleFunc.indicatorConst 1 hs hμs x) = condexpInd hm μ s x := by
+  rw [Lp.simple_func.coe_indicator_const]; exact condexp_L1_clm_indicator_const_Lp hs hμs x
 #align measure_theory.condexp_L1_clm_indicator_const MeasureTheory.condexpL1Clm_indicatorConst
 
 /-- Auxiliary lemma used in the proof of `set_integral_condexp_L1_clm`. -/
@@ -2114,10 +2076,7 @@ theorem condexp_of_not_le (hm_not : ¬m ≤ m0) : μ[f|m] = 0 := by rw [condexp,
 #align measure_theory.condexp_of_not_le MeasureTheory.condexp_of_not_le
 
 theorem condexp_of_not_sigmaFinite (hm : m ≤ m0) (hμm_not : ¬SigmaFinite (μ.trim hm)) :
-    μ[f|m] = 0 := by
-  rw [condexp, dif_pos hm, dif_neg]
-  push_neg
-  exact fun h => absurd h hμm_not
+    μ[f|m] = 0 := by rw [condexp, dif_pos hm, dif_neg]; push_neg; exact fun h => absurd h hμm_not
 #align measure_theory.condexp_of_not_sigma_finite MeasureTheory.condexp_of_not_sigmaFinite
 
 theorem condexp_of_sigmaFinite (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] :
@@ -2135,10 +2094,8 @@ theorem condexp_of_sigmaFinite (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)]
 #align measure_theory.condexp_of_sigma_finite MeasureTheory.condexp_of_sigmaFinite
 
 theorem condexp_of_stronglyMeasurable (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] {f : α → F'}
-    (hf : strongly_measurable[m] f) (hfi : Integrable f μ) : μ[f|m] = f :=
-  by
-  rw [condexp_of_sigma_finite hm, if_pos hfi, if_pos hf]
-  infer_instance
+    (hf : strongly_measurable[m] f) (hfi : Integrable f μ) : μ[f|m] = f := by
+  rw [condexp_of_sigma_finite hm, if_pos hfi, if_pos hf]; infer_instance
 #align measure_theory.condexp_of_strongly_measurable MeasureTheory.condexp_of_stronglyMeasurable
 
 theorem condexp_const (hm : m ≤ m0) (c : F') [FiniteMeasure μ] : μ[fun x : α => c|m] = fun _ => c :=
@@ -2194,13 +2151,9 @@ theorem condexp_zero : μ[(0 : α → F')|m] = 0 :=
 theorem stronglyMeasurable_condexp : strongly_measurable[m] (μ[f|m]) :=
   by
   by_cases hm : m ≤ m0
-  swap;
-  · rw [condexp_of_not_le hm]
-    exact strongly_measurable_zero
+  swap; · rw [condexp_of_not_le hm]; exact strongly_measurable_zero
   by_cases hμm : sigma_finite (μ.trim hm)
-  swap;
-  · rw [condexp_of_not_sigma_finite hm hμm]
-    exact strongly_measurable_zero
+  swap; · rw [condexp_of_not_sigma_finite hm hμm]; exact strongly_measurable_zero
   haveI : sigma_finite (μ.trim hm) := hμm
   rw [condexp_of_sigma_finite hm]
   swap; · infer_instance
@@ -2234,13 +2187,9 @@ theorem condexp_of_aeStronglyMeasurable' (hm : m ≤ m0) [hμm : SigmaFinite (μ
 theorem integrable_condexp : Integrable (μ[f|m]) μ :=
   by
   by_cases hm : m ≤ m0
-  swap;
-  · rw [condexp_of_not_le hm]
-    exact integrable_zero _ _ _
+  swap; · rw [condexp_of_not_le hm]; exact integrable_zero _ _ _
   by_cases hμm : sigma_finite (μ.trim hm)
-  swap;
-  · rw [condexp_of_not_sigma_finite hm hμm]
-    exact integrable_zero _ _ _
+  swap; · rw [condexp_of_not_sigma_finite hm hμm]; exact integrable_zero _ _ _
   haveI : sigma_finite (μ.trim hm) := hμm
   exact (integrable_condexp_L1 f).congr (condexp_ae_eq_condexp_L1 hm f).symm
 #align measure_theory.integrable_condexp MeasureTheory.integrable_condexp
@@ -2257,10 +2206,8 @@ theorem set_integral_condexp (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : In
 theorem integral_condexp (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] (hf : Integrable f μ) :
     (∫ x, (μ[f|m]) x ∂μ) = ∫ x, f x ∂μ :=
   by
-  suffices (∫ x in Set.univ, (μ[f|m]) x ∂μ) = ∫ x in Set.univ, f x ∂μ
-    by
-    simp_rw [integral_univ] at this
-    exact this
+  suffices (∫ x in Set.univ, (μ[f|m]) x ∂μ) = ∫ x in Set.univ, f x ∂μ by
+    simp_rw [integral_univ] at this; exact this
   exact set_integral_condexp hm hf (@MeasurableSet.univ _ m)
 #align measure_theory.integral_condexp MeasureTheory.integral_condexp
 
@@ -2292,9 +2239,7 @@ theorem condexp_bot' [hμ : μ.ae.ne_bot] (f : α → F') :
     rfl
   haveI : is_finite_measure μ := hμ_finite
   by_cases hf : integrable f μ
-  swap;
-  · rw [integral_undef hf, smul_zero, condexp_undef hf]
-    rfl
+  swap; · rw [integral_undef hf, smul_zero, condexp_undef hf]; rfl
   have h_meas : strongly_measurable[⊥] (μ[f|⊥]) := strongly_measurable_condexp
   obtain ⟨c, h_eq⟩ := strongly_measurable_bot_iff.mp h_meas
   rw [h_eq]
@@ -2317,23 +2262,17 @@ theorem condexp_bot_ae_eq (f : α → F') :
     simp only [h, ae_zero]
 #align measure_theory.condexp_bot_ae_eq MeasureTheory.condexp_bot_ae_eq
 
-theorem condexp_bot [ProbabilityMeasure μ] (f : α → F') : μ[f|⊥] = fun _ => ∫ x, f x ∂μ :=
-  by
-  refine' (condexp_bot' f).trans _
-  rw [measure_univ, ENNReal.one_toReal, inv_one, one_smul]
+theorem condexp_bot [ProbabilityMeasure μ] (f : α → F') : μ[f|⊥] = fun _ => ∫ x, f x ∂μ := by
+  refine' (condexp_bot' f).trans _; rw [measure_univ, ENNReal.one_toReal, inv_one, one_smul]
 #align measure_theory.condexp_bot MeasureTheory.condexp_bot
 
 theorem condexp_add (hf : Integrable f μ) (hg : Integrable g μ) :
     μ[f + g|m] =ᵐ[μ] μ[f|m] + μ[g|m] :=
   by
   by_cases hm : m ≤ m0
-  swap;
-  · simp_rw [condexp_of_not_le hm]
-    simp
+  swap; · simp_rw [condexp_of_not_le hm]; simp
   by_cases hμm : sigma_finite (μ.trim hm)
-  swap;
-  · simp_rw [condexp_of_not_sigma_finite hm hμm]
-    simp
+  swap; · simp_rw [condexp_of_not_sigma_finite hm hμm]; simp
   haveI : sigma_finite (μ.trim hm) := hμm
   refine' (condexp_ae_eq_condexp_L1 hm _).trans _
   rw [condexp_L1_add hf hg]
@@ -2357,13 +2296,9 @@ theorem condexp_finset_sum {ι : Type _} {s : Finset ι} {f : ι → α → F'}
 theorem condexp_smul (c : 𝕜) (f : α → F') : μ[c • f|m] =ᵐ[μ] c • μ[f|m] :=
   by
   by_cases hm : m ≤ m0
-  swap;
-  · simp_rw [condexp_of_not_le hm]
-    simp
+  swap; · simp_rw [condexp_of_not_le hm]; simp
   by_cases hμm : sigma_finite (μ.trim hm)
-  swap;
-  · simp_rw [condexp_of_not_sigma_finite hm hμm]
-    simp
+  swap; · simp_rw [condexp_of_not_sigma_finite hm hμm]; simp
   haveI : sigma_finite (μ.trim hm) := hμm
   refine' (condexp_ae_eq_condexp_L1 hm _).trans _
   rw [condexp_L1_smul c f]
@@ -2462,12 +2397,8 @@ theorem tendsto_condexp_unique (fs gs : ℕ → α → F') (f g : α → F')
     (h_int_bound_gs : Integrable bound_gs μ) (hfs_bound : ∀ n, ∀ᵐ x ∂μ, ‖fs n x‖ ≤ bound_fs x)
     (hgs_bound : ∀ n, ∀ᵐ x ∂μ, ‖gs n x‖ ≤ bound_gs x) (hfg : ∀ n, μ[fs n|m] =ᵐ[μ] μ[gs n|m]) :
     μ[f|m] =ᵐ[μ] μ[g|m] := by
-  by_cases hm : m ≤ m0
-  swap
-  · simp_rw [condexp_of_not_le hm]
-  by_cases hμm : sigma_finite (μ.trim hm)
-  swap
-  · simp_rw [condexp_of_not_sigma_finite hm hμm]
+  by_cases hm : m ≤ m0; swap; · simp_rw [condexp_of_not_le hm]
+  by_cases hμm : sigma_finite (μ.trim hm); swap; · simp_rw [condexp_of_not_sigma_finite hm hμm]
   haveI : sigma_finite (μ.trim hm) := hμm
   refine' (condexp_ae_eq_condexp_L1 hm f).trans ((condexp_ae_eq_condexp_L1 hm g).trans _).symm
   rw [← Lp.ext_iff]

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

@@ -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.basic
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit e0736bb5b48bdadbca19dbd857e12bee38ccfbb8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -556,6 +556,10 @@ instance [hm : Fact (m ≤ m0)] [CompleteSpace F] [hp : Fact (1 ≤ p)] :
   rw [(Lp_meas_subgroup_to_Lp_trim_iso F p μ hm.elim).completeSpace_iff]
   infer_instance
 
+-- For now just no-lint this; lean4's tree-based logging will make this easier to debug.
+-- One possible change might be to generalize `𝕜` from `is_R_or_C` to `normed_field`, as this
+-- result may well hold there.
+@[nolint fails_quickly]
 instance [hm : Fact (m ≤ m0)] [CompleteSpace F] [hp : Fact (1 ≤ p)] :
     CompleteSpace (lpMeas F 𝕜 m p μ) :=
   by
@@ -1371,8 +1375,7 @@ theorem condexpIndSmul_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (hs
     (hμs : μ s ≠ ∞) (c : 𝕜) (x : F) :
     condexpIndSmul hm hs hμs (c • x) = c • condexpIndSmul hm hs hμs x := by
   rw [condexp_ind_smul, condexp_ind_smul, to_span_singleton_smul',
-    (to_span_singleton ℝ x).smul_compLpL_apply c
-      ↑(condexp_L2 ℝ hm (indicator_const_Lp 2 hs hμs (1 : ℝ)))]
+    (to_span_singleton ℝ x).smul_compLpL c, smul_apply]
 #align measure_theory.condexp_ind_smul_smul' MeasureTheory.condexpIndSmul_smul'
 
 theorem condexpIndSmul_ae_eq_smul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :

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

@@ -306,7 +306,7 @@ theorem lpMeas.aeStronglyMeasurable' {m m0 : MeasurableSpace α} {μ : Measure 
 
 theorem mem_lpMeas_self {m0 : MeasurableSpace α} (μ : Measure α) (f : lp F p μ) :
     f ∈ lpMeas F 𝕜 m0 p μ :=
-  mem_lpMeas_iff_aeStronglyMeasurable'.mpr (lp.aeStronglyMeasurable f)
+  mem_lpMeas_iff_aeStronglyMeasurable'.mpr (lp.aEStronglyMeasurable f)
 #align measure_theory.mem_Lp_meas_self MeasureTheory.mem_lpMeas_self
 
 theorem lpMeasSubgroup_coe {m m0 : MeasurableSpace α} {μ : Measure α} {f : lpMeasSubgroup F m p μ} :
@@ -2441,7 +2441,7 @@ theorem condexp_nonpos {E} [NormedLatticeAddCommGroup E] [CompleteSpace E] [Norm
   `condexp_L1`. -/
 theorem tendsto_condexpL1_of_dominated_convergence (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     {fs : ℕ → α → F'} {f : α → F'} (bound_fs : α → ℝ)
-    (hfs_meas : ∀ n, AeStronglyMeasurable (fs n) μ) (h_int_bound_fs : Integrable bound_fs μ)
+    (hfs_meas : ∀ n, AEStronglyMeasurable (fs n) μ) (h_int_bound_fs : Integrable bound_fs μ)
     (hfs_bound : ∀ n, ∀ᵐ x ∂μ, ‖fs n x‖ ≤ bound_fs x)
     (hfs : ∀ᵐ x ∂μ, Tendsto (fun n => fs n x) atTop (𝓝 (f x))) :
     Tendsto (fun n => condexpL1 hm μ (fs n)) atTop (𝓝 (condexpL1 hm μ f)) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -1122,7 +1122,7 @@ theorem condexpL2_ae_eq_zero_of_ae_eq_zero (hs : measurable_set[m] s) (hμs : μ
     dsimp only at hx
     rw [Pi.zero_apply] at hx⊢
     · rwa [ENNReal.coe_eq_zero, nnnorm_eq_zero] at hx
-    · refine' Measurable.coe_nNReal_eNNReal (Measurable.nnnorm _)
+    · refine' Measurable.coe_nnreal_ennreal (Measurable.nnnorm _)
       rw [Lp_meas_coe]
       exact (Lp.strongly_measurable _).Measurable
   refine' le_antisymm _ (zero_le _)

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

@@ -1895,7 +1895,7 @@ theorem set_integral_condexpL1Clm (f : α →₁[μ] F') (hs : measurable_set[m]
   have hS_meas0 : ∀ i, MeasurableSet (S i) := fun i => hm _ (hS_meas i)
   have hs_eq : s = ⋃ i, S i ∩ s := by
     simp_rw [Set.inter_comm]
-    rw [← Set.inter_unionᵢ, Union_spanning_sets (μ.trim hm), Set.inter_univ]
+    rw [← Set.inter_iUnion, Union_spanning_sets (μ.trim hm), Set.inter_univ]
   have hS_finite : ∀ i, μ (S i ∩ s) < ∞ :=
     by
     refine' fun i => (measure_mono (Set.inter_subset_left _ _)).trans_lt _

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

@@ -1010,10 +1010,10 @@ theorem integrableOn_condexpL2_of_measure_ne_top (hm : m ≤ m0) (hμs : μ s 
   integrableOn_lp_of_measure_ne_top (condexpL2 𝕜 hm f : α →₂[μ] E) fact_one_le_two_ennreal.elim hμs
 #align measure_theory.integrable_on_condexp_L2_of_measure_ne_top MeasureTheory.integrableOn_condexpL2_of_measure_ne_top
 
