measure_theory.function.conditional_expectation.condexp_L1 ⟷ Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

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

@@ -391,15 +391,15 @@ theorem dominatedFinMeasAdditive_condexpInd (hm : m ≤ m0) (μ : Measure α)
 
 variable {G}
 
-#print MeasureTheory.set_integral_condexpInd /-
-theorem set_integral_condexpInd (hs : measurable_set[m] s) (ht : MeasurableSet t) (hμs : μ s ≠ ∞)
+#print MeasureTheory.setIntegral_condexpInd /-
+theorem setIntegral_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)
+      setIntegral_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
+    _ = (μ (t ∩ s)).toReal • x := setIntegral_condexpIndSMul hs ht hμs hμt x
+#align measure_theory.set_integral_condexp_ind MeasureTheory.setIntegral_condexpInd
 -/
 
 #print MeasureTheory.condexpInd_of_measurable /-
@@ -465,9 +465,9 @@ theorem condexpL1CLM_indicatorConst (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
 #align measure_theory.condexp_L1_clm_indicator_const MeasureTheory.condexpL1CLM_indicatorConst
 -/
 
-#print MeasureTheory.set_integral_condexpL1CLM_of_measure_ne_top /-
+#print MeasureTheory.setIntegral_condexpL1CLM_of_measure_ne_top /-
 /-- 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)
+theorem setIntegral_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'
@@ -492,14 +492,14 @@ theorem set_integral_condexpL1CLM_of_measure_ne_top (f : α →₁[μ] F') (hs :
       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
+#align measure_theory.set_integral_condexp_L1_clm_of_measure_ne_top MeasureTheory.setIntegral_condexpL1CLM_of_measure_ne_top
 -/
 
-#print MeasureTheory.set_integral_condexpL1CLM /-
+#print MeasureTheory.setIntegral_condexpL1CLM /-
 /-- 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) :
+theorem setIntegral_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)
@@ -539,7 +539,7 @@ theorem set_integral_condexpL1CLM (f : α →₁[μ] F') (hs : measurable_set[m]
     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
+#align measure_theory.set_integral_condexp_L1_clm MeasureTheory.setIntegral_condexpL1CLM
 -/
 
 #print MeasureTheory.aestronglyMeasurable'_condexpL1CLM /-
@@ -662,17 +662,17 @@ theorem integrable_condexpL1 (f : α → F') : Integrable (condexpL1 hm μ f) μ
 #align measure_theory.integrable_condexp_L1 MeasureTheory.integrable_condexpL1
 -/
 
-#print MeasureTheory.set_integral_condexpL1 /-
+#print MeasureTheory.setIntegral_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) :
+theorem setIntegral_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
+#align measure_theory.set_integral_condexp_L1 MeasureTheory.setIntegral_condexpL1
 -/
 
 #print MeasureTheory.condexpL1_add /-

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

@@ -40,7 +40,7 @@ open scoped NNReal ENNReal Topology BigOperators MeasureTheory
 
 namespace MeasureTheory
 
-variable {α β F F' G G' 𝕜 : Type _} {p : ℝ≥0∞} [IsROrC 𝕜]
+variable {α β F F' G G' 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

@@ -512,7 +512,7 @@ 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
@@ -528,7 +528,7 @@ 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)) :=
@@ -536,8 +536,8 @@ 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
 -/

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

@@ -359,7 +359,7 @@ theorem norm_condexpInd_apply_le (x : G) : ‖condexpInd hm μ s x‖ ≤ (μ s)
 
 #print MeasureTheory.norm_condexpInd_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.opNorm_le_bound _ ENNReal.toReal_nonneg norm_condexpInd_apply_le
 #align measure_theory.norm_condexp_ind_le MeasureTheory.norm_condexpInd_le
 -/
 

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

@@ -435,40 +435,40 @@ section CondexpL1
 variable {m m0 : MeasurableSpace α} {μ : Measure α} {hm : m ≤ m0} [SigmaFinite (μ.trim hm)]
   {f g : α → F'} {s : Set α}
 
-#print MeasureTheory.condexpL1Clm /-
+#print MeasureTheory.condexpL1CLM /-
 /-- 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)] :
+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
+#align measure_theory.condexp_L1_clm MeasureTheory.condexpL1CLM
 -/
 
-#print MeasureTheory.condexpL1Clm_smul /-
-theorem condexpL1Clm_smul (c : 𝕜) (f : α →₁[μ] F') :
-    condexpL1Clm hm μ (c • f) = c • condexpL1Clm hm μ f :=
+#print MeasureTheory.condexpL1CLM_smul /-
+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
+#align measure_theory.condexp_L1_clm_smul MeasureTheory.condexpL1CLM_smul
 -/
 