-theorem integrable_condexpL2_of_isFiniteMeasure (hm : m ≤ m0) [IsFiniteMeasure μ] {f : α →₂[μ] E} :
+theorem integrable_condexpL2_of_finiteMeasure (hm : m ≤ m0) [FiniteMeasure μ] {f : α →₂[μ] E} :
     Integrable (condexpL2 𝕜 hm f) μ :=
   integrableOn_univ.mp <| integrableOn_condexpL2_of_measure_ne_top hm (measure_ne_top _ _) f
-#align measure_theory.integrable_condexp_L2_of_is_finite_measure MeasureTheory.integrable_condexpL2_of_isFiniteMeasure
+#align measure_theory.integrable_condexp_L2_of_is_finite_measure MeasureTheory.integrable_condexpL2_of_finiteMeasure
 
 theorem norm_condexpL2_le_one (hm : m ≤ m0) : ‖@condexpL2 α E 𝕜 _ _ _ _ _ _ μ hm‖ ≤ 1 :=
   haveI : Fact (m ≤ m0) := ⟨hm⟩
@@ -2138,8 +2138,7 @@ theorem condexp_of_stronglyMeasurable (hm : m ≤ m0) [hμm : SigmaFinite (μ.tr
   infer_instance
 #align measure_theory.condexp_of_strongly_measurable MeasureTheory.condexp_of_stronglyMeasurable
 
-theorem condexp_const (hm : m ≤ m0) (c : F') [IsFiniteMeasure μ] :
-    μ[fun x : α => c|m] = fun _ => c :=
+theorem condexp_const (hm : m ≤ m0) (c : F') [FiniteMeasure μ] : μ[fun x : α => c|m] = fun _ => c :=
   condexp_of_stronglyMeasurable hm (@stronglyMeasurable_const _ _ m _ _) (integrable_const c)
 #align measure_theory.condexp_const MeasureTheory.condexp_const
 
@@ -2315,7 +2314,7 @@ theorem condexp_bot_ae_eq (f : α → F') :
     simp only [h, ae_zero]
 #align measure_theory.condexp_bot_ae_eq MeasureTheory.condexp_bot_ae_eq
 
-theorem condexp_bot [IsProbabilityMeasure μ] (f : α → F') : μ[f|⊥] = fun _ => ∫ x, f x ∂μ :=
+theorem condexp_bot [ProbabilityMeasure μ] (f : α → F') : μ[f|⊥] = fun _ => ∫ x, f x ∂μ :=
   by
   refine' (condexp_bot' f).trans _
   rw [measure_univ, ENNReal.one_toReal, inv_one, one_smul]

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

@@ -134,15 +134,15 @@ theorem sub [AddGroup β] [TopologicalAddGroup β] {f g : α → β} (hfm : AeSt
   rw [hx1, hx2]
 #align measure_theory.ae_strongly_measurable'.sub MeasureTheory.AeStronglyMeasurable'.sub
 
-theorem constSmul [SMul 𝕜 β] [ContinuousConstSMul 𝕜 β] (c : 𝕜) (hf : AeStronglyMeasurable' m f μ) :
+theorem const_smul [SMul 𝕜 β] [ContinuousConstSMul 𝕜 β] (c : 𝕜) (hf : AeStronglyMeasurable' m f μ) :
     AeStronglyMeasurable' m (c • f) μ :=
   by
   rcases hf with ⟨f', h_f'_meas, hff'⟩
   refine' ⟨c • f', h_f'_meas.const_smul c, _⟩
   exact eventually_eq.fun_comp hff' fun x => c • x
-#align measure_theory.ae_strongly_measurable'.const_smul MeasureTheory.AeStronglyMeasurable'.constSmul
+#align measure_theory.ae_strongly_measurable'.const_smul MeasureTheory.AeStronglyMeasurable'.const_smul
 
-theorem constInner {𝕜 β} [IsROrC 𝕜] [NormedAddCommGroup β] [InnerProductSpace 𝕜 β] {f : α → β}
+theorem const_inner {𝕜 β} [IsROrC 𝕜] [NormedAddCommGroup β] [InnerProductSpace 𝕜 β] {f : α → β}
     (hfm : AeStronglyMeasurable' m f μ) (c : β) :
     AeStronglyMeasurable' m (fun x => (inner c (f x) : 𝕜)) μ :=
   by
@@ -152,7 +152,7 @@ theorem constInner {𝕜 β} [IsROrC 𝕜] [NormedAddCommGroup β] [InnerProduct
       hf_ae.mono fun x hx => _⟩
   dsimp only
   rw [hx]
-#align measure_theory.ae_strongly_measurable'.const_inner MeasureTheory.AeStronglyMeasurable'.constInner
+#align measure_theory.ae_strongly_measurable'.const_inner MeasureTheory.AeStronglyMeasurable'.const_inner
 
 /-- An `m`-strongly measurable function almost everywhere equal to `f`. -/
 def mk (f : α → β) (hfm : AeStronglyMeasurable' m f μ) : α → β :=
@@ -168,22 +168,22 @@ theorem ae_eq_mk {f : α → β} (hfm : AeStronglyMeasurable' m f μ) : f =ᵐ[
   hfm.choose_spec.2
 #align measure_theory.ae_strongly_measurable'.ae_eq_mk MeasureTheory.AeStronglyMeasurable'.ae_eq_mk
 
-theorem continuousComp {γ} [TopologicalSpace γ] {f : α → β} {g : β → γ} (hg : Continuous g)
+theorem continuous_comp {γ} [TopologicalSpace γ] {f : α → β} {g : β → γ} (hg : Continuous g)
     (hf : AeStronglyMeasurable' m f μ) : AeStronglyMeasurable' m (g ∘ f) μ :=
   ⟨fun x => g (hf.mk _ x),
     @Continuous.comp_stronglyMeasurable _ _ _ m _ _ _ _ hg hf.stronglyMeasurable_mk,
     hf.ae_eq_mk.mono fun x hx => by rw [Function.comp_apply, hx]⟩
-#align measure_theory.ae_strongly_measurable'.continuous_comp MeasureTheory.AeStronglyMeasurable'.continuousComp
+#align measure_theory.ae_strongly_measurable'.continuous_comp MeasureTheory.AeStronglyMeasurable'.continuous_comp
 
 end AeStronglyMeasurable'
 
-theorem aeStronglyMeasurable'OfAeStronglyMeasurable'Trim {α β} {m m0 m0' : MeasurableSpace α}
+theorem aeStronglyMeasurable'_of_aeStronglyMeasurable'_trim {α β} {m m0 m0' : MeasurableSpace α}
     [TopologicalSpace β] (hm0 : m0 ≤ m0') {μ : Measure α} {f : α → β}
     (hf : AeStronglyMeasurable' m f (μ.trim hm0)) : AeStronglyMeasurable' m f μ :=
   by
   obtain ⟨g, hg_meas, hfg⟩ := hf
   exact ⟨g, hg_meas, ae_eq_of_ae_eq_trim hfg⟩
-#align measure_theory.ae_strongly_measurable'_of_ae_strongly_measurable'_trim MeasureTheory.aeStronglyMeasurable'OfAeStronglyMeasurable'Trim
+#align measure_theory.ae_strongly_measurable'_of_ae_strongly_measurable'_trim MeasureTheory.aeStronglyMeasurable'_of_aeStronglyMeasurable'_trim
 
 theorem StronglyMeasurable.aeStronglyMeasurable' {α β} {m m0 : MeasurableSpace α}
     [TopologicalSpace β] {μ : Measure α} {f : α → β} (hf : strongly_measurable[m] f) :
@@ -204,7 +204,7 @@ theorem ae_eq_trim_iff_of_aeStronglyMeasurable' {α β} [TopologicalSpace β] [M
 another σ-algebra `m₂` (hypothesis `hs`), the set `s` is `m` measurable and a function `f` almost
 everywhere supported on `s` is `m`-ae-strongly-measurable, then `f` is also
 `m₂`-ae-strongly-measurable. -/
-theorem AeStronglyMeasurable'.aeStronglyMeasurable'OfMeasurableSpaceLeOn {α E}
+theorem AeStronglyMeasurable'.aeStronglyMeasurable'_of_measurableSpace_le_on {α E}
     {m m₂ m0 : MeasurableSpace α} {μ : Measure α} [TopologicalSpace E] [Zero E] (hm : m ≤ m0)
     {s : Set α} {f : α → E} (hs_m : measurable_set[m] s)
     (hs : ∀ t, measurable_set[m] (s ∩ t) → measurable_set[m₂] (s ∩ t))
@@ -226,7 +226,7 @@ theorem AeStronglyMeasurable'.aeStronglyMeasurable'OfMeasurableSpaceLeOn {α E}
   exact
     hf_ind.strongly_measurable_of_measurable_space_le_on hs_m hs fun x hxs =>
       Set.indicator_of_not_mem hxs _
-#align measure_theory.ae_strongly_measurable'.ae_strongly_measurable'_of_measurable_space_le_on MeasureTheory.AeStronglyMeasurable'.aeStronglyMeasurable'OfMeasurableSpaceLeOn
+#align measure_theory.ae_strongly_measurable'.ae_strongly_measurable'_of_measurable_space_le_on MeasureTheory.AeStronglyMeasurable'.aeStronglyMeasurable'_of_measurableSpace_le_on
 
 variable {α β γ E E' F F' G G' H 𝕜 : Type _} {p : ℝ≥0∞} [IsROrC 𝕜]
   -- 𝕜 for ℝ or ℂ
@@ -339,7 +339,7 @@ variable {ι : Type _} {m m0 : MeasurableSpace α} {μ : Measure α}
 
 /-- If `f` belongs to `Lp_meas_subgroup F m p μ`, then the measurable function it is almost
 everywhere equal to (given by `ae_measurable.mk`) belongs to `ℒp` for the measure `μ.trim hm`. -/
-theorem memℒpTrimOfMemLpMeasSubgroup (hm : m ≤ m0) (f : lp F p μ)
+theorem memℒp_trim_of_mem_lpMeasSubgroup (hm : m ≤ m0) (f : lp F p μ)
     (hf_meas : f ∈ lpMeasSubgroup F m p μ) :
     Memℒp (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp hf_meas).some p (μ.trim hm) :=
   by
@@ -355,12 +355,12 @@ theorem memℒpTrimOfMemLpMeasSubgroup (hm : m ≤ m0) (f : lp F p μ)
     exact snorm_congr_ae hfg.symm
   rw [h_snorm_fg]
   exact Lp.snorm_lt_top f
-#align measure_theory.mem_ℒp_trim_of_mem_Lp_meas_subgroup MeasureTheory.memℒpTrimOfMemLpMeasSubgroup
+#align measure_theory.mem_ℒp_trim_of_mem_Lp_meas_subgroup MeasureTheory.memℒp_trim_of_mem_lpMeasSubgroup
 
 /-- If `f` belongs to `Lp` for the measure `μ.trim hm`, then it belongs to the subgroup
 `Lp_meas_subgroup F m p μ`. -/
 theorem mem_lpMeasSubgroup_toLp_of_trim (hm : m ≤ m0) (f : lp F p (μ.trim hm)) :
-    (memℒpOfMemℒpTrim hm (lp.memℒp f)).toLp f ∈ lpMeasSubgroup F m p μ :=
+    (memℒp_of_memℒp_trim hm (lp.memℒp f)).toLp f ∈ lpMeasSubgroup F m p μ :=
   by
   let hf_mem_ℒp := mem_ℒp_of_mem_ℒp_trim hm (Lp.mem_ℒp f)
   rw [mem_Lp_meas_subgroup_iff_ae_strongly_measurable']
@@ -374,7 +374,7 @@ variable (F p μ)
 /-- Map from `Lp_meas_subgroup` to `Lp F p (μ.trim hm)`. -/
 def lpMeasSubgroupToLpTrim (hm : m ≤ m0) (f : lpMeasSubgroup F m p μ) : lp F p (μ.trim hm) :=
   Memℒp.toLp (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp f.Mem).some
-    (memℒpTrimOfMemLpMeasSubgroup hm f f.Mem)
+    (memℒp_trim_of_mem_lpMeasSubgroup hm f f.Mem)
 #align measure_theory.Lp_meas_subgroup_to_Lp_trim MeasureTheory.lpMeasSubgroupToLpTrim
 
 variable (𝕜)
@@ -382,7 +382,7 @@ variable (𝕜)
 /-- Map from `Lp_meas` to `Lp F p (μ.trim hm)`. -/
 def lpMeasToLpTrim (hm : m ≤ m0) (f : lpMeas F 𝕜 m p μ) : lp F p (μ.trim hm) :=
   Memℒp.toLp (mem_lpMeas_iff_aeStronglyMeasurable'.mp f.Mem).some
-    (memℒpTrimOfMemLpMeasSubgroup hm f f.Mem)
+    (memℒp_trim_of_mem_lpMeasSubgroup hm f f.Mem)
 #align measure_theory.Lp_meas_to_Lp_trim MeasureTheory.lpMeasToLpTrim
 
 variable {𝕜}
@@ -390,21 +390,21 @@ variable {𝕜}
 /-- Map from `Lp F p (μ.trim hm)` to `Lp_meas_subgroup`, inverse of
 `Lp_meas_subgroup_to_Lp_trim`. -/
 def lpTrimToLpMeasSubgroup (hm : m ≤ m0) (f : lp F p (μ.trim hm)) : lpMeasSubgroup F m p μ :=
-  ⟨(memℒpOfMemℒpTrim hm (lp.memℒp f)).toLp f, mem_lpMeasSubgroup_toLp_of_trim hm f⟩
+  ⟨(memℒp_of_memℒp_trim hm (lp.memℒp f)).toLp f, mem_lpMeasSubgroup_toLp_of_trim hm f⟩
 #align measure_theory.Lp_trim_to_Lp_meas_subgroup MeasureTheory.lpTrimToLpMeasSubgroup
 
 variable (𝕜)
 
 /-- Map from `Lp F p (μ.trim hm)` to `Lp_meas`, inverse of `Lp_meas_to_Lp_trim`. -/
 def lpTrimToLpMeas (hm : m ≤ m0) (f : lp F p (μ.trim hm)) : lpMeas F 𝕜 m p μ :=
-  ⟨(memℒpOfMemℒpTrim hm (lp.memℒp f)).toLp f, mem_lpMeasSubgroup_toLp_of_trim hm f⟩
+  ⟨(memℒp_of_memℒp_trim hm (lp.memℒp f)).toLp f, mem_lpMeasSubgroup_toLp_of_trim hm f⟩
 #align measure_theory.Lp_trim_to_Lp_meas MeasureTheory.lpTrimToLpMeas
 
 variable {F 𝕜 p μ}
 
 theorem lpMeasSubgroupToLpTrim_ae_eq (hm : m ≤ m0) (f : lpMeasSubgroup F m p μ) :
     lpMeasSubgroupToLpTrim F p μ hm f =ᵐ[μ] f :=
-  (ae_eq_of_ae_eq_trim (Memℒp.coeFn_toLp (memℒpTrimOfMemLpMeasSubgroup hm (↑f) f.Mem))).trans
+  (ae_eq_of_ae_eq_trim (Memℒp.coeFn_toLp (memℒp_trim_of_mem_lpMeasSubgroup hm (↑f) f.Mem))).trans
     (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp f.Mem).choose_spec.2.symm
 #align measure_theory.Lp_meas_subgroup_to_Lp_trim_ae_eq MeasureTheory.lpMeasSubgroupToLpTrim_ae_eq
 
@@ -415,7 +415,7 @@ theorem lpTrimToLpMeasSubgroup_ae_eq (hm : m ≤ m0) (f : lp F p (μ.trim hm)) :
 
 theorem lpMeasToLpTrim_ae_eq (hm : m ≤ m0) (f : lpMeas F 𝕜 m p μ) :
     lpMeasToLpTrim F 𝕜 p μ hm f =ᵐ[μ] f :=
-  (ae_eq_of_ae_eq_trim (Memℒp.coeFn_toLp (memℒpTrimOfMemLpMeasSubgroup hm (↑f) f.Mem))).trans
+  (ae_eq_of_ae_eq_trim (Memℒp.coeFn_toLp (memℒp_trim_of_mem_lpMeasSubgroup hm (↑f) f.Mem))).trans
     (mem_lpMeasSubgroup_iff_aeStronglyMeasurable'.mp f.Mem).choose_spec.2.symm
 #align measure_theory.Lp_meas_to_Lp_trim_ae_eq MeasureTheory.lpMeasToLpTrim_ae_eq
 
@@ -611,7 +611,7 @@ theorem lpMeasToLpTrimLie_symm_indicator [one_le_p : Fact (1 ≤ p)] [NormedSpac
 theorem lpMeasToLpTrimLie_symm_toLp [one_le_p : Fact (1 ≤ p)] [NormedSpace ℝ F] (hm : m ≤ m0)
     (f : α → F) (hf : Memℒp f p (μ.trim hm)) :
     ((lpMeasToLpTrimLie F ℝ p μ hm).symm (hf.toLp f) : lp F p μ) =
-      (memℒpOfMemℒpTrim hm hf).toLp f :=
+      (memℒp_of_memℒp_trim hm hf).toLp f :=
   by
   ext1
   rw [← Lp_meas_coe]
@@ -629,7 +629,7 @@ variable {m m0 : MeasurableSpace α} {μ : Measure α} [Fact (1 ≤ p)] [NormedS
 
 /-- Auxiliary lemma for `Lp.induction_strongly_measurable`. -/
 @[elab_as_elim]
-theorem lp.inductionStronglyMeasurableAux (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : lp F p μ → Prop)
+theorem lp.induction_strongly_measurable_aux (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : lp F p μ → Prop)
     (h_ind :
       ∀ (c : F) {s : Set α} (hs : measurable_set[m] s) (hμs : μ s < ∞),
         P (lp.simpleFunc.indicatorConst p (hm s hs) hμs.Ne c))
@@ -676,7 +676,7 @@ theorem lp.inductionStronglyMeasurableAux (hm : m ≤ m0) (hp_ne_top : p ≠ ∞
         h_disj hfP hgP
   · change IsClosed ((Lp_meas_to_Lp_trim_lie F ℝ p μ hm).symm ⁻¹' { g : Lp_meas F ℝ m p μ | P ↑g })
     exact IsClosed.preimage (LinearIsometryEquiv.continuous _) h_closed
-#align measure_theory.Lp.induction_strongly_measurable_aux MeasureTheory.lp.inductionStronglyMeasurableAux
+#align measure_theory.Lp.induction_strongly_measurable_aux MeasureTheory.lp.induction_strongly_measurable_aux
 
 /-- To prove something for an `Lp` function a.e. strongly measurable with respect to a
 sub-σ-algebra `m` in a normed space, it suffices to show that
@@ -686,7 +686,7 @@ sub-σ-algebra `m` in a normed space, it suffices to show that
   closed.
 -/
 @[elab_as_elim]
-theorem lp.inductionStronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : lp F p μ → Prop)
+theorem lp.induction_stronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : lp F p μ → Prop)
     (h_ind :
       ∀ (c : F) {s : Set α} (hs : measurable_set[m] s) (hμs : μ s < ∞),
         P (lp.simpleFunc.indicatorConst p (hm s hs) hμs.Ne c))
@@ -754,7 +754,7 @@ theorem lp.inductionStronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (
   rw [← mem_ℒp.to_Lp_congr hf'_Lp hf hff'.symm] at hPf⊢
   rw [← mem_ℒp.to_Lp_congr hg'_Lp hg hgg'.symm] at hPg⊢
   exact h_add hf'_Lp hg'_Lp hf'_meas hg'_meas h_disj hPf hPg
-#align measure_theory.Lp.induction_strongly_measurable MeasureTheory.lp.inductionStronglyMeasurable
+#align measure_theory.Lp.induction_strongly_measurable MeasureTheory.lp.induction_stronglyMeasurable
 
 /-- To prove something for an arbitrary `mem_ℒp` function a.e. strongly measurable with respect
 to a sub-σ-algebra `m` in a normed space, it suffices to show that
@@ -765,7 +765,7 @@ to a sub-σ-algebra `m` in a normed space, it suffices to show that
 * the property is closed under the almost-everywhere equal relation.
 -/
 @[elab_as_elim]
-theorem Memℒp.inductionStronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : (α → F) → Prop)
+theorem Memℒp.induction_stronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ ∞) (P : (α → F) → Prop)
     (h_ind : ∀ (c : F) ⦃s⦄, measurable_set[m] s → μ s < ∞ → P (s.indicator fun _ => c))
     (h_add :
       ∀ ⦃f g : α → F⦄,
@@ -793,7 +793,7 @@ theorem Memℒp.inductionStronglyMeasurable (hm : m ≤ m0) (hp_ne_top : p ≠ 
     specialize h_add h_disj hf_mem hg_mem hfm hgm hfP' hgP'
     refine' h_ae _ (hf_mem.add hg_mem) h_add
     exact (hf_mem.coe_fn_to_Lp.symm.add hg_mem.coe_fn_to_Lp.symm).trans (Lp.coe_fn_add _ _).symm
-#align measure_theory.mem_ℒp.induction_strongly_measurable MeasureTheory.Memℒp.inductionStronglyMeasurable
+#align measure_theory.mem_ℒp.induction_strongly_measurable MeasureTheory.Memℒp.induction_stronglyMeasurable
 
 end Induction
 
@@ -1000,20 +1000,20 @@ def condexpL2 (hm : m ≤ m0) : (α →₂[μ] E) →L[𝕜] lpMeas E 𝕜 m 2 
 
 variable {𝕜}
 
-theorem aeStronglyMeasurable'CondexpL2 (hm : m ≤ m0) (f : α →₂[μ] E) :
+theorem aeStronglyMeasurable'_condexpL2 (hm : m ≤ m0) (f : α →₂[μ] E) :
     AeStronglyMeasurable' m (condexpL2 𝕜 hm f) μ :=
   lpMeas.aeStronglyMeasurable' _
-#align measure_theory.ae_strongly_measurable'_condexp_L2 MeasureTheory.aeStronglyMeasurable'CondexpL2
+#align measure_theory.ae_strongly_measurable'_condexp_L2 MeasureTheory.aeStronglyMeasurable'_condexpL2
 
-theorem integrableOnCondexpL2OfMeasureNeTop (hm : m ≤ m0) (hμs : μ s ≠ ∞) (f : α →₂[μ] E) :
+theorem integrableOn_condexpL2_of_measure_ne_top (hm : m ≤ m0) (hμs : μ s ≠ ∞) (f : α →₂[μ] E) :
     IntegrableOn (condexpL2 𝕜 hm f) s μ :=
-  integrableOnLpOfMeasureNeTop (condexpL2 𝕜 hm f : α →₂[μ] E) fact_one_le_two_ennreal.elim hμs
-#align measure_theory.integrable_on_condexp_L2_of_measure_ne_top MeasureTheory.integrableOnCondexpL2OfMeasureNeTop
+  integrableOn_lp_of_measure_ne_top (condexpL2 𝕜 hm f : α →₂[μ] E) fact_one_le_two_ennreal.elim hμs
+#align measure_theory.integrable_on_condexp_L2_of_measure_ne_top MeasureTheory.integrableOn_condexpL2_of_measure_ne_top
 
-theorem integrableCondexpL2OfIsFiniteMeasure (hm : m ≤ m0) [IsFiniteMeasure μ] {f : α →₂[μ] E} :
+theorem integrable_condexpL2_of_isFiniteMeasure (hm : m ≤ m0) [IsFiniteMeasure μ] {f : α →₂[μ] E} :
     Integrable (condexpL2 𝕜 hm f) μ :=
-  integrableOn_univ.mp <| integrableOnCondexpL2OfMeasureNeTop hm (measure_ne_top _ _) f
-#align measure_theory.integrable_condexp_L2_of_is_finite_measure MeasureTheory.integrableCondexpL2OfIsFiniteMeasure
+  integrableOn_univ.mp <| integrableOn_condexpL2_of_measure_ne_top hm (measure_ne_top _ _) f
+#align measure_theory.integrable_condexp_L2_of_is_finite_measure MeasureTheory.integrable_condexpL2_of_isFiniteMeasure
 
 theorem norm_condexpL2_le_one (hm : m ≤ m0) : ‖@condexpL2 α E 𝕜 _ _ _ _ _ _ μ hm‖ ≤ 1 :=
   haveI : Fact (m ≤ m0) := ⟨hm⟩
@@ -1159,8 +1159,8 @@ end Real
 /-- `condexp_L2` commutes with taking inner products with constants. See the lemma
 `condexp_L2_comp_continuous_linear_map` for a more general result about commuting with continuous
 linear maps. -/
-theorem condexpL2_constInner (hm : m ≤ m0) (f : lp E 2 μ) (c : E) :
-    condexpL2 𝕜 hm (((lp.memℒp f).constInner c).toLp fun a => ⟪c, f a⟫) =ᵐ[μ] fun a =>
+theorem condexpL2_const_inner (hm : m ≤ m0) (f : lp E 2 μ) (c : E) :
+    condexpL2 𝕜 hm (((lp.memℒp f).const_inner c).toLp fun a => ⟪c, f a⟫) =ᵐ[μ] fun a =>
       ⟪c, condexpL2 𝕜 hm f a⟫ :=
   by
   rw [Lp_meas_coe]
@@ -1176,7 +1176,7 @@ theorem condexpL2_constInner (hm : m ≤ m0) (f : lp E 2 μ) (c : E) :
       (fun s hs hμs => integrable_on_condexp_L2_of_measure_ne_top hm hμs.Ne _) _ _ _ _
   · intro s hs hμs
     rw [integrable_on, integrable_congr (ae_restrict_of_ae h_eq)]
-    exact (integrable_on_condexp_L2_of_measure_ne_top hm hμs.ne _).constInner _
+    exact (integrable_on_condexp_L2_of_measure_ne_top hm hμs.ne _).const_inner _
   · intro s hs hμs
     rw [← Lp_meas_coe, integral_condexp_L2_eq_of_fin_meas_real _ hs hμs.ne,
       integral_congr_ae (ae_restrict_of_ae h_eq), Lp_meas_coe, ←
@@ -1184,12 +1184,12 @@ theorem condexpL2_constInner (hm : m ≤ m0) (f : lp E 2 μ) (c : E) :
       ← inner_condexp_L2_left_eq_right, condexp_L2_indicator_of_measurable,
       L2.inner_indicator_const_Lp_eq_set_integral_inner 𝕜 f (hm s hs) c hμs.ne,
       set_integral_congr_ae (hm s hs)
-        ((mem_ℒp.coe_fn_to_Lp ((Lp.mem_ℒp f).constInner c)).mono fun x hx hxs => hx)]
+        ((mem_ℒp.coe_fn_to_Lp ((Lp.mem_ℒp f).const_inner c)).mono fun x hx hxs => hx)]
   · rw [← Lp_meas_coe]
     exact Lp_meas.ae_strongly_measurable' _
   · refine' ae_strongly_measurable'.congr _ h_eq.symm
-    exact (Lp_meas.ae_strongly_measurable' _).constInner _
-#align measure_theory.condexp_L2_const_inner MeasureTheory.condexpL2_constInner
+    exact (Lp_meas.ae_strongly_measurable' _).const_inner _
+#align measure_theory.condexp_L2_const_inner MeasureTheory.condexpL2_const_inner
 
 /-- `condexp_L2` verifies the equality of integrals defining the conditional expectation. -/
 theorem integral_condexpL2_eq (hm : m ≤ m0) (f : lp E' 2 μ) (hs : measurable_set[m] s)
@@ -1204,9 +1204,9 @@ theorem integral_condexpL2_eq (hm : m ≤ m0) (f : lp E' 2 μ) (hs : measurable_
   intro c
   simp_rw [Pi.sub_apply, inner_sub_right]
   rw [integral_sub
-      ((integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs).constInner c)
-      ((integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs).constInner c)]
-  have h_ae_eq_f := mem_ℒp.coe_fn_to_Lp ((Lp.mem_ℒp f).constInner c)
+      ((integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs).const_inner c)
+      ((integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs).const_inner c)]
+  have h_ae_eq_f := mem_ℒp.coe_fn_to_Lp ((Lp.mem_ℒp f).const_inner c)
   rw [← Lp_meas_coe, sub_eq_zero, ←
     set_integral_congr_ae (hm s hs) ((condexp_L2_const_inner hm f c).mono fun x hx _ => hx), ←
     set_integral_congr_ae (hm s hs) (h_ae_eq_f.mono fun x hx _ => hx)]
@@ -1312,8 +1312,9 @@ theorem lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : Measurable
 
 /-- If the measure `μ.trim hm` is sigma-finite, then the conditional expectation of a measurable set
 with finite measure is integrable. -/
-theorem integrableCondexpL2Indicator (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hs : MeasurableSet s)
-    (hμs : μ s ≠ ∞) (x : E') : Integrable (condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x)) μ :=
+theorem integrable_condexpL2_indicator (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
+    (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : E') :
+    Integrable (condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x)) μ :=
   by
   refine'
     integrable_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) (ENNReal.mul_lt_top hμs ENNReal.coe_ne_top) _
@@ -1323,7 +1324,7 @@ theorem integrableCondexpL2Indicator (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
   · refine' fun t ht hμt =>
       (set_lintegral_nnnorm_condexp_L2_indicator_le hm hs hμs x ht hμt).trans _
     exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
-#align measure_theory.integrable_condexp_L2_indicator MeasureTheory.integrableCondexpL2Indicator
+#align measure_theory.integrable_condexp_L2_indicator MeasureTheory.integrable_condexpL2_indicator
 
 end CondexpL2Indicator
 
@@ -1336,7 +1337,7 @@ def condexpIndSmul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
   (toSpanSingleton ℝ x).compLpL 2 μ (condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)))
 #align measure_theory.condexp_ind_smul MeasureTheory.condexpIndSmul
 
-theorem aeStronglyMeasurable'CondexpIndSmul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
+theorem aeStronglyMeasurable'_condexpIndSmul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
     (x : G) : AeStronglyMeasurable' m (condexpIndSmul hm hs hμs x) μ :=
   by
   have h : ae_strongly_measurable' m (condexp_L2 ℝ hm (indicator_const_Lp 2 hs hμs (1 : ℝ))) μ :=
@@ -1350,7 +1351,7 @@ theorem aeStronglyMeasurable'CondexpIndSmul (hm : m ≤ m0) (hs : MeasurableSet
     refine' eventually_eq.trans _ (coe_fn_comp_LpL _ _).symm
     rw [Lp_meas_coe]
   exact ae_strongly_measurable'.continuous_comp (to_span_singleton ℝ x).Continuous h
-#align measure_theory.ae_strongly_measurable'_condexp_ind_smul MeasureTheory.aeStronglyMeasurable'CondexpIndSmul
+#align measure_theory.ae_strongly_measurable'_condexp_ind_smul MeasureTheory.aeStronglyMeasurable'_condexpIndSmul
 
 theorem condexpIndSmul_add (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x y : G) :
     condexpIndSmul hm hs hμs (x + y) = condexpIndSmul hm hs hμs x + condexpIndSmul hm hs hμs y :=
@@ -1409,7 +1410,7 @@ theorem lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableSet s
 