-#print MeasureTheory.condexpL1Clm_indicatorConstLp /-
-theorem condexpL1Clm_indicatorConstLp (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : F') :
-    (condexpL1Clm hm μ) (indicatorConstLp 1 hs hμs x) = condexpInd hm μ s x :=
+#print MeasureTheory.condexpL1CLM_indicatorConstLp /-
+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
+#align measure_theory.condexp_L1_clm_indicator_const_Lp MeasureTheory.condexpL1CLM_indicatorConstLp
 -/
 
-#print MeasureTheory.condexpL1Clm_indicatorConst /-
-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
+#print MeasureTheory.condexpL1CLM_indicatorConst /-
+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
+#align measure_theory.condexp_L1_clm_indicator_const MeasureTheory.condexpL1CLM_indicatorConst
 -/
 
-#print MeasureTheory.set_integral_condexpL1Clm_of_measure_ne_top /-
+#print MeasureTheory.set_integral_condexpL1CLM_of_measure_ne_top /-
 /-- 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 :=
+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
@@ -492,15 +492,15 @@ theorem set_integral_condexpL1Clm_of_measure_ne_top (f : α →₁[μ] F') (hs :
       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
+#align measure_theory.set_integral_condexp_L1_clm_of_measure_ne_top MeasureTheory.set_integral_condexpL1CLM_of_measure_ne_top
 -/
 
-#print MeasureTheory.set_integral_condexpL1Clm /-
+#print MeasureTheory.set_integral_condexpL1CLM /-
 /-- 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 :=
+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)
@@ -539,12 +539,12 @@ theorem set_integral_condexpL1Clm (f : α →₁[μ] F') (hs : measurable_set[m]
     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
+#align measure_theory.set_integral_condexp_L1_clm MeasureTheory.set_integral_condexpL1CLM
 -/
 
-#print MeasureTheory.aestronglyMeasurable'_condexpL1Clm /-
-theorem aestronglyMeasurable'_condexpL1Clm (f : α →₁[μ] F') :
-    AEStronglyMeasurable' m (condexpL1Clm hm μ f) μ :=
+#print MeasureTheory.aestronglyMeasurable'_condexpL1CLM /-
+theorem aestronglyMeasurable'_condexpL1CLM (f : α →₁[μ] F') :
+    AEStronglyMeasurable' m (condexpL1CLM hm μ f) μ :=
   by
   refine'
     Lp.induction ENNReal.one_ne_top
@@ -563,11 +563,11 @@ 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
 -/
 
-#print MeasureTheory.condexpL1Clm_lpMeas /-
-theorem condexpL1Clm_lpMeas (f : lpMeas F' ℝ m 1 μ) : condexpL1Clm hm μ (f : α →₁[μ] F') = ↑f :=
+#print MeasureTheory.condexpL1CLM_lpMeas /-
+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
@@ -592,14 +592,14 @@ theorem condexpL1Clm_lpMeas (f : lpMeas F' ℝ m 1 μ) : condexpL1Clm hm μ (f :
       exact LinearIsometryEquiv.continuous _
     · refine' continuous_induced_dom.comp _
       exact LinearIsometryEquiv.continuous _
-#align measure_theory.condexp_L1_clm_Lp_meas MeasureTheory.condexpL1Clm_lpMeas
+#align measure_theory.condexp_L1_clm_Lp_meas MeasureTheory.condexpL1CLM_lpMeas
 -/
 
-#print MeasureTheory.condexpL1Clm_of_aestronglyMeasurable' /-
-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'
+#print MeasureTheory.condexpL1CLM_of_aestronglyMeasurable' /-
+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'
 -/
 
 #print MeasureTheory.condexpL1 /-
@@ -617,7 +617,7 @@ theorem condexpL1_undef (hf : ¬Integrable f μ) : condexpL1 hm μ f = 0 :=
 -/
 
 #print MeasureTheory.condexpL1_eq /-
-theorem condexpL1_eq (hf : Integrable f μ) : condexpL1 hm μ f = condexpL1Clm hm μ (hf.toL1 f) :=
+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
 -/

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

@@ -375,7 +375,7 @@ 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
+  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
 -/
 

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.CondexpL2
+import MeasureTheory.Function.ConditionalExpectation.CondexpL2
 
 #align_import measure_theory.function.conditional_expectation.condexp_L1 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.condexp_L1
-! 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.CondexpL2
 
+#align_import measure_theory.function.conditional_expectation.condexp_L1 from "leanprover-community/mathlib"@"e160cefedc932ce41c7049bf0c4b0f061d06216e"
+
 /-! # Conditional expectation in L1
 
 > 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.condexp_L1
-! 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.CondexpL2
 
 /-! # Conditional expectation in L1
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains two more steps of the construction of the conditional expectation, which is
 completed in `measure_theory.function.conditional_expectation.basic`. See that file for a
 description of the full process.