 /-- If the measure `μ.trim hm` is sigma-finite, then the conditional expectation of a measurable set
 with finite measure is integrable. -/
-theorem integrableCondexpIndSmul (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hs : MeasurableSet s)
+theorem integrable_condexpIndSmul (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hs : MeasurableSet s)
     (hμs : μ s ≠ ∞) (x : G) : Integrable (condexpIndSmul hm hs hμs x) μ :=
   by
   refine'
@@ -1418,7 +1419,7 @@ theorem integrableCondexpIndSmul (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hs
   · exact Lp.ae_strongly_measurable _
   · refine' fun t ht hμt => (set_lintegral_nnnorm_condexp_ind_smul_le hm hs hμs x ht hμt).trans _
     exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
-#align measure_theory.integrable_condexp_ind_smul MeasureTheory.integrableCondexpIndSmul
+#align measure_theory.integrable_condexp_ind_smul MeasureTheory.integrable_condexpIndSmul
 
 theorem condexpIndSmul_empty {x : G} :
     condexpIndSmul hm MeasurableSet.empty ((@measure_empty _ _ μ).le.trans_lt ENNReal.coe_lt_top).Ne
@@ -1513,13 +1514,13 @@ section CondexpIndL1Fin
 as a function in L1. -/
 def condexpIndL1Fin (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
     (x : G) : α →₁[μ] G :=
-  (integrableCondexpIndSmul hm hs hμs x).toL1 _
+  (integrable_condexpIndSmul hm hs hμs x).toL1 _
 #align measure_theory.condexp_ind_L1_fin MeasureTheory.condexpIndL1Fin
 
 theorem condexpIndL1Fin_ae_eq_condexpIndSmul (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :
     condexpIndL1Fin hm hs hμs x =ᵐ[μ] condexpIndSmul hm hs hμs x :=
-  (integrableCondexpIndSmul hm hs hμs x).coeFn_toL1
+  (integrable_condexpIndSmul hm hs hμs x).coeFn_toL1
 #align measure_theory.condexp_ind_L1_fin_ae_eq_condexp_ind_smul MeasureTheory.condexpIndL1Fin_ae_eq_condexpIndSmul
 
 variable {hm : m ≤ m0} [SigmaFinite (μ.trim hm)]
@@ -1736,11 +1737,11 @@ theorem condexpInd_ae_eq_condexpIndSmul (hm : m ≤ m0) [SigmaFinite (μ.trim hm
 
 variable {hm : m ≤ m0} [SigmaFinite (μ.trim hm)]
 
-theorem aeStronglyMeasurable'CondexpInd (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :
+theorem aeStronglyMeasurable'_condexpInd (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :
     AeStronglyMeasurable' m (condexpInd hm μ s x) μ :=
-  AeStronglyMeasurable'.congr (aeStronglyMeasurable'CondexpIndSmul hm hs hμs x)
+  AeStronglyMeasurable'.congr (aeStronglyMeasurable'_condexpIndSmul hm hs hμs x)
     (condexpInd_ae_eq_condexpIndSmul hm hs hμs x).symm
-#align measure_theory.ae_strongly_measurable'_condexp_ind MeasureTheory.aeStronglyMeasurable'CondexpInd
+#align measure_theory.ae_strongly_measurable'_condexp_ind MeasureTheory.aeStronglyMeasurable'_condexpInd
 
 @[simp]
 theorem condexpInd_empty : condexpInd hm μ ∅ = (0 : G →L[ℝ] α →₁[μ] G) :=
@@ -1784,10 +1785,11 @@ theorem condexpInd_disjoint_union (hs : MeasurableSet s) (ht : MeasurableSet t)
 
 variable (G)
 
-theorem dominatedFinMeasAdditiveCondexpInd (hm : m ≤ m0) (μ : Measure α) [SigmaFinite (μ.trim hm)] :
+theorem dominatedFinMeasAdditive_condexpInd (hm : m ≤ m0) (μ : Measure α)
+    [SigmaFinite (μ.trim hm)] :
     DominatedFinMeasAdditive μ (condexpInd hm μ : Set α → G →L[ℝ] α →₁[μ] G) 1 :=
   ⟨fun s t => condexpInd_disjoint_union, fun s _ _ => norm_condexpInd_le.trans (one_mul _).symm.le⟩
-#align measure_theory.dominated_fin_meas_additive_condexp_ind MeasureTheory.dominatedFinMeasAdditiveCondexpInd
+#align measure_theory.dominated_fin_meas_additive_condexp_ind MeasureTheory.dominatedFinMeasAdditive_condexpInd
 
 variable {G}
 
@@ -1833,18 +1835,18 @@ variable {m m0 : MeasurableSpace α} {μ : Measure α} {hm : m ≤ m0} [SigmaFin
 /-- Conditional expectation of a function as a linear map from `α →₁[μ] F'` to itself. -/
 def condexpL1Clm (hm : m ≤ m0) (μ : Measure α) [SigmaFinite (μ.trim hm)] :
     (α →₁[μ] F') →L[ℝ] α →₁[μ] F' :=
-  L1.setToL1 (dominatedFinMeasAdditiveCondexpInd F' hm μ)
+  L1.setToL1 (dominatedFinMeasAdditive_condexpInd F' hm μ)
 #align measure_theory.condexp_L1_clm MeasureTheory.condexpL1Clm
 
 theorem condexpL1Clm_smul (c : 𝕜) (f : α →₁[μ] F') :
     condexpL1Clm hm μ (c • f) = c • condexpL1Clm hm μ f :=
-  L1.setToL1_smul (dominatedFinMeasAdditiveCondexpInd F' hm μ) (fun c s x => condexpInd_smul' c x) c
-    f
+  L1.setToL1_smul (dominatedFinMeasAdditive_condexpInd F' hm μ) (fun c s x => condexpInd_smul' c x)
+    c f
 #align measure_theory.condexp_L1_clm_smul MeasureTheory.condexpL1Clm_smul
 
 theorem condexpL1Clm_indicatorConstLp (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : F') :
     (condexpL1Clm hm μ) (indicatorConstLp 1 hs hμs x) = condexpInd hm μ s x :=
-  L1.setToL1_indicatorConstLp (dominatedFinMeasAdditiveCondexpInd F' hm μ) hs hμs x
+  L1.setToL1_indicatorConstLp (dominatedFinMeasAdditive_condexpInd F' hm μ) hs hμs x
 #align measure_theory.condexp_L1_clm_indicator_const_Lp MeasureTheory.condexpL1Clm_indicatorConstLp
 
 theorem condexpL1Clm_indicatorConst (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : F') :
@@ -1927,7 +1929,7 @@ theorem set_integral_condexpL1Clm (f : α →₁[μ] F') (hs : measurable_set[m]
   exact tendsto_nhds_unique h_left h_right
 #align measure_theory.set_integral_condexp_L1_clm MeasureTheory.set_integral_condexpL1Clm
 
-theorem aeStronglyMeasurable'CondexpL1Clm (f : α →₁[μ] F') :
+theorem aeStronglyMeasurable'_condexpL1Clm (f : α →₁[μ] F') :
     AeStronglyMeasurable' m (condexpL1Clm hm μ f) μ :=
   by
   refine'
@@ -1947,7 +1949,7 @@ theorem aeStronglyMeasurable'CondexpL1Clm (f : α →₁[μ] F') :
     rw [this]
     refine' IsClosed.preimage (condexp_L1_clm hm μ).Continuous _
     exact is_closed_ae_strongly_measurable' hm
-#align measure_theory.ae_strongly_measurable'_condexp_L1_clm MeasureTheory.aeStronglyMeasurable'CondexpL1Clm
+#align measure_theory.ae_strongly_measurable'_condexp_L1_clm MeasureTheory.aeStronglyMeasurable'_condexpL1Clm
 
 theorem condexpL1Clm_lpMeas (f : lpMeas F' ℝ m 1 μ) : condexpL1Clm hm μ (f : α →₁[μ] F') = ↑f :=
   by
@@ -1984,15 +1986,15 @@ theorem condexpL1Clm_of_aeStronglyMeasurable' (f : α →₁[μ] F') (hfm : AeSt
 /-- Conditional expectation of a function, in L1. Its value is 0 if the function is not
 integrable. The function-valued `condexp` should be used instead in most cases. -/
 def condexpL1 (hm : m ≤ m0) (μ : Measure α) [SigmaFinite (μ.trim hm)] (f : α → F') : α →₁[μ] F' :=
-  setToFun μ (condexpInd hm μ) (dominatedFinMeasAdditiveCondexpInd F' hm μ) f
+  setToFun μ (condexpInd hm μ) (dominatedFinMeasAdditive_condexpInd F' hm μ) f
 #align measure_theory.condexp_L1 MeasureTheory.condexpL1
 
 theorem condexpL1_undef (hf : ¬Integrable f μ) : condexpL1 hm μ f = 0 :=
-  setToFun_undef (dominatedFinMeasAdditiveCondexpInd F' hm μ) hf
+  setToFun_undef (dominatedFinMeasAdditive_condexpInd F' hm μ) hf
 #align measure_theory.condexp_L1_undef MeasureTheory.condexpL1_undef
 
 theorem condexpL1_eq (hf : Integrable f μ) : condexpL1 hm μ f = condexpL1Clm hm μ (hf.toL1 f) :=
-  setToFun_eq (dominatedFinMeasAdditiveCondexpInd F' hm μ) hf
+  setToFun_eq (dominatedFinMeasAdditive_condexpInd F' hm μ) hf
 #align measure_theory.condexp_L1_eq MeasureTheory.condexpL1_eq
 
 @[simp]
@@ -2005,7 +2007,7 @@ theorem condexpL1_measure_zero (hm : m ≤ m0) : condexpL1 hm (0 : Measure α) f
   setToFun_measure_zero _ rfl
 #align measure_theory.condexp_L1_measure_zero MeasureTheory.condexpL1_measure_zero
 
-theorem aeStronglyMeasurable'CondexpL1 {f : α → F'} :
+theorem aeStronglyMeasurable'_condexpL1 {f : α → F'} :
     AeStronglyMeasurable' m (condexpL1 hm μ f) μ :=
   by
   by_cases hf : integrable f μ
@@ -2014,16 +2016,16 @@ theorem aeStronglyMeasurable'CondexpL1 {f : α → F'} :
   · rw [condexp_L1_undef hf]
     refine' ae_strongly_measurable'.congr _ (coe_fn_zero _ _ _).symm
     exact strongly_measurable.ae_strongly_measurable' (@strongly_measurable_zero _ _ m _ _)
-#align measure_theory.ae_strongly_measurable'_condexp_L1 MeasureTheory.aeStronglyMeasurable'CondexpL1
+#align measure_theory.ae_strongly_measurable'_condexp_L1 MeasureTheory.aeStronglyMeasurable'_condexpL1
 
 theorem condexpL1_congr_ae (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (h : f =ᵐ[μ] g) :
     condexpL1 hm μ f = condexpL1 hm μ g :=
   setToFun_congr_ae _ h
 #align measure_theory.condexp_L1_congr_ae MeasureTheory.condexpL1_congr_ae
 
-theorem integrableCondexpL1 (f : α → F') : Integrable (condexpL1 hm μ f) μ :=
-  L1.integrableCoeFn _
-#align measure_theory.integrable_condexp_L1 MeasureTheory.integrableCondexpL1
+theorem integrable_condexpL1 (f : α → F') : Integrable (condexpL1 hm μ f) μ :=
+  L1.integrable_coeFn _
+#align measure_theory.integrable_condexp_L1 MeasureTheory.integrable_condexpL1
 
 /-- The integral of the conditional expectation `condexp_L1` over an `m`-measurable set is equal to
 the integral of `f` on that set. See also `set_integral_condexp`, the similar statement for
@@ -2095,7 +2097,7 @@ irreducible_def condexp (m : MeasurableSpace α) {m0 : MeasurableSpace α} (μ :
     if h : SigmaFinite (μ.trim hm) ∧ Integrable f μ then
       if strongly_measurable[m] f then f
       else
-        (@aeStronglyMeasurable'CondexpL1 _ _ _ _ _ m m0 μ hm h.1 _).mk
+        (@aeStronglyMeasurable'_condexpL1 _ _ _ _ _ m m0 μ hm h.1 _).mk
           (@condexpL1 _ _ _ _ _ _ _ hm μ h.1 f)
     else 0
   else 0
@@ -2118,7 +2120,8 @@ theorem condexp_of_not_sigmaFinite (hm : m ≤ m0) (hμm_not : ¬SigmaFinite (μ
 theorem condexp_of_sigmaFinite (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] :
     μ[f|m] =
       if Integrable f μ then
-        if strongly_measurable[m] f then f else aeStronglyMeasurable'CondexpL1.mk (condexpL1 hm μ f)
+        if strongly_measurable[m] f then f
+        else aeStronglyMeasurable'_condexpL1.mk (condexpL1 hm μ f)
       else 0 :=
   by
   rw [condexp, dif_pos hm]
@@ -2137,7 +2140,7 @@ theorem condexp_of_stronglyMeasurable (hm : m ≤ m0) [hμm : SigmaFinite (μ.tr
 
 theorem condexp_const (hm : m ≤ m0) (c : F') [IsFiniteMeasure μ] :
     μ[fun x : α => c|m] = fun _ => c :=
-  condexp_of_stronglyMeasurable hm (@stronglyMeasurable_const _ _ m _ _) (integrableConst c)
+  condexp_of_stronglyMeasurable hm (@stronglyMeasurable_const _ _ m _ _) (integrable_const c)
 #align measure_theory.condexp_const MeasureTheory.condexp_const
 
 theorem condexp_ae_eq_condexpL1 (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] (f : α → F') :
@@ -2226,7 +2229,7 @@ theorem condexp_of_aeStronglyMeasurable' (hm : m ≤ m0) [hμm : SigmaFinite (μ
       ((integrable_congr hf.ae_eq_mk).mp hfi)]
 #align measure_theory.condexp_of_ae_strongly_measurable' MeasureTheory.condexp_of_aeStronglyMeasurable'
 
-theorem integrableCondexp : Integrable (μ[f|m]) μ :=
+theorem integrable_condexp : Integrable (μ[f|m]) μ :=
   by
   by_cases hm : m ≤ m0
   swap;
@@ -2238,7 +2241,7 @@ theorem integrableCondexp : Integrable (μ[f|m]) μ :=
     exact integrable_zero _ _ _
   haveI : sigma_finite (μ.trim hm) := hμm
   exact (integrable_condexp_L1 f).congr (condexp_ae_eq_condexp_L1 hm f).symm
-#align measure_theory.integrable_condexp MeasureTheory.integrableCondexp
+#align measure_theory.integrable_condexp MeasureTheory.integrable_condexp
 
 /-- The integral of the conditional expectation `μ[f|hm]` over an `m`-measurable set is equal to
 the integral of `f` on that set. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/55d771df074d0dd020139ee1cd4b95521422df9f

@@ -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.basic
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -142,7 +142,7 @@ theorem constSmul [SMul 𝕜 β] [ContinuousConstSMul 𝕜 β] (c : 𝕜) (hf :
   exact eventually_eq.fun_comp hff' fun x => c • x
 #align measure_theory.ae_strongly_measurable'.const_smul MeasureTheory.AeStronglyMeasurable'.constSmul
 