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

@@ -69,21 +69,26 @@ variable {m m0 : MeasurableSpace α} {μ : Measure α} {s t : Set α} [NormedSpa
 
 section CondexpIndL1Fin
 
+#print MeasureTheory.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 _
+  (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)]
+#print MeasureTheory.condexpIndL1Fin_ae_eq_condexpIndSMul /-
+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
+    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)]
 
+#print MeasureTheory.condexpIndL1Fin_add /-
 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
@@ -97,7 +102,9 @@ theorem condexpIndL1Fin_add (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x y :
   refine' (Lp.coe_fn_add _ _).trans (eventually_of_forall fun a => _)
   rfl
 #align measure_theory.condexp_ind_L1_fin_add MeasureTheory.condexpIndL1Fin_add
+-/
 
+#print MeasureTheory.condexpIndL1Fin_smul /-
 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
@@ -109,7 +116,9 @@ theorem condexpIndL1Fin_smul (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (c : 
   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
+-/
 
+#print 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 :=
@@ -122,7 +131,9 @@ theorem condexpIndL1Fin_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (hs
   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'
+-/
 
+#print MeasureTheory.norm_condexpIndL1Fin_le /-
 theorem norm_condexpIndL1Fin_le (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :
     ‖condexpIndL1Fin hm hs hμs x‖ ≤ (μ s).toReal * ‖x‖ :=
   by
@@ -143,7 +154,9 @@ theorem norm_condexpIndL1Fin_le (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x
   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
+-/
 
+#print MeasureTheory.condexpIndL1Fin_disjoint_union /-
 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)
@@ -169,6 +182,7 @@ theorem condexpIndL1Fin_disjoint_union (hs : MeasurableSet s) (ht : MeasurableSe
   refine' eventually_of_forall fun y => _
   rfl
 #align measure_theory.condexp_ind_L1_fin_disjoint_union MeasureTheory.condexpIndL1Fin_disjoint_union
+-/
 
 end CondexpIndL1Fin
 
@@ -176,30 +190,39 @@ open scoped Classical
 
 section CondexpIndL1
 
+#print MeasureTheory.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)]
 
+#print MeasureTheory.condexpIndL1_of_measurableSet_of_measure_ne_top /-
 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
+-/
 
+#print MeasureTheory.condexpIndL1_of_measure_eq_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
+-/
 
+#print MeasureTheory.condexpIndL1_of_not_measurableSet /-
 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
+-/
 
+#print MeasureTheory.condexpIndL1_add /-
 theorem condexpIndL1_add (x y : G) :
     condexpIndL1 hm μ s (x + y) = condexpIndL1 hm μ s x + condexpIndL1 hm μ s y :=
   by
@@ -210,7 +233,9 @@ theorem condexpIndL1_add (x y : G) :
   · 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
+-/
 
+#print MeasureTheory.condexpIndL1_smul /-
 theorem condexpIndL1_smul (c : ℝ) (x : G) :
     condexpIndL1 hm μ s (c • x) = c • condexpIndL1 hm μ s x :=
   by
@@ -221,7 +246,9 @@ theorem condexpIndL1_smul (c : ℝ) (x : G) :
   · 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
+-/
 
+#print 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
@@ -232,7 +259,9 @@ theorem condexpIndL1_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (c : 
   · 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'
+-/
 
+#print MeasureTheory.norm_condexpIndL1_le /-
 theorem norm_condexpIndL1_le (x : G) : ‖condexpIndL1 hm μ s x‖ ≤ (μ s).toReal * ‖x‖ :=
   by
   by_cases hs : MeasurableSet s
@@ -245,11 +274,15 @@ theorem norm_condexpIndL1_le (x : G) : ‖condexpIndL1 hm μ s x‖ ≤ (μ s).t
   · 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
+-/
 
+#print MeasureTheory.continuous_condexpIndL1 /-
 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
+-/
 
+#print MeasureTheory.condexpIndL1_disjoint_union /-
 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 :=
@@ -261,9 +294,11 @@ theorem condexpIndL1_disjoint_union (hs : MeasurableSet s) (ht : MeasurableSet t
     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
 
+#print MeasureTheory.condexpInd /-
 /-- 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
@@ -273,23 +308,29 @@ def condexpInd {m m0 : MeasurableSpace α} (hm : m ≤ m0) (μ : Measure α) [Si
   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)]
+#print MeasureTheory.condexpInd_ae_eq_condexpIndSMul /-
+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 :=
+    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
+#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) :
+#print MeasureTheory.aestronglyMeasurable'_condexpInd /-
+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
+  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
+-/
 
+#print MeasureTheory.condexpInd_empty /-
 @[simp]
 theorem condexpInd_empty : condexpInd hm μ ∅ = (0 : G →L[ℝ] α →₁[μ] G) :=
   by
@@ -301,51 +342,67 @@ theorem condexpInd_empty : condexpInd hm μ ∅ = (0 : G →L[ℝ] α →₁[μ]
   refine' eventually_eq.trans _ (Lp.coe_fn_zero G 1 μ).symm
   rfl
 #align measure_theory.condexp_ind_empty MeasureTheory.condexpInd_empty
+-/
 
+#print MeasureTheory.condexpInd_smul' /-
 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'
+-/
 
+#print MeasureTheory.norm_condexpInd_apply_le /-
 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
+-/
 
+#print MeasureTheory.norm_condexpInd_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
+-/
 
+#print MeasureTheory.condexpInd_disjoint_union_apply /-
 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
+-/
 
+#print MeasureTheory.condexpInd_disjoint_union /-
 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)
 
+#print MeasureTheory.dominatedFinMeasAdditive_condexpInd /-
 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}
 
+#print MeasureTheory.set_integral_condexpInd /-
 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 :=
+    ∫ 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
+        ((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
+-/
 
+#print MeasureTheory.condexpInd_of_measurable /-
 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
@@ -359,7 +416,9 @@ theorem condexpInd_of_measurable (hs : measurable_set[m] s) (hμs : μ s ≠ ∞
   rw [hx]
   by_cases hx_mem : x ∈ s <;> simp [hx_mem]
 #align measure_theory.condexp_ind_of_measurable MeasureTheory.condexpInd_of_measurable
+-/
 
+#print MeasureTheory.condexpInd_nonneg /-
 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
@@ -367,6 +426,7 @@ theorem condexpInd_nonneg {E} [NormedLatticeAddCommGroup E] [NormedSpace ℝ E]
   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
 
@@ -375,28 +435,37 @@ section CondexpL1
 variable {m m0 : MeasurableSpace α} {μ : Measure α} {hm : m ≤ m0} [SigmaFinite (μ.trim hm)]
   {f g : α → F'} {s : Set α}
 
+#print MeasureTheory.condexpL1Clm /-
 /-- 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
+-/
 
+#print MeasureTheory.condexpL1Clm_smul /-
 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
+-/
 
+#print MeasureTheory.condexpL1Clm_indicatorConstLp /-
 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
+-/
 
+#print MeasureTheory.condexpL1Clm_indicatorConst /-
 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
+-/
 
+#print MeasureTheory.set_integral_condexpL1Clm_of_measure_ne_top /-
 /-- 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 :=
@@ -424,7 +493,9 @@ theorem set_integral_condexpL1Clm_of_measure_ne_top (f : α →₁[μ] F') (hs :
   · 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
+-/
 
+#print MeasureTheory.set_integral_condexpL1Clm /-
 /-- 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`. -/
@@ -469,8 +540,10 @@ theorem set_integral_condexpL1Clm (f : α →₁[μ] F') (hs : measurable_set[m]
   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') :
+#print MeasureTheory.aestronglyMeasurable'_condexpL1Clm /-
+theorem aestronglyMeasurable'_condexpL1Clm (f : α →₁[μ] F') :
     AEStronglyMeasurable' m (condexpL1Clm hm μ f) μ :=
   by
   refine'
@@ -490,8 +563,10 @@ 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
+-/
 
+#print MeasureTheory.condexpL1Clm_lpMeas /-
 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
@@ -518,37 +593,51 @@ theorem condexpL1Clm_lpMeas (f : lpMeas F' ℝ m 1 μ) : condexpL1Clm hm μ (f :
     · 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) :
+#print MeasureTheory.condexpL1Clm_of_aestronglyMeasurable' /-
+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'
+#align measure_theory.condexp_L1_clm_of_ae_strongly_measurable' MeasureTheory.condexpL1Clm_of_aestronglyMeasurable'
+-/
 
+#print MeasureTheory.condexpL1 /-
 /-- 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
+-/
 
+#print MeasureTheory.condexpL1_undef /-
 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
+-/
 