-theorem constInner {𝕜 β} [IsROrC 𝕜] [InnerProductSpace 𝕜 β] {f : α → β}
+theorem constInner {𝕜 β} [IsROrC 𝕜] [NormedAddCommGroup β] [InnerProductSpace 𝕜 β] {f : α → β}
     (hfm : AeStronglyMeasurable' m f μ) (c : β) :
     AeStronglyMeasurable' m (fun x => (inner c (f x) : 𝕜)) μ :=
   by
@@ -233,10 +233,11 @@ variable {α β γ E E' F F' G G' H 𝕜 : Type _} {p : ℝ≥0∞} [IsROrC 𝕜
   [TopologicalSpace β]
   -- β for a generic topological space
   -- E for an inner product space
+  [NormedAddCommGroup E]
   [InnerProductSpace 𝕜 E]
   -- E' for an inner product space on which we compute integrals
-  [InnerProductSpace 𝕜 E']
-  [CompleteSpace E'] [NormedSpace ℝ E']
+  [NormedAddCommGroup E']
+  [InnerProductSpace 𝕜 E'] [CompleteSpace E'] [NormedSpace ℝ E']
   -- F for a Lp submodule
   [NormedAddCommGroup F]
   [NormedSpace 𝕜 F]
@@ -823,6 +824,8 @@ theorem lpMeas.ae_eq_zero_of_forall_set_integral_eq_zero (hm : m ≤ m0) (f : lp
 
 include 𝕜
 
+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, measurable_set[m] s → μ s < ∞ → IntegrableOn f s μ)
@@ -867,10 +870,12 @@ theorem lp.ae_eq_of_forall_set_integral_eq' (hm : m ≤ m0) (f g : lp E' p μ) (
   have hfg_meas : ae_strongly_measurable' m (⇑(f - g)) μ :=
     ae_strongly_measurable'.congr (hf_meas.sub hg_meas) (Lp.coe_fn_sub f g).symm
   exact
-    Lp.ae_eq_zero_of_forall_set_integral_eq_zero' hm (f - g) hp_ne_zero hp_ne_top hfg_int hfg'
+    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}
+
 omit 𝕜
 
 theorem ae_eq_of_forall_set_integral_eq_of_sigma_finite' (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
@@ -988,7 +993,7 @@ variable (𝕜)
 
 /-- Conditional expectation of a function in L2 with respect to a sigma-algebra -/
 def condexpL2 (hm : m ≤ m0) : (α →₂[μ] E) →L[𝕜] lpMeas E 𝕜 m 2 μ :=
-  @orthogonalProjection 𝕜 (α →₂[μ] E) _ _ (lpMeas E 𝕜 m 2 μ)
+  @orthogonalProjection 𝕜 (α →₂[μ] E) _ _ _ (lpMeas E 𝕜 m 2 μ)
     haveI : Fact (m ≤ m0) := ⟨hm⟩
     inferInstance
 #align measure_theory.condexp_L2 MeasureTheory.condexpL2
@@ -1010,13 +1015,13 @@ theorem integrableCondexpL2OfIsFiniteMeasure (hm : m ≤ m0) [IsFiniteMeasure μ
   integrableOn_univ.mp <| integrableOnCondexpL2OfMeasureNeTop hm (measure_ne_top _ _) f
 #align measure_theory.integrable_condexp_L2_of_is_finite_measure MeasureTheory.integrableCondexpL2OfIsFiniteMeasure
 
-theorem norm_condexpL2_le_one (hm : m ≤ m0) : ‖@condexpL2 α E 𝕜 _ _ _ _ _ μ hm‖ ≤ 1 :=
+theorem norm_condexpL2_le_one (hm : m ≤ m0) : ‖@condexpL2 α E 𝕜 _ _ _ _ _ _ μ hm‖ ≤ 1 :=
   haveI : Fact (m ≤ m0) := ⟨hm⟩
   orthogonalProjection_norm_le _
 #align measure_theory.norm_condexp_L2_le_one MeasureTheory.norm_condexpL2_le_one
 
 theorem norm_condexpL2_le (hm : m ≤ m0) (f : α →₂[μ] E) : ‖condexpL2 𝕜 hm f‖ ≤ ‖f‖ :=
-  ((@condexpL2 _ E 𝕜 _ _ _ _ _ μ hm).le_opNorm f).trans
+  ((@condexpL2 _ E 𝕜 _ _ _ _ _ _ μ hm).le_opNorm f).trans
     (mul_le_of_le_one_left (norm_nonneg _) (norm_condexpL2_le_one hm))
 #align measure_theory.norm_condexp_L2_le MeasureTheory.norm_condexpL2_le
 
@@ -1167,7 +1172,7 @@ theorem condexpL2_constInner (hm : m ≤ m0) (f : lp E 2 μ) (c : E) :
   have h_eq : h_mem_Lp.to_Lp _ =ᵐ[μ] fun a => ⟪c, condexp_L2 𝕜 hm f a⟫ := h_mem_Lp.coe_fn_to_Lp
   refine' eventually_eq.trans _ h_eq
   refine'
-    Lp.ae_eq_of_forall_set_integral_eq' hm _ _ two_ne_zero ENNReal.coe_ne_top
+    Lp.ae_eq_of_forall_set_integral_eq' 𝕜 hm _ _ two_ne_zero ENNReal.coe_ne_top
       (fun s hs hμs => integrable_on_condexp_L2_of_measure_ne_top hm hμs.Ne _) _ _ _ _
   · intro s hs hμs
     rw [integrable_on, integrable_congr (ae_restrict_of_ae h_eq)]
@@ -1193,7 +1198,7 @@ theorem integral_condexpL2_eq (hm : m ≤ m0) (f : lp E' 2 μ) (hs : measurable_
   rw [← sub_eq_zero, Lp_meas_coe, ←
     integral_sub' (integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs)
       (integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs)]
-  refine' integral_eq_zero_of_forall_integral_inner_eq_zero _ _ _
+  refine' integral_eq_zero_of_forall_integral_inner_eq_zero 𝕜 _ _ _
   · rw [integrable_congr (ae_restrict_of_ae (Lp.coe_fn_sub (↑(condexp_L2 𝕜 hm f)) f).symm)]
     exact integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs
   intro c
@@ -1208,8 +1213,8 @@ theorem integral_condexpL2_eq (hm : m ≤ m0) (f : lp E' 2 μ) (hs : measurable_
   exact integral_condexp_L2_eq_of_fin_meas_real _ hs hμs
 #align measure_theory.integral_condexp_L2_eq MeasureTheory.integral_condexpL2_eq
 
-variable {E'' 𝕜' : Type _} [IsROrC 𝕜'] [InnerProductSpace 𝕜' E''] [CompleteSpace E'']
-  [NormedSpace ℝ E'']
+variable {E'' 𝕜' : Type _} [IsROrC 𝕜'] [NormedAddCommGroup E''] [InnerProductSpace 𝕜' E'']
+  [CompleteSpace E''] [NormedSpace ℝ E'']
 
 variable (𝕜 𝕜')
 
@@ -1217,7 +1222,7 @@ theorem condexpL2_comp_continuousLinearMap (hm : m ≤ m0) (T : E' →L[ℝ] E''
     (condexpL2 𝕜' hm (T.compLp f) : α →₂[μ] E'') =ᵐ[μ] T.compLp (condexpL2 𝕜 hm f : α →₂[μ] E') :=
   by
   refine'
-    Lp.ae_eq_of_forall_set_integral_eq' hm _ _ two_ne_zero ENNReal.coe_ne_top
+    Lp.ae_eq_of_forall_set_integral_eq' 𝕜' hm _ _ two_ne_zero ENNReal.coe_ne_top
       (fun s hs hμs => integrable_on_condexp_L2_of_measure_ne_top hm hμs.Ne _)
       (fun s hs hμs => integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs.Ne) _ _
       _
@@ -1430,7 +1435,7 @@ theorem set_integral_condexpL2_indicator (hs : measurable_set[m] s) (ht : Measur
   calc
     (∫ x in s, (condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ))) x ∂μ) =
         ∫ x in s, indicatorConstLp 2 ht hμt (1 : ℝ) x ∂μ :=
-      @integral_condexpL2_eq α _ ℝ _ _ _ _ _ _ _ _ hm (indicatorConstLp 2 ht hμt (1 : ℝ)) hs hμs
+      @integral_condexpL2_eq α _ ℝ _ _ _ _ _ _ _ _ _ hm (indicatorConstLp 2 ht hμt (1 : ℝ)) hs hμs
     _ = (μ (t ∩ s)).toReal • 1 := (set_integral_indicatorConstLp (hm s hs) ht hμt (1 : ℝ))
     _ = (μ (t ∩ s)).toReal := by rw [smul_eq_mul, mul_one]
     

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

@@ -1016,7 +1016,7 @@ theorem norm_condexpL2_le_one (hm : m ≤ m0) : ‖@condexpL2 α E 𝕜 _ _ _ _
 #align measure_theory.norm_condexp_L2_le_one MeasureTheory.norm_condexpL2_le_one
 
 theorem norm_condexpL2_le (hm : m ≤ m0) (f : α →₂[μ] E) : ‖condexpL2 𝕜 hm f‖ ≤ ‖f‖ :=
-  ((@condexpL2 _ E 𝕜 _ _ _ _ _ μ hm).le_op_norm f).trans
+  ((@condexpL2 _ E 𝕜 _ _ _ _ _ μ hm).le_opNorm f).trans
     (mul_le_of_le_one_left (norm_nonneg _) (norm_condexpL2_le_one hm))
 #align measure_theory.norm_condexp_L2_le MeasureTheory.norm_condexpL2_le
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

@@ -1431,7 +1431,7 @@ theorem set_integral_condexpL2_indicator (hs : measurable_set[m] s) (ht : Measur
     (∫ x in s, (condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ))) x ∂μ) =
         ∫ x in s, indicatorConstLp 2 ht hμt (1 : ℝ) x ∂μ :=
       @integral_condexpL2_eq α _ ℝ _ _ _ _ _ _ _ _ hm (indicatorConstLp 2 ht hμt (1 : ℝ)) hs hμs
-    _ = (μ (t ∩ s)).toReal • 1 := set_integral_indicatorConstLp (hm s hs) ht hμt (1 : ℝ)
+    _ = (μ (t ∩ s)).toReal • 1 := (set_integral_indicatorConstLp (hm s hs) ht hμt (1 : ℝ))
     _ = (μ (t ∩ s)).toReal := by rw [smul_eq_mul, mul_one]
     
 #align measure_theory.set_integral_condexp_L2_indicator MeasureTheory.set_integral_condexpL2_indicator
@@ -1445,7 +1445,7 @@ theorem set_integral_condexpIndSmul (hs : measurable_set[m] s) (ht : MeasurableS
       set_integral_congr_ae (hm s hs)
         ((condexpIndSmul_ae_eq_smul hm ht hμt x).mono fun x hx hxs => hx)
     _ = (∫ a in s, condexpL2 ℝ hm (indicatorConstLp 2 ht hμt (1 : ℝ)) a ∂μ) • x :=
-      integral_smul_const _ x
+      (integral_smul_const _ x)
     _ = (μ (t ∩ s)).toReal • x := by rw [set_integral_condexp_L2_indicator hs ht hμs hμt]
     
 #align measure_theory.set_integral_condexp_ind_smul MeasureTheory.set_integral_condexpIndSmul
@@ -2366,7 +2366,7 @@ theorem condexp_neg (f : α → F') : μ[-f|m] =ᵐ[μ] -μ[f|m] := by
   letI : Module ℝ (α → F') := @Pi.module α (fun _ => F') ℝ _ _ fun _ => inferInstance <;>
     calc
       μ[-f|m] = μ[(-1 : ℝ) • f|m] := by rw [neg_one_smul ℝ f]
-      _ =ᵐ[μ] (-1 : ℝ) • μ[f|m] := condexp_smul (-1) f
+      _ =ᵐ[μ] (-1 : ℝ) • μ[f|m] := (condexp_smul (-1) f)
       _ = -μ[f|m] := neg_one_smul ℝ (μ[f|m])
       
 #align measure_theory.condexp_neg MeasureTheory.condexp_neg

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 
 ! This file was ported from Lean 3 source module measure_theory.function.conditional_expectation.basic
-! leanprover-community/mathlib commit a75898643b2d774cced9ae7c0b28c21663b99666
+! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -1167,7 +1167,7 @@ theorem condexpL2_constInner (hm : m ≤ m0) (f : lp E 2 μ) (c : E) :
   have h_eq : h_mem_Lp.to_Lp _ =ᵐ[μ] fun a => ⟪c, condexp_L2 𝕜 hm f a⟫ := h_mem_Lp.coe_fn_to_Lp
   refine' eventually_eq.trans _ h_eq
   refine'
-    Lp.ae_eq_of_forall_set_integral_eq' hm _ _ ennreal.zero_lt_two.ne.symm ENNReal.coe_ne_top
+    Lp.ae_eq_of_forall_set_integral_eq' hm _ _ two_ne_zero ENNReal.coe_ne_top
       (fun s hs hμs => integrable_on_condexp_L2_of_measure_ne_top hm hμs.Ne _) _ _ _ _
   · intro s hs hμs
     rw [integrable_on, integrable_congr (ae_restrict_of_ae h_eq)]
@@ -1217,7 +1217,7 @@ theorem condexpL2_comp_continuousLinearMap (hm : m ≤ m0) (T : E' →L[ℝ] E''
     (condexpL2 𝕜' hm (T.compLp f) : α →₂[μ] E'') =ᵐ[μ] T.compLp (condexpL2 𝕜 hm f : α →₂[μ] E') :=
   by
   refine'
-    Lp.ae_eq_of_forall_set_integral_eq' hm _ _ ennreal.zero_lt_two.ne.symm ENNReal.coe_ne_top
+    Lp.ae_eq_of_forall_set_integral_eq' hm _ _ two_ne_zero ENNReal.coe_ne_top
       (fun s hs hμs => integrable_on_condexp_L2_of_measure_ne_top hm hμs.Ne _)
       (fun s hs hμs => integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs.Ne) _ _
       _
@@ -1290,7 +1290,7 @@ theorem set_lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : Measur
       rw [lintegral_mul_const, Lp_meas_coe]
       exact (Lp.strongly_measurable _).ennnorm
     _ ≤ μ (s ∩ t) * ‖x‖₊ :=
-      ENNReal.mul_le_mul (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) le_rfl
+      mul_le_mul_right' (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) _
     
 #align measure_theory.set_lintegral_nnnorm_condexp_L2_indicator_le MeasureTheory.set_lintegral_nnnorm_condexpL2_indicator_le
 
@@ -1302,8 +1302,7 @@ theorem lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : Measurable
   · rw [Lp_meas_coe]
     exact (Lp.ae_strongly_measurable _).ennnorm
   refine' (set_lintegral_nnnorm_condexp_L2_indicator_le hm hs hμs x ht hμt).trans _
-  refine' ENNReal.mul_le_mul _ le_rfl
-  exact measure_mono (Set.inter_subset_left _ _)
+  exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
 #align measure_theory.lintegral_nnnorm_condexp_L2_indicator_le MeasureTheory.lintegral_nnnorm_condexpL2_indicator_le
 
 /-- If the measure `μ.trim hm` is sigma-finite, then the conditional expectation of a measurable set
@@ -1318,7 +1317,7 @@ theorem integrableCondexpL2Indicator (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     exact Lp.ae_strongly_measurable _
   · refine' fun t ht hμt =>
       (set_lintegral_nnnorm_condexp_L2_indicator_le hm hs hμs x ht hμt).trans _
-    exact ENNReal.mul_le_mul (measure_mono (Set.inter_subset_left _ _)) le_rfl
+    exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
 #align measure_theory.integrable_condexp_L2_indicator MeasureTheory.integrableCondexpL2Indicator
 
 end CondexpL2Indicator
@@ -1390,7 +1389,7 @@ theorem set_lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableS
       rw [lintegral_mul_const, Lp_meas_coe]
       exact (Lp.strongly_measurable _).ennnorm
     _ ≤ μ (s ∩ t) * ‖x‖₊ :=
-      ENNReal.mul_le_mul (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) le_rfl
+      mul_le_mul_right' (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) _
     
 #align measure_theory.set_lintegral_nnnorm_condexp_ind_smul_le MeasureTheory.set_lintegral_nnnorm_condexpIndSmul_le
 