+#print MeasureTheory.condexpL1_eq /-
 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
+-/
 
+#print MeasureTheory.condexpL1_zero /-
 @[simp]
 theorem condexpL1_zero : condexpL1 hm μ (0 : α → F') = 0 :=
   setToFun_zero _
 #align measure_theory.condexp_L1_zero MeasureTheory.condexpL1_zero
+-/
 
+#print MeasureTheory.condexpL1_measure_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'} :
+#print MeasureTheory.aestronglyMeasurable'_condexpL1 /-
+theorem aestronglyMeasurable'_condexpL1 {f : α → F'} :
     AEStronglyMeasurable' m (condexpL1 hm μ f) μ :=
   by
   by_cases hf : integrable f μ
@@ -557,17 +646,23 @@ 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
+-/
 
+#print MeasureTheory.condexpL1_congr_ae /-
 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
+-/
 
+#print MeasureTheory.integrable_condexpL1 /-
 theorem integrable_condexpL1 (f : α → F') : Integrable (condexpL1 hm μ f) μ :=
   L1.integrable_coeFn _
 #align measure_theory.integrable_condexp_L1 MeasureTheory.integrable_condexpL1
+-/
 
+#print MeasureTheory.set_integral_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`. -/
@@ -578,34 +673,46 @@ theorem set_integral_condexpL1 (hf : Integrable f μ) (hs : measurable_set[m] s)
   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
+-/
 
+#print MeasureTheory.condexpL1_add /-
 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
+-/
 
+#print MeasureTheory.condexpL1_neg /-
 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
+-/
 
+#print MeasureTheory.condexpL1_smul /-
 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
+-/
 
+#print MeasureTheory.condexpL1_sub /-
 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)
+#print MeasureTheory.condexpL1_of_aestronglyMeasurable' /-
+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'
+#align measure_theory.condexp_L1_of_ae_strongly_measurable' MeasureTheory.condexpL1_of_aestronglyMeasurable'
+-/
 
+#print MeasureTheory.condexpL1_mono /-
 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 :=
@@ -615,6 +722,7 @@ theorem condexpL1_mono {E} [NormedLatticeAddCommGroup E] [CompleteSpace E] [Norm
     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
 

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

@@ -284,11 +284,11 @@ 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) :
-    AeStronglyMeasurable' m (condexpInd hm μ s x) μ :=
-  AeStronglyMeasurable'.congr (aeStronglyMeasurable'_condexpIndSmul hm hs hμs x)
+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
+#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) :=
@@ -470,8 +470,8 @@ 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') :
-    AeStronglyMeasurable' m (condexpL1Clm hm μ f) μ :=
+theorem aEStronglyMeasurable'_condexpL1Clm (f : α →₁[μ] F') :
+    AEStronglyMeasurable' m (condexpL1Clm hm μ f) μ :=
   by
   refine'
     Lp.induction ENNReal.one_ne_top
@@ -490,7 +490,7 @@ 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
@@ -519,10 +519,10 @@ theorem condexpL1Clm_lpMeas (f : lpMeas F' ℝ m 1 μ) : condexpL1Clm hm μ (f :
       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) :
+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'
+#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. -/
@@ -548,8 +548,8 @@ 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'} :
-    AeStronglyMeasurable' m (condexpL1 hm μ f) μ :=
+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]
@@ -557,7 +557,7 @@ 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 :=
@@ -597,14 +597,14 @@ theorem condexpL1_sub (hf : Integrable f μ) (hg : Integrable g μ) :
   setToFun_sub _ hf hg
 #align measure_theory.condexp_L1_sub MeasureTheory.condexpL1_sub
 
-theorem condexpL1_of_aeStronglyMeasurable' (hfm : AeStronglyMeasurable' m f μ)
+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'
+#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) :

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

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

@@ -332,14 +332,18 @@ theorem dominatedFinMeasAdditive_condexpInd (hm : m ≤ m0) (μ : Measure α)
 