@@ -1400,8 +1399,7 @@ theorem lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableSet s
   refine' lintegral_le_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) _ fun t ht hμt => _
   · exact (Lp.ae_strongly_measurable _).ennnorm
   refine' (set_lintegral_nnnorm_condexp_ind_smul_le hm hs hμs x ht hμt).trans _
-  refine' ENNReal.mul_le_mul _ le_rfl
-  exact measure_mono (Set.inter_subset_left _ _)
+  exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
 #align measure_theory.lintegral_nnnorm_condexp_ind_smul_le MeasureTheory.lintegral_nnnorm_condexpIndSmul_le
 
 /-- If the measure `μ.trim hm` is sigma-finite, then the conditional expectation of a measurable set
@@ -1414,7 +1412,7 @@ theorem integrableCondexpIndSmul (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hs
       _
   · exact Lp.ae_strongly_measurable _
   · refine' fun t ht hμt => (set_lintegral_nnnorm_condexp_ind_smul_le hm hs hμs x ht hμt).trans _
-    exact ENNReal.mul_le_mul (measure_mono (Set.inter_subset_left _ _)) le_rfl
+    exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
 #align measure_theory.integrable_condexp_ind_smul MeasureTheory.integrableCondexpIndSmul
 
 theorem condexpIndSmul_empty {x : G} :

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

@@ -83,7 +83,7 @@ noncomputable section
 
 open TopologicalSpace MeasureTheory.lp Filter ContinuousLinearMap
 
-open NNReal Ennreal Topology BigOperators MeasureTheory
+open NNReal ENNReal Topology BigOperators MeasureTheory
 
 namespace MeasureTheory
 
@@ -961,7 +961,7 @@ theorem lintegral_nnnorm_le_of_forall_fin_meas_integral_eq (hm : m ≤ m0) {f g
     (hs : measurable_set[m] s) (hμs : μ s ≠ ∞) : (∫⁻ x in s, ‖g x‖₊ ∂μ) ≤ ∫⁻ x in s, ‖f x‖₊ ∂μ :=
   by
   rw [← of_real_integral_norm_eq_lintegral_nnnorm hfi, ←
-    of_real_integral_norm_eq_lintegral_nnnorm hgi, Ennreal.ofReal_le_ofReal_iff]
+    of_real_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 _
 #align measure_theory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq MeasureTheory.lintegral_nnnorm_le_of_forall_fin_meas_integral_eq
@@ -1023,7 +1023,7 @@ theorem norm_condexpL2_le (hm : m ≤ m0) (f : α →₂[μ] E) : ‖condexpL2 
 theorem snorm_condexpL2_le (hm : m ≤ m0) (f : α →₂[μ] E) :
     snorm (condexpL2 𝕜 hm f) 2 μ ≤ snorm f 2 μ :=
   by
-  rw [Lp_meas_coe, ← Ennreal.toReal_le_toReal (Lp.snorm_ne_top _) (Lp.snorm_ne_top _), ←
+  rw [Lp_meas_coe, ← ENNReal.toReal_le_toReal (Lp.snorm_ne_top _) (Lp.snorm_ne_top _), ←
     Lp.norm_def, ← Lp.norm_def, Submodule.norm_coe]
   exact norm_condexp_L2_le hm f
 #align measure_theory.snorm_condexp_L2_le MeasureTheory.snorm_condexpL2_le
@@ -1032,7 +1032,7 @@ theorem norm_condexpL2_coe_le (hm : m ≤ m0) (f : α →₂[μ] E) :
     ‖(condexpL2 𝕜 hm f : α →₂[μ] E)‖ ≤ ‖f‖ :=
   by
   rw [Lp.norm_def, Lp.norm_def, ← Lp_meas_coe]
-  refine' (Ennreal.toReal_le_toReal _ (Lp.snorm_ne_top _)).mpr (snorm_condexp_L2_le hm f)
+  refine' (ENNReal.toReal_le_toReal _ (Lp.snorm_ne_top _)).mpr (snorm_condexp_L2_le hm f)
   exact Lp.snorm_ne_top _
 #align measure_theory.norm_condexp_L2_coe_le MeasureTheory.norm_condexpL2_coe_le
 
@@ -1116,8 +1116,8 @@ theorem condexpL2_ae_eq_zero_of_ae_eq_zero (hs : measurable_set[m] s) (hμs : μ
     refine' h_nnnorm_eq_zero.mono fun x hx => _
     dsimp only at hx
     rw [Pi.zero_apply] at hx⊢
-    · rwa [Ennreal.coe_eq_zero, nnnorm_eq_zero] at hx
-    · refine' Measurable.coe_nNReal_ennreal (Measurable.nnnorm _)
+    · rwa [ENNReal.coe_eq_zero, nnnorm_eq_zero] at hx
+    · refine' Measurable.coe_nNReal_eNNReal (Measurable.nnnorm _)
       rw [Lp_meas_coe]
       exact (Lp.strongly_measurable _).Measurable
   refine' le_antisymm _ (zero_le _)
@@ -1167,7 +1167,7 @@ theorem condexpL2_constInner (hm : m ≤ m0) (f : lp E 2 μ) (c : E) :
   have h_eq : h_mem_Lp.to_Lp _ =ᵐ[μ] fun a => ⟪c, condexp_L2 𝕜 hm f a⟫ := h_mem_Lp.coe_fn_to_Lp
   refine' eventually_eq.trans _ h_eq
   refine'
-    Lp.ae_eq_of_forall_set_integral_eq' hm _ _ ennreal.zero_lt_two.ne.symm Ennreal.coe_ne_top
+    Lp.ae_eq_of_forall_set_integral_eq' hm _ _ ennreal.zero_lt_two.ne.symm ENNReal.coe_ne_top
       (fun s hs hμs => integrable_on_condexp_L2_of_measure_ne_top hm hμs.Ne _) _ _ _ _
   · intro s hs hμs
     rw [integrable_on, integrable_congr (ae_restrict_of_ae h_eq)]
@@ -1217,7 +1217,7 @@ theorem condexpL2_comp_continuousLinearMap (hm : m ≤ m0) (T : E' →L[ℝ] E''
     (condexpL2 𝕜' hm (T.compLp f) : α →₂[μ] E'') =ᵐ[μ] T.compLp (condexpL2 𝕜 hm f : α →₂[μ] E') :=
   by
   refine'
-    Lp.ae_eq_of_forall_set_integral_eq' hm _ _ ennreal.zero_lt_two.ne.symm Ennreal.coe_ne_top
+    Lp.ae_eq_of_forall_set_integral_eq' hm _ _ ennreal.zero_lt_two.ne.symm ENNReal.coe_ne_top
       (fun s hs hμs => integrable_on_condexp_L2_of_measure_ne_top hm hμs.Ne _)
       (fun s hs hμs => integrable_on_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs.Ne) _ _
       _
@@ -1286,11 +1286,11 @@ theorem set_lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : Measur
         ((condexpL2_indicator_ae_eq_smul 𝕜 hm hs hμs x).mono fun a ha hat => by rw [ha])
     _ = (∫⁻ a in t, ‖condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a‖₊ ∂μ) * ‖x‖₊ :=
       by
-      simp_rw [nnnorm_smul, Ennreal.coe_mul]
+      simp_rw [nnnorm_smul, ENNReal.coe_mul]
       rw [lintegral_mul_const, Lp_meas_coe]
       exact (Lp.strongly_measurable _).ennnorm
     _ ≤ μ (s ∩ t) * ‖x‖₊ :=
-      Ennreal.mul_le_mul (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) le_rfl
+      ENNReal.mul_le_mul (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) le_rfl
     
 #align measure_theory.set_lintegral_nnnorm_condexp_L2_indicator_le MeasureTheory.set_lintegral_nnnorm_condexpL2_indicator_le
 
@@ -1302,7 +1302,7 @@ theorem lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : Measurable
   · rw [Lp_meas_coe]
     exact (Lp.ae_strongly_measurable _).ennnorm
   refine' (set_lintegral_nnnorm_condexp_L2_indicator_le hm hs hμs x ht hμt).trans _
-  refine' Ennreal.mul_le_mul _ le_rfl
+  refine' ENNReal.mul_le_mul _ le_rfl
   exact measure_mono (Set.inter_subset_left _ _)
 #align measure_theory.lintegral_nnnorm_condexp_L2_indicator_le MeasureTheory.lintegral_nnnorm_condexpL2_indicator_le
 
@@ -1312,13 +1312,13 @@ theorem integrableCondexpL2Indicator (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     (hμs : μ s ≠ ∞) (x : E') : Integrable (condexpL2 𝕜 hm (indicatorConstLp 2 hs hμs x)) μ :=
   by
   refine'
-    integrable_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) (Ennreal.mul_lt_top hμs Ennreal.coe_ne_top) _
+    integrable_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) (ENNReal.mul_lt_top hμs ENNReal.coe_ne_top) _
       _
   · rw [Lp_meas_coe]
     exact Lp.ae_strongly_measurable _
   · refine' fun t ht hμt =>
       (set_lintegral_nnnorm_condexp_L2_indicator_le hm hs hμs x ht hμt).trans _
-    exact Ennreal.mul_le_mul (measure_mono (Set.inter_subset_left _ _)) le_rfl
+    exact ENNReal.mul_le_mul (measure_mono (Set.inter_subset_left _ _)) le_rfl
 #align measure_theory.integrable_condexp_L2_indicator MeasureTheory.integrableCondexpL2Indicator
 
 end CondexpL2Indicator
@@ -1386,11 +1386,11 @@ theorem set_lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableS
         ((condexpIndSmul_ae_eq_smul hm hs hμs x).mono fun a ha hat => by rw [ha])
     _ = (∫⁻ a in t, ‖condexpL2 ℝ hm (indicatorConstLp 2 hs hμs (1 : ℝ)) a‖₊ ∂μ) * ‖x‖₊ :=
       by
-      simp_rw [nnnorm_smul, Ennreal.coe_mul]
+      simp_rw [nnnorm_smul, ENNReal.coe_mul]
       rw [lintegral_mul_const, Lp_meas_coe]
       exact (Lp.strongly_measurable _).ennnorm
     _ ≤ μ (s ∩ t) * ‖x‖₊ :=
-      Ennreal.mul_le_mul (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) le_rfl
+      ENNReal.mul_le_mul (lintegral_nnnorm_condexpL2_indicator_le_real hs hμs ht hμt) le_rfl
     
 #align measure_theory.set_lintegral_nnnorm_condexp_ind_smul_le MeasureTheory.set_lintegral_nnnorm_condexpIndSmul_le
 
@@ -1400,7 +1400,7 @@ theorem lintegral_nnnorm_condexpIndSmul_le (hm : m ≤ m0) (hs : MeasurableSet s
   refine' lintegral_le_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) _ fun t ht hμt => _
   · exact (Lp.ae_strongly_measurable _).ennnorm
   refine' (set_lintegral_nnnorm_condexp_ind_smul_le hm hs hμs x ht hμt).trans _
-  refine' Ennreal.mul_le_mul _ le_rfl
+  refine' ENNReal.mul_le_mul _ le_rfl
   exact measure_mono (Set.inter_subset_left _ _)
 #align measure_theory.lintegral_nnnorm_condexp_ind_smul_le MeasureTheory.lintegral_nnnorm_condexpIndSmul_le
 
@@ -1410,15 +1410,15 @@ theorem integrableCondexpIndSmul (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hs
     (hμs : μ s ≠ ∞) (x : G) : Integrable (condexpIndSmul hm hs hμs x) μ :=
   by
   refine'
-    integrable_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) (Ennreal.mul_lt_top hμs Ennreal.coe_ne_top) _
+    integrable_of_forall_fin_meas_le' hm (μ s * ‖x‖₊) (ENNReal.mul_lt_top hμs ENNReal.coe_ne_top) _
       _
   · exact Lp.ae_strongly_measurable _
   · refine' fun t ht hμt => (set_lintegral_nnnorm_condexp_ind_smul_le hm hs hμs x ht hμt).trans _
-    exact Ennreal.mul_le_mul (measure_mono (Set.inter_subset_left _ _)) le_rfl
+    exact ENNReal.mul_le_mul (measure_mono (Set.inter_subset_left _ _)) le_rfl
 #align measure_theory.integrable_condexp_ind_smul MeasureTheory.integrableCondexpIndSmul
 
 theorem condexpIndSmul_empty {x : G} :
-    condexpIndSmul hm MeasurableSet.empty ((@measure_empty _ _ μ).le.trans_lt Ennreal.coe_lt_top).Ne
+    condexpIndSmul hm MeasurableSet.empty ((@measure_empty _ _ μ).le.trans_lt ENNReal.coe_lt_top).Ne
         x =
       0 :=
   by
@@ -1475,7 +1475,7 @@ theorem condexpL2_indicator_nonneg (hm : m ≤ m0) (hs : MeasurableSet s) (hμs
       exact fun _ => hx.symm
     rw [set_integral_congr_ae (hm t ht) h_ae,
       set_integral_condexp_L2_indicator ht hs ((le_trim hm).trans_lt hμt).Ne hμs]
-    exact Ennreal.toReal_nonneg
+    exact ENNReal.toReal_nonneg
 #align measure_theory.condexp_L2_indicator_nonneg MeasureTheory.condexpL2_indicator_nonneg
 
 theorem condexpIndSmul_nonneg {E} [NormedLatticeAddCommGroup E] [NormedSpace ℝ E] [OrderedSMul ℝ E]
@@ -1565,9 +1565,9 @@ theorem norm_condexpIndL1Fin_le (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x
   by
   have : 0 ≤ ∫ a : α, ‖condexp_ind_L1_fin hm hs hμs x a‖ ∂μ :=
     integral_nonneg fun a => norm_nonneg _
-  rw [L1.norm_eq_integral_norm, ← Ennreal.toReal_ofReal (norm_nonneg x), ← Ennreal.toReal_mul, ←
-    Ennreal.toReal_ofReal this,
-    Ennreal.toReal_le_toReal Ennreal.ofReal_ne_top (Ennreal.mul_ne_top hμs Ennreal.ofReal_ne_top),
+  rw [L1.norm_eq_integral_norm, ← ENNReal.toReal_ofReal (norm_nonneg x), ← ENNReal.toReal_mul, ←
+    ENNReal.toReal_ofReal this,
+    ENNReal.toReal_le_toReal ENNReal.ofReal_ne_top (ENNReal.mul_ne_top hμs ENNReal.ofReal_ne_top),
     of_real_integral_norm_eq_lintegral_nnnorm]
   swap
   · rw [← mem_ℒp_one_iff_integrable]
@@ -1587,7 +1587,7 @@ theorem condexpIndL1Fin_disjoint_union (hs : MeasurableSet s) (ht : MeasurableSe
     (hμt : μ t ≠ ∞) (hst : s ∩ t = ∅) (x : G) :
     condexpIndL1Fin hm (hs.union ht)
         ((measure_union_le s t).trans_lt
-            (lt_top_iff_ne_top.mpr (Ennreal.add_ne_top.mpr ⟨hμs, hμt⟩))).Ne
+            (lt_top_iff_ne_top.mpr (ENNReal.add_ne_top.mpr ⟨hμs, hμt⟩))).Ne
         x =
       condexpIndL1Fin hm hs hμs x + condexpIndL1Fin hm ht hμt x :=
   by
@@ -1687,10 +1687,10 @@ theorem norm_condexpIndL1_le (x : G) : ‖condexpIndL1 hm μ s x‖ ≤ (μ s).t
   swap;
   · simp_rw [condexp_ind_L1_of_not_measurable_set hs]
     rw [Lp.norm_zero]
-    exact mul_nonneg Ennreal.toReal_nonneg (norm_nonneg _)
+    exact mul_nonneg ENNReal.toReal_nonneg (norm_nonneg _)
   by_cases hμs : μ s = ∞
   · rw [condexp_ind_L1_of_measure_eq_top hμs x, Lp.norm_zero]
-    exact mul_nonneg Ennreal.toReal_nonneg (norm_nonneg _)
+    exact mul_nonneg ENNReal.toReal_nonneg (norm_nonneg _)
   · rw [condexp_ind_L1_of_measurable_set_of_measure_ne_top hs hμs x]
     exact norm_condexp_ind_L1_fin_le hs hμs x
 #align measure_theory.norm_condexp_ind_L1_le MeasureTheory.norm_condexpIndL1_le
@@ -1761,7 +1761,7 @@ theorem norm_condexpInd_apply_le (x : G) : ‖condexpInd hm μ s x‖ ≤ (μ s)
 #align measure_theory.norm_condexp_ind_apply_le MeasureTheory.norm_condexpInd_apply_le
 