 variable {G}
 
-theorem set_integral_condexpInd (hs : MeasurableSet[m] s) (ht : MeasurableSet t) (hμs : μ s ≠ ∞)
+theorem setIntegral_condexpInd (hs : MeasurableSet[m] s) (ht : MeasurableSet t) (hμs : μ s ≠ ∞)
     (hμt : μ t ≠ ∞) (x : G') : ∫ a in s, condexpInd G' hm μ t x a ∂μ = (μ (t ∩ s)).toReal • x :=
   calc
     ∫ a in s, condexpInd G' hm μ t x a ∂μ = ∫ a in s, condexpIndSMul hm ht hμt x a ∂μ :=
-      set_integral_congr_ae (hm s hs)
+      setIntegral_congr_ae (hm s hs)
         ((condexpInd_ae_eq_condexpIndSMul hm ht hμt x).mono fun _ hx _ => 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
+    _ = (μ (t ∩ s)).toReal • x := setIntegral_condexpIndSMul hs ht hμs hμt x
+#align measure_theory.set_integral_condexp_ind MeasureTheory.setIntegral_condexpInd
+
+@[deprecated]
+alias set_integral_condexpInd :=
+  setIntegral_condexpInd -- deprecated on 2024-04-17
 
 theorem condexpInd_of_measurable (hs : MeasurableSet[m] s) (hμs : μ s ≠ ∞) (c : G) :
     condexpInd G hm μ s c = indicatorConstLp 1 (hm s hs) hμs c := by
@@ -398,34 +402,38 @@ theorem condexpL1CLM_indicatorConst (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
   rw [Lp.simpleFunc.coe_indicatorConst]; exact condexpL1CLM_indicatorConstLp hs hμs x
 #align measure_theory.condexp_L1_clm_indicator_const MeasureTheory.condexpL1CLM_indicatorConst
 
-/-- Auxiliary lemma used in the proof of `set_integral_condexpL1CLM`. -/
-theorem set_integral_condexpL1CLM_of_measure_ne_top (f : α →₁[μ] F') (hs : MeasurableSet[m] s)
+/-- Auxiliary lemma used in the proof of `setIntegral_condexpL1CLM`. -/
+theorem setIntegral_condexpL1CLM_of_measure_ne_top (f : α →₁[μ] F') (hs : MeasurableSet[m] s)
     (hμs : μ s ≠ ∞) : ∫ x in s, condexpL1CLM F' 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, condexpL1CLM F' hm μ f x ∂μ = ∫ x in s, f x ∂μ) _ _
     (isClosed_eq _ _) f
   · intro x t ht hμt
     simp_rw [condexpL1CLM_indicatorConst ht hμt.ne x]
-    rw [Lp.simpleFunc.coe_indicatorConst, set_integral_indicatorConstLp (hm _ hs)]
-    exact set_integral_condexpInd hs ht hμs hμt.ne x
+    rw [Lp.simpleFunc.coe_indicatorConst, setIntegral_indicatorConstLp (hm _ hs)]
+    exact setIntegral_condexpInd hs ht hμs hμt.ne x
   · intro f g hf_Lp hg_Lp _ hf hg
     simp_rw [(condexpL1CLM F' hm μ).map_add]
-    rw [set_integral_congr_ae (hm s hs) ((Lp.coeFn_add (condexpL1CLM F' hm μ (hf_Lp.toLp f))
+    rw [setIntegral_congr_ae (hm s hs) ((Lp.coeFn_add (condexpL1CLM F' hm μ (hf_Lp.toLp f))
       (condexpL1CLM F' hm μ (hg_Lp.toLp g))).mono fun x hx _ => hx)]
-    rw [set_integral_congr_ae (hm s hs)
+    rw [setIntegral_congr_ae (hm s hs)
       ((Lp.coeFn_add (hf_Lp.toLp f) (hg_Lp.toLp g)).mono fun x hx _ => hx)]
     simp_rw [Pi.add_apply]
     rw [integral_add (L1.integrable_coeFn _).integrableOn (L1.integrable_coeFn _).integrableOn,
       integral_add (L1.integrable_coeFn _).integrableOn (L1.integrable_coeFn _).integrableOn, hf,
       hg]
-  · exact (continuous_set_integral s).comp (condexpL1CLM F' 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
+  · exact (continuous_setIntegral s).comp (condexpL1CLM F' hm μ).continuous
+  · exact continuous_setIntegral s
+#align measure_theory.set_integral_condexp_L1_clm_of_measure_ne_top MeasureTheory.setIntegral_condexpL1CLM_of_measure_ne_top
+
+@[deprecated]
+alias set_integral_condexpL1CLM_of_measure_ne_top :=
+  setIntegral_condexpL1CLM_of_measure_ne_top -- deprecated on 2024-04-17
 
 /-- The integral of the conditional expectation `condexpL1CLM` over an `m`-measurable set is equal
-to the integral of `f` on that set. See also `set_integral_condexp`, the similar statement for
+to the integral of `f` on that set. See also `setIntegral_condexp`, the similar statement for
 `condexp`. -/
-theorem set_integral_condexpL1CLM (f : α →₁[μ] F') (hs : MeasurableSet[m] s) :
+theorem setIntegral_condexpL1CLM (f : α →₁[μ] F') (hs : MeasurableSet[m] s) :
     ∫ x in s, condexpL1CLM F' hm μ f x ∂μ = ∫ x in s, f x ∂μ := by
   let S := spanningSets (μ.trim hm)
   have hS_meas : ∀ i, MeasurableSet[m] (S i) := measurable_spanningSets (μ.trim hm)
@@ -444,21 +452,25 @@ theorem set_integral_condexpL1CLM (f : α →₁[μ] F') (hs : MeasurableSet[m]
   have h_eq_forall :
     (fun i => ∫ x in S i ∩ s, condexpL1CLM F' hm μ f x ∂μ) = fun i => ∫ x in S i ∩ s, f x ∂μ :=
     funext fun i =>
-      set_integral_condexpL1CLM_of_measure_ne_top f (@MeasurableSet.inter α m _ _ (hS_meas i) hs)
+      setIntegral_condexpL1CLM_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) atTop (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
+      tendsto_setIntegral_of_monotone (fun i => (hS_meas0 i).inter (hm s hs)) h_mono
         (L1.integrable_coeFn f).integrableOn
     rwa [← hs_eq] at h
   have h_left : Tendsto (fun i => ∫ x in S i ∩ s, condexpL1CLM F' hm μ f x ∂μ) atTop
       (𝓝 (∫ x in s, condexpL1CLM F' hm μ f x ∂μ)) := by
-    have h := tendsto_set_integral_of_monotone (fun i => (hS_meas0 i).inter (hm s hs)) h_mono
+    have h := tendsto_setIntegral_of_monotone (fun i => (hS_meas0 i).inter (hm s hs)) h_mono
       (L1.integrable_coeFn (condexpL1CLM F' 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
+#align measure_theory.set_integral_condexp_L1_clm MeasureTheory.setIntegral_condexpL1CLM
+
+@[deprecated]
+alias set_integral_condexpL1CLM :=
+  setIntegral_condexpL1CLM -- deprecated on 2024-04-17
 
 theorem aestronglyMeasurable'_condexpL1CLM (f : α →₁[μ] F') :
     AEStronglyMeasurable' m (condexpL1CLM F' hm μ f) μ := by
@@ -551,14 +563,18 @@ theorem integrable_condexpL1 (f : α → F') : Integrable (condexpL1 hm μ f) μ
 #align measure_theory.integrable_condexp_L1 MeasureTheory.integrable_condexpL1
 
 /-- The integral of the conditional expectation `condexpL1` over an `m`-measurable set is equal to
-the integral of `f` on that set. See also `set_integral_condexp`, the similar statement for
+the integral of `f` on that set. See also `setIntegral_condexp`, the similar statement for
 `condexp`. -/
-theorem set_integral_condexpL1 (hf : Integrable f μ) (hs : MeasurableSet[m] s) :
+theorem setIntegral_condexpL1 (hf : Integrable f μ) (hs : MeasurableSet[m] s) :
     ∫ x in s, condexpL1 hm μ f x ∂μ = ∫ x in s, f x ∂μ := by
   simp_rw [condexpL1_eq hf]
-  rw [set_integral_condexpL1CLM (hf.toL1 f) hs]
-  exact set_integral_congr_ae (hm s hs) (hf.coeFn_toL1.mono fun x hx _ => hx)
-#align measure_theory.set_integral_condexp_L1 MeasureTheory.set_integral_condexpL1
+  rw [setIntegral_condexpL1CLM (hf.toL1 f) hs]
+  exact setIntegral_congr_ae (hm s hs) (hf.coeFn_toL1.mono fun x hx _ => hx)
+#align measure_theory.set_integral_condexp_L1 MeasureTheory.setIntegral_condexpL1
+
+@[deprecated]
+alias set_integral_condexpL1 :=
+  setIntegral_condexpL1 -- deprecated on 2024-04-17
 
 theorem condexpL1_add (hf : Integrable f μ) (hg : Integrable g μ) :
     condexpL1 hm μ (f + g) = condexpL1 hm μ f + condexpL1 hm μ g :=

@@ -184,11 +184,11 @@ 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 [condexpIndL1, And.intro hs hμs, dif_pos, Ne.def, not_false_iff, and_self_iff]
+  simp only [condexpIndL1, And.intro hs hμs, dif_pos, Ne, 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 [condexpIndL1, hμs, eq_self_iff_true, not_true, Ne.def, dif_neg, not_false_iff,
+  simp only [condexpIndL1, hμs, eq_self_iff_true, not_true, Ne, dif_neg, not_false_iff,
     and_false_iff]
 #align measure_theory.condexp_ind_L1_of_measure_eq_top MeasureTheory.condexpIndL1_of_measure_eq_top
 

Fixes #11441.