 theorem norm_condexpInd_le : ‖(condexpInd hm μ s : G →L[ℝ] α →₁[μ] G)‖ ≤ (μ s).toReal :=
-  ContinuousLinearMap.op_norm_le_bound _ Ennreal.toReal_nonneg norm_condexpInd_apply_le
+  ContinuousLinearMap.op_norm_le_bound _ ENNReal.toReal_nonneg norm_condexpInd_apply_le
 #align measure_theory.norm_condexp_ind_le MeasureTheory.norm_condexpInd_le
 
 theorem condexpInd_disjoint_union_apply (hs : MeasurableSet s) (ht : MeasurableSet t)
@@ -1856,7 +1856,7 @@ theorem set_integral_condexpL1Clm_of_measure_ne_top (f : α →₁[μ] F') (hs :
     (hμs : μ s ≠ ∞) : (∫ x in s, condexpL1Clm hm μ f x ∂μ) = ∫ x in s, f x ∂μ :=
   by
   refine'
-    Lp.induction Ennreal.one_ne_top
+    Lp.induction ENNReal.one_ne_top
       (fun f : α →₁[μ] F' => (∫ x in s, condexp_L1_clm hm μ f x ∂μ) = ∫ x in s, f x ∂μ) _ _
       (isClosed_eq _ _) f
   · intro x t ht hμt
@@ -1928,7 +1928,7 @@ theorem aeStronglyMeasurable'CondexpL1Clm (f : α →₁[μ] F') :
     AeStronglyMeasurable' m (condexpL1Clm hm μ f) μ :=
   by
   refine'
-    Lp.induction Ennreal.one_ne_top
+    Lp.induction ENNReal.one_ne_top
       (fun f : α →₁[μ] F' => ae_strongly_measurable' m (condexp_L1_clm hm μ f) μ) _ _ _ f
   · intro c s hs hμs
     rw [condexp_L1_clm_indicator_const hs hμs.ne c]
@@ -1953,7 +1953,7 @@ theorem condexpL1Clm_lpMeas (f : lpMeas F' ℝ m 1 μ) : condexpL1Clm hm μ (f :
     simp only [LinearIsometryEquiv.symm_apply_apply]
   rw [hfg]
   refine'
-    @Lp.induction α F' m _ 1 (μ.trim hm) _ Ennreal.coe_ne_top
+    @Lp.induction α F' m _ 1 (μ.trim hm) _ ENNReal.coe_ne_top
       (fun g : α →₁[μ.trim hm] F' =>
         condexp_L1_clm hm μ ((Lp_meas_to_Lp_trim_lie F' ℝ 1 μ hm).symm g : α →₁[μ] F') =
           ↑((Lp_meas_to_Lp_trim_lie F' ℝ 1 μ hm).symm g))
@@ -2280,7 +2280,7 @@ theorem condexp_bot' [hμ : μ.ae.ne_bot] (f : α → F') :
   · have h : ¬sigma_finite (μ.trim bot_le) := by rwa [sigma_finite_trim_bot_iff]
     rw [not_is_finite_measure_iff] at hμ_finite
     rw [condexp_of_not_sigma_finite bot_le h]
-    simp only [hμ_finite, Ennreal.top_toReal, inv_zero, zero_smul]
+    simp only [hμ_finite, ENNReal.top_toReal, inv_zero, zero_smul]
     rfl
   haveI : is_finite_measure μ := hμ_finite
   by_cases hf : integrable f μ
@@ -2293,7 +2293,7 @@ theorem condexp_bot' [hμ : μ.ae.ne_bot] (f : α → F') :
   have h_integral : (∫ x, (μ[f|⊥]) x ∂μ) = ∫ x, f x ∂μ := integral_condexp bot_le hf
   simp_rw [h_eq, integral_const] at h_integral
   rw [← h_integral, ← smul_assoc, smul_eq_mul, inv_mul_cancel, one_smul]
-  rw [Ne.def, Ennreal.toReal_eq_zero_iff, Auto.not_or_eq, measure.measure_univ_eq_zero, ← ae_eq_bot,
+  rw [Ne.def, ENNReal.toReal_eq_zero_iff, Auto.not_or_eq, measure.measure_univ_eq_zero, ← ae_eq_bot,
     ← Ne.def, ← ne_bot_iff]
   exact ⟨hμ, measure_ne_top μ Set.univ⟩
 #align measure_theory.condexp_bot' MeasureTheory.condexp_bot'
@@ -2312,7 +2312,7 @@ theorem condexp_bot_ae_eq (f : α → F') :
 theorem condexp_bot [IsProbabilityMeasure μ] (f : α → F') : μ[f|⊥] = fun _ => ∫ x, f x ∂μ :=
   by
   refine' (condexp_bot' f).trans _
-  rw [measure_univ, Ennreal.one_toReal, inv_one, one_smul]
+  rw [measure_univ, ENNReal.one_toReal, inv_one, one_smul]
 #align measure_theory.condexp_bot MeasureTheory.condexp_bot
 
 theorem condexp_add (hf : Integrable f μ) (hg : Integrable g μ) :

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

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

@@ -40,7 +40,7 @@ The conditional expectation and its properties
   with respect to `m`.
 * `integrable_condexp` : `condexp` is integrable.
 * `stronglyMeasurable_condexp` : `condexp` is `m`-strongly-measurable.
-* `set_integral_condexp (hf : Integrable f μ) (hs : MeasurableSet[m] s)` : if `m ≤ m0` (the
+* `setIntegral_condexp (hf : Integrable f μ) (hs : MeasurableSet[m] s)` : if `m ≤ m0` (the
   σ-algebra over which the measure is defined), then the conditional expectation verifies
   `∫ x in s, condexp m μ f x ∂μ = ∫ x in s, f x ∂μ` for any `m`-measurable set `s`.
 
@@ -49,7 +49,7 @@ linear map `condexpL1CLM` from `L1` to `L1`. `condexp` should be used in most ca
 
 Uniqueness of the conditional expectation
 
-* `ae_eq_condexp_of_forall_set_integral_eq`: an a.e. `m`-measurable function which verifies the
+* `ae_eq_condexp_of_forall_setIntegral_eq`: an a.e. `m`-measurable function which verifies the
   equality of integrals is a.e. equal to `condexp`.
 
 ## Notations
@@ -218,32 +218,40 @@ theorem integrable_condexp : Integrable (μ[f|m]) μ := by
 
 /-- The integral of the conditional expectation `μ[f|hm]` over an `m`-measurable set is equal to
 the integral of `f` on that set. -/
-theorem set_integral_condexp (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : Integrable f μ)
+theorem setIntegral_condexp (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : Integrable f μ)
     (hs : MeasurableSet[m] s) : ∫ x in s, (μ[f|m]) x ∂μ = ∫ x in s, f x ∂μ := by
-  rw [set_integral_congr_ae (hm s hs) ((condexp_ae_eq_condexpL1 hm f).mono fun x hx _ => hx)]
-  exact set_integral_condexpL1 hf hs
-#align measure_theory.set_integral_condexp MeasureTheory.set_integral_condexp
+  rw [setIntegral_congr_ae (hm s hs) ((condexp_ae_eq_condexpL1 hm f).mono fun x hx _ => hx)]
+  exact setIntegral_condexpL1 hf hs
+#align measure_theory.set_integral_condexp MeasureTheory.setIntegral_condexp
+
+@[deprecated]
+alias set_integral_condexp :=
+  setIntegral_condexp -- deprecated on 2024-04-17
 
 theorem integral_condexp (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] (hf : Integrable f μ) :
     ∫ x, (μ[f|m]) x ∂μ = ∫ x, f x ∂μ := by
   suffices ∫ x in Set.univ, (μ[f|m]) x ∂μ = ∫ x in Set.univ, f x ∂μ by
     simp_rw [integral_univ] at this; exact this
-  exact set_integral_condexp hm hf (@MeasurableSet.univ _ m)
+  exact setIntegral_condexp hm hf (@MeasurableSet.univ _ m)
 #align measure_theory.integral_condexp MeasureTheory.integral_condexp
 
 /-- **Uniqueness of the conditional expectation**
 If a function is a.e. `m`-measurable, verifies an integrability condition and has same integral
 as `f` on all `m`-measurable sets, then it is a.e. equal to `μ[f|hm]`. -/
-theorem ae_eq_condexp_of_forall_set_integral_eq (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
+theorem ae_eq_condexp_of_forall_setIntegral_eq (hm : m ≤ m0) [SigmaFinite (μ.trim hm)]
     {f g : α → F'} (hf : Integrable f μ)
     (hg_int_finite : ∀ s, MeasurableSet[m] s → μ s < ∞ → IntegrableOn g s μ)
     (hg_eq : ∀ s : Set α, MeasurableSet[m] s → μ s < ∞ → ∫ x in s, g x ∂μ = ∫ x in s, f x ∂μ)
     (hgm : AEStronglyMeasurable' m g μ) : g =ᵐ[μ] μ[f|m] := by
-  refine' ae_eq_of_forall_set_integral_eq_of_sigmaFinite' hm hg_int_finite
+  refine' ae_eq_of_forall_setIntegral_eq_of_sigmaFinite' hm hg_int_finite
     (fun s _ _ => integrable_condexp.integrableOn) (fun s hs hμs => _) hgm
     (StronglyMeasurable.aeStronglyMeasurable' stronglyMeasurable_condexp)
-  rw [hg_eq s hs hμs, set_integral_condexp hm hf hs]
-#align measure_theory.ae_eq_condexp_of_forall_set_integral_eq MeasureTheory.ae_eq_condexp_of_forall_set_integral_eq
+  rw [hg_eq s hs hμs, setIntegral_condexp hm hf hs]
+#align measure_theory.ae_eq_condexp_of_forall_set_integral_eq MeasureTheory.ae_eq_condexp_of_forall_setIntegral_eq
+
+@[deprecated]
+alias ae_eq_condexp_of_forall_set_integral_eq :=
+  ae_eq_condexp_of_forall_setIntegral_eq -- deprecated on 2024-04-17
 
 theorem condexp_bot' [hμ : NeZero μ] (f : α → F') :
     μ[f|⊥] = fun _ => (μ Set.univ).toReal⁻¹ • ∫ x, f x ∂μ := by
@@ -334,14 +342,14 @@ theorem condexp_condexp_of_le {m₁ m₂ m0 : MeasurableSpace α} {μ : Measure
   haveI : SigmaFinite (μ.trim (hm₁₂.trans hm₂)) := hμm₁
   by_cases hf : Integrable f μ
   swap; · simp_rw [condexp_undef hf, condexp_zero]; rfl
-  refine' ae_eq_of_forall_set_integral_eq_of_sigmaFinite' (hm₁₂.trans hm₂)
+  refine' ae_eq_of_forall_setIntegral_eq_of_sigmaFinite' (hm₁₂.trans hm₂)
     (fun s _ _ => integrable_condexp.integrableOn)
     (fun s _ _ => integrable_condexp.integrableOn) _
     (StronglyMeasurable.aeStronglyMeasurable' stronglyMeasurable_condexp)
     (StronglyMeasurable.aeStronglyMeasurable' stronglyMeasurable_condexp)
   intro s hs _
-  rw [set_integral_condexp (hm₁₂.trans hm₂) integrable_condexp hs]
-  rw [set_integral_condexp (hm₁₂.trans hm₂) hf hs, set_integral_condexp hm₂ hf (hm₁₂ s hs)]
+  rw [setIntegral_condexp (hm₁₂.trans hm₂) integrable_condexp hs]
+  rw [setIntegral_condexp (hm₁₂.trans hm₂) hf hs, setIntegral_condexp hm₂ hf (hm₁₂ s hs)]
 #align measure_theory.condexp_condexp_of_le MeasureTheory.condexp_condexp_of_le
 
 theorem condexp_mono {E} [NormedLatticeAddCommGroup E] [CompleteSpace E] [NormedSpace ℝ E]

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -317,7 +317,7 @@ theorem condexp_neg (f : α → F') : μ[-f|m] =ᵐ[μ] -μ[f|m] := by
   letI : Module ℝ (α → F') := @Pi.module α (fun _ => F') ℝ _ _ fun _ => inferInstance
   calc
     μ[-f|m] = μ[(-1 : ℝ) • f|m] := by rw [neg_one_smul ℝ f]
-    _ =ᵐ[μ] (-1 : ℝ) • μ[f|m] := (condexp_smul (-1) f)
+    _ =ᵐ[μ] (-1 : ℝ) • μ[f|m] := condexp_smul (-1) f
     _ = -μ[f|m] := neg_one_smul ℝ (μ[f|m])
 #align measure_theory.condexp_neg MeasureTheory.condexp_neg
 

@@ -117,7 +117,7 @@ theorem condexp_of_sigmaFinite (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)]
         else aestronglyMeasurable'_condexpL1.mk (condexpL1 hm μ f)
       else 0 := by
   rw [condexp, dif_pos hm]
-  simp only [hμm, Ne.def, true_and_iff]
+  simp only [hμm, Ne, true_and_iff]
   by_cases hf : Integrable f μ
   · rw [dif_pos hf, if_pos hf]
   · rw [dif_neg hf, if_neg hf]
@@ -262,7 +262,7 @@ theorem condexp_bot' [hμ : NeZero μ] (f : α → F') :
   have h_integral : ∫ x, (μ[f|⊥]) x ∂μ = ∫ x, f x ∂μ := integral_condexp bot_le hf
   simp_rw [h_eq, integral_const] at h_integral
   rw [← h_integral, ← smul_assoc, smul_eq_mul, inv_mul_cancel, one_smul]
-  rw [Ne.def, ENNReal.toReal_eq_zero_iff, not_or]
+  rw [Ne, ENNReal.toReal_eq_zero_iff, not_or]
   exact ⟨NeZero.ne _, measure_ne_top μ Set.univ⟩
 #align measure_theory.condexp_bot' MeasureTheory.condexp_bot'
 

Fixes #11441.