@@ -275,7 +275,7 @@ theorem condexpInd_ae_eq_condexpIndSMul (hm : m ≤ m0) [SigmaFinite (μ.trim hm
     (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :
     condexpInd G hm μ s x =ᵐ[μ] condexpIndSMul hm hs hμs x := by
   refine' EventuallyEq.trans _ (condexpIndL1Fin_ae_eq_condexpIndSMul hm hs hμs x)
-  simp [condexpInd, condexpIndL1, hs, hμs]; rfl
+  simp [condexpInd, condexpIndL1, 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)]

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.

@@ -37,7 +37,7 @@ open scoped NNReal ENNReal Topology BigOperators MeasureTheory
 
 namespace MeasureTheory
 
-variable {α β F F' G G' 𝕜 : Type*} {p : ℝ≥0∞} [IsROrC 𝕜]
+variable {α β F F' G G' 𝕜 : Type*} {p : ℝ≥0∞} [RCLike 𝕜]
   -- 𝕜 for ℝ or ℂ
   -- F for a Lp submodule
   [NormedAddCommGroup F]

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

@@ -127,8 +127,7 @@ theorem condexpIndL1Fin_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (hs
 
 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, ‖condexpIndL1Fin hm hs hμs x a‖ ∂μ :=
-    integral_nonneg fun a => norm_nonneg _
+  have : 0 ≤ ∫ a : α, ‖condexpIndL1Fin hm hs hμs x a‖ ∂μ := by positivity
   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),

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

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

@@ -163,8 +163,7 @@ theorem condexpIndL1Fin_disjoint_union (hs : MeasurableSet s) (ht : MeasurableSe
   push_cast
   rw [((toSpanSingleton ℝ x).compLpL 2 μ).map_add]
   refine' (Lp.coeFn_add _ _).trans _
-  refine' eventually_of_forall fun y => _
-  rfl
+  filter_upwards with y using rfl
 #align measure_theory.condexp_ind_L1_fin_disjoint_union MeasureTheory.condexpIndL1Fin_disjoint_union
 
 end CondexpIndL1Fin

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

@@ -484,7 +484,7 @@ theorem condexpL1CLM_lpMeas (f : lpMeas F' ℝ m 1 μ) :
     condexpL1CLM F' hm μ (f : α →₁[μ] F') = ↑f := by
   let g := lpMeasToLpTrimLie F' ℝ 1 μ hm f
   have hfg : f = (lpMeasToLpTrimLie F' ℝ 1 μ hm).symm g := by
-    simp only [LinearIsometryEquiv.symm_apply_apply]
+    simp only [g, 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' =>
     condexpL1CLM F' hm μ ((lpMeasToLpTrimLie F' ℝ 1 μ hm).symm g : α →₁[μ] F') =

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

@@ -110,7 +110,7 @@ theorem condexpIndL1Fin_smul (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (c : 
   rw [condexpIndSMul_smul hs hμs c x]
   refine' (Lp.coeFn_smul _ _).trans _
   refine' (condexpIndL1Fin_ae_eq_condexpIndSMul hm hs hμs x).mono fun y hy => _
-  rw [Pi.smul_apply, Pi.smul_apply, hy]
+  simp only [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)
@@ -122,7 +122,7 @@ theorem condexpIndL1Fin_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (hs
   rw [condexpIndSMul_smul' hs hμs c x]
   refine' (Lp.coeFn_smul _ _).trans _
   refine' (condexpIndL1Fin_ae_eq_condexpIndSMul hm hs hμs x).mono fun y hy => _
-  rw [Pi.smul_apply, Pi.smul_apply, hy]
+  simp only [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) :

Co-authored-by: adomani <adomani@gmail.com>

@@ -309,7 +309,7 @@ theorem norm_condexpInd_apply_le (x : G) : ‖condexpInd G hm μ s x‖ ≤ (μ
 #align measure_theory.norm_condexp_ind_apply_le MeasureTheory.norm_condexpInd_apply_le
 
 theorem norm_condexpInd_le : ‖(condexpInd G 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.opNorm_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)

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.

@@ -19,7 +19,7 @@ The contitional expectation of an `L²` function is defined in
   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`).
 
 ## Main definitions
@@ -372,63 +372,63 @@ set_option linter.uppercaseLean3 false
 variable {m m0 : MeasurableSpace α} {