@@ -280,9 +280,9 @@ theorem condexp_bot [IsProbabilityMeasure μ] (f : α → F') : μ[f|⊥] = fun
 theorem condexp_add (hf : Integrable f μ) (hg : Integrable g μ) :
     μ[f + g|m] =ᵐ[μ] μ[f|m] + μ[g|m] := by
   by_cases hm : m ≤ m0
-  swap; · simp_rw [condexp_of_not_le hm]; simp; rfl
+  swap; · simp_rw [condexp_of_not_le hm]; simp
   by_cases hμm : SigmaFinite (μ.trim hm)
-  swap; · simp_rw [condexp_of_not_sigmaFinite hm hμm]; simp; rfl
+  swap; · simp_rw [condexp_of_not_sigmaFinite hm hμm]; simp
   haveI : SigmaFinite (μ.trim hm) := hμm
   refine' (condexp_ae_eq_condexpL1 hm _).trans _
   rw [condexpL1_add hf hg]
@@ -302,9 +302,9 @@ theorem condexp_finset_sum {ι : Type*} {s : Finset ι} {f : ι → α → F'}
 
 theorem condexp_smul (c : 𝕜) (f : α → F') : μ[c • f|m] =ᵐ[μ] c • μ[f|m] := by
   by_cases hm : m ≤ m0
-  swap; · simp_rw [condexp_of_not_le hm]; simp; rfl
+  swap; · simp_rw [condexp_of_not_le hm]; simp
   by_cases hμm : SigmaFinite (μ.trim hm)
-  swap; · simp_rw [condexp_of_not_sigmaFinite hm hμm]; simp; rfl
+  swap; · simp_rw [condexp_of_not_sigmaFinite hm hμm]; simp
   haveI : SigmaFinite (μ.trim hm) := hμm
   refine' (condexp_ae_eq_condexpL1 hm _).trans _
   rw [condexpL1_smul c f]

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.

@@ -71,7 +71,7 @@ open scoped ENNReal Topology BigOperators MeasureTheory
 
 namespace MeasureTheory
 
-variable {α F F' 𝕜 : Type*} {p : ℝ≥0∞} [IsROrC 𝕜]
+variable {α F F' 𝕜 : Type*} {p : ℝ≥0∞} [RCLike 𝕜]
   -- 𝕜 for ℝ or ℂ
   -- F for a Lp submodule
   [NormedAddCommGroup F]

After #9949, Pi.smul_apply can be used in simp again. This PR cleans up some workarounds.

@@ -310,7 +310,7 @@ theorem condexp_smul (c : 𝕜) (f : α → F') : μ[c • f|m] =ᵐ[μ] c • 
   rw [condexpL1_smul c f]
   refine' (@condexp_ae_eq_condexpL1 _ _ _ _ _ m _ _ hm _ f).mp _
   refine' (coeFn_smul c (condexpL1 hm μ f)).mono fun x hx1 hx2 => _
-  rw [hx1, Pi.smul_apply, Pi.smul_apply, hx2]
+  simp only [hx1, hx2, Pi.smul_apply]
 #align measure_theory.condexp_smul MeasureTheory.condexp_smul
 
 theorem condexp_neg (f : α → F') : μ[-f|m] =ᵐ[μ] -μ[f|m] := by

Rename

• Complex.equivRealProdClm → Complex.equivRealProdCLM;
  • TODO: should this one use CLE?
• Complex.reClm → Complex.reCLM;
• Complex.imClm → Complex.imCLM;
• Complex.conjLie → Complex.conjLIE;
• Complex.conjCle → Complex.conjCLE;
• Complex.ofRealLi → Complex.ofRealLI;
• Complex.ofRealClm → Complex.ofRealCLM;
• fderivInnerClm → fderivInnerCLM;
• LinearPMap.adjointDomainMkClm → LinearPMap.adjointDomainMkCLM;
• LinearPMap.adjointDomainMkClmExtend → LinearPMap.adjointDomainMkCLMExtend;
• IsROrC.reClm → IsROrC.reCLM;
• IsROrC.imClm → IsROrC.imCLM;
• IsROrC.conjLie → IsROrC.conjLIE;
• IsROrC.conjCle → IsROrC.conjCLE;
• IsROrC.ofRealLi → IsROrC.ofRealLI;
• IsROrC.ofRealClm → IsROrC.ofRealCLM;
• MeasureTheory.condexpL1Clm → MeasureTheory.condexpL1CLM;
• algebraMapClm → algebraMapCLM;
• WeakDual.CharacterSpace.toClm → WeakDual.CharacterSpace.toCLM;
• BoundedContinuousFunction.evalClm → BoundedContinuousFunction.evalCLM;
• ContinuousMap.evalClm → ContinuousMap.evalCLM;
• TrivSqZeroExt.fstClm → TrivSqZeroExt.fstClm;
• TrivSqZeroExt.sndClm → TrivSqZeroExt.sndCLM;
• TrivSqZeroExt.inlClm → TrivSqZeroExt.inlCLM;
• TrivSqZeroExt.inrClm → TrivSqZeroExt.inrCLM

and related theorems.

@@ -22,11 +22,11 @@ The construction is done in four steps:
   is integrable and define a map `Set α → (E →L[ℝ] (α →₁[μ] E))` which to a set associates a linear
   map. That linear map sends `x ∈ E` to the conditional expectation of the indicator of the set
   with value `x`.
-* Extend that map to `condexpL1Clm : (α →₁[μ] E) →L[ℝ] (α →₁[μ] E)`. This is done using the same
+* Extend that map to `condexpL1CLM : (α →₁[μ] E) →L[ℝ] (α →₁[μ] E)`. This is done using the same
   construction as the Bochner integral (see the file `MeasureTheory/Integral/SetToL1`).
 * Define the conditional expectation of a function `f : α → E`, which is an integrable function
   `α → E` equal to 0 if `f` is not integrable, and equal to an `m`-measurable representative of
-  `condexpL1Clm` applied to `[f]`, the equivalence class of `f` in `L¹`.
+  `condexpL1CLM` applied to `[f]`, the equivalence class of `f` in `L¹`.
 
 The first step is done in `MeasureTheory.Function.ConditionalExpectation.CondexpL2`, the two
 next steps in `MeasureTheory.Function.ConditionalExpectation.CondexpL1` and the final step is
@@ -45,7 +45,7 @@ The conditional expectation and its properties
   `∫ x in s, condexp m μ f x ∂μ = ∫ x in s, f x ∂μ` for any `m`-measurable set `s`.
 
 While `condexp` is function-valued, we also define `condexpL1` with value in `L1` and a continuous
-linear map `condexpL1Clm` from `L1` to `L1`. `condexp` should be used in most cases.
+linear map `condexpL1CLM` from `L1` to `L1`. `condexp` should be used in most cases.
 
 Uniqueness of the conditional expectation
 
@@ -149,12 +149,12 @@ theorem condexp_ae_eq_condexpL1 (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)
 set_option linter.uppercaseLean3 false in
 #align measure_theory.condexp_ae_eq_condexp_L1 MeasureTheory.condexp_ae_eq_condexpL1
 
-theorem condexp_ae_eq_condexpL1Clm (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : Integrable f μ) :
-    μ[f|m] =ᵐ[μ] condexpL1Clm F' hm μ (hf.toL1 f) := by
+theorem condexp_ae_eq_condexpL1CLM (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : Integrable f μ) :
+    μ[f|m] =ᵐ[μ] condexpL1CLM F' hm μ (hf.toL1 f) := by
   refine' (condexp_ae_eq_condexpL1 hm f).trans (eventually_of_forall fun x => _)
   rw [condexpL1_eq hf]
 set_option linter.uppercaseLean3 false in
-#align measure_theory.condexp_ae_eq_condexp_L1_clm MeasureTheory.condexp_ae_eq_condexpL1Clm
+#align measure_theory.condexp_ae_eq_condexp_L1_clm MeasureTheory.condexp_ae_eq_condexpL1CLM
 
 theorem condexp_undef (hf : ¬Integrable f μ) : μ[f|m] = 0 := by
   by_cases hm : m ≤ m0

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

This has nice performance benefits.

@@ -71,7 +71,7 @@ open scoped ENNReal Topology BigOperators MeasureTheory
 
 namespace MeasureTheory
 
-variable {α F F' 𝕜 : Type _} {p : ℝ≥0∞} [IsROrC 𝕜]
+variable {α F F' 𝕜 : Type*} {p : ℝ≥0∞} [IsROrC 𝕜]
   -- 𝕜 for ℝ or ℂ
   -- F for a Lp submodule
   [NormedAddCommGroup F]
@@ -290,7 +290,7 @@ theorem condexp_add (hf : Integrable f μ) (hg : Integrable g μ) :
     ((condexp_ae_eq_condexpL1 hm _).symm.add (condexp_ae_eq_condexpL1 hm _).symm)
 #align measure_theory.condexp_add MeasureTheory.condexp_add
 
-theorem condexp_finset_sum {ι : Type _} {s : Finset ι} {f : ι → α → F'}
+theorem condexp_finset_sum {ι : Type*} {s : Finset ι} {f : ι → α → F'}
     (hf : ∀ i ∈ s, Integrable (f i) μ) : μ[∑ i in s, f i|m] =ᵐ[μ] ∑ i in s, μ[f i|m] := by
   induction' s using Finset.induction_on with i s his heq hf
   · rw [Finset.sum_empty, Finset.sum_empty, condexp_zero]

Assume NeZero μ instead of μ.ae.NeBot everywhere, and sometimes instead of μ ≠ 0.

API changes

• Convex.average_mem, Convex.set_average_mem, ConvexOn.average_mem_epigraph, ConcaveOn.average_mem_hypograph, ConvexOn.map_average_le, ConcaveOn.le_map_average: assume [NeZero μ] instead of μ ≠ 0;
• MeasureTheory.condexp_bot', essSup_const', essInf_const', MeasureTheory.laverage_const, MeasureTheory.laverage_one, MeasureTheory.average_const: assume [NeZero μ] instead of [μ.ae.NeBot]
• MeasureTheory.Measure.measure_ne_zero: replace with an instance;
• remove @[simp] from MeasureTheory.ae_restrict_neBot, use ≠ 0 in the RHS;
• turn MeasureTheory.IsProbabilityMeasure.ae_neBot into a theorem because inferInstance can find it now;
• add instances:
  • [NeZero μ] : NeZero (μ univ);
  • [NeZero (μ s)] : NeZero (μ.restrict s);
  • [NeZero μ] : μ.ae.NeBot;
  • [IsProbabilityMeasure μ] : NeZero μ;
  • [IsFiniteMeasure μ] [NeZero μ] : IsProbabilityMeasure ((μ univ)⁻¹ • μ) this was a theorem MeasureTheory.isProbabilityMeasureSmul assuming μ ≠ 0;

@@ -245,7 +245,7 @@ theorem ae_eq_condexp_of_forall_set_integral_eq (hm : m ≤ m0) [SigmaFinite (μ
   rw [hg_eq s hs hμs, set_integral_condexp hm hf hs]
 #align measure_theory.ae_eq_condexp_of_forall_set_integral_eq MeasureTheory.ae_eq_condexp_of_forall_set_integral_eq
 
-theorem condexp_bot' [hμ : μ.ae.NeBot] (f : α → F') :
+theorem condexp_bot' [hμ : NeZero μ] (f : α → F') :
     μ[f|⊥] = fun _ => (μ Set.univ).toReal⁻¹ • ∫ x, f x ∂μ := by
   by_cases hμ_finite : IsFiniteMeasure μ
   swap
@@ -254,7 +254,6 @@ theorem condexp_bot' [hμ : μ.ae.NeBot] (f : α → F') :
     rw [condexp_of_not_sigmaFinite bot_le h]
     simp only [hμ_finite, ENNReal.top_toReal, inv_zero, zero_smul]
     rfl
-  haveI : IsFiniteMeasure μ := hμ_finite
   by_cases hf : Integrable f μ
   swap; · rw [integral_undef hf, smul_zero, condexp_undef hf]; rfl
   have h_meas : StronglyMeasurable[⊥] (μ[f|⊥]) := stronglyMeasurable_condexp
@@ -263,18 +262,15 @@ theorem condexp_bot' [hμ : μ.ae.NeBot] (f : α → F') :
   have h_integral : ∫ x, (μ[f|⊥]) x ∂μ = ∫ x, f x ∂μ := integral_condexp bot_le hf
   simp_rw [h_eq, integral_const] at h_integral
   rw [← h_integral, ← smul_assoc, smul_eq_mul, inv_mul_cancel, one_smul]
-  rw [Ne.def, ENNReal.toReal_eq_zero_iff, Measure.measure_univ_eq_zero, ← ae_eq_bot, not_or,
-    ← Ne.def, ← neBot_iff]
-  exact ⟨hμ, measure_ne_top μ Set.univ⟩
+  rw [Ne.def, ENNReal.toReal_eq_zero_iff, not_or]
+  exact ⟨NeZero.ne _, measure_ne_top μ Set.univ⟩
 #align measure_theory.condexp_bot' MeasureTheory.condexp_bot'
 
 theorem condexp_bot_ae_eq (f : α → F') :
     μ[f|⊥] =ᵐ[μ] fun _ => (μ Set.univ).toReal⁻¹ • ∫ x, f x ∂μ := by
-  by_cases μ.ae.NeBot
-  · refine' eventually_of_forall fun x => _
-    rw [condexp_bot' f]
-  · rw [neBot_iff, Classical.not_not, ae_eq_bot] at h
-    simp only [h, ae_zero]; norm_cast
+  rcases eq_zero_or_neZero μ with rfl | hμ
+  · rw [ae_zero]; exact eventually_bot
+  · exact eventually_of_forall <| congr_fun (condexp_bot' f)
 #align measure_theory.condexp_bot_ae_eq MeasureTheory.condexp_bot_ae_eq
 
 theorem condexp_bot [IsProbabilityMeasure μ] (f : α → F') : μ[f|⊥] = fun _ => ∫ x, f x ∂μ := by

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 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.basic
-! 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.ConditionalExpectation.CondexpL1
 
+#align_import measure_theory.function.conditional_expectation.basic from "leanprover-community/mathlib"@"d8bbb04e2d2a44596798a9207ceefc0fb236e41e"
+
 /-! # Conditional expectation
 
 We build the conditional expectation of an integrable function `f` with value in a Banach space

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -230,7 +230,7 @@ theorem set_integral_condexp (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hf : In
 theorem integral_condexp (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] (hf : Integrable f μ) :
     ∫ x, (μ[f|m]) x ∂μ = ∫ x, f x ∂μ := by
   suffices ∫ x in Set.univ, (μ[f|m]) x ∂μ = ∫ x in Set.univ, f x ∂μ by
-    simp_rw [integral_univ] at this ; exact this
+    simp_rw [integral_univ] at this; exact this
   exact set_integral_condexp hm hf (@MeasurableSet.univ _ m)
 #align measure_theory.integral_condexp MeasureTheory.integral_condexp
 

@@ -203,12 +203,12 @@ theorem condexp_congr_ae (h : f =ᵐ[μ] g) : μ[f|m] =ᵐ[μ] μ[g|m] := by
       (condexp_ae_eq_condexpL1 hm g).symm)
 #align measure_theory.condexp_congr_ae MeasureTheory.condexp_congr_ae
 
-theorem condexp_of_aEStronglyMeasurable' (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] {f : α → F'}
+theorem condexp_of_aestronglyMeasurable' (hm : m ≤ m0) [hμm : SigmaFinite (μ.trim hm)] {f : α → F'}
     (hf : AEStronglyMeasurable' m f μ) (hfi : Integrable f μ) : μ[f|m] =ᵐ[μ] f := by
   refine' ((condexp_congr_ae hf.ae_eq_mk).trans _).trans hf.ae_eq_mk.symm
   rw [condexp_of_stronglyMeasurable hm hf.stronglyMeasurable_mk
     ((integrable_congr hf.ae_eq_mk).mp hfi)]
-#align measure_theory.condexp_of_ae_strongly_measurable' MeasureTheory.condexp_of_aEStronglyMeasurable'
+#align measure_theory.condexp_of_ae_strongly_measurable' MeasureTheory.condexp_of_aestronglyMeasurable'
 
 theorem integrable_condexp : Integrable (μ[f|m]) μ := by
   by_cases hm : m ≤ m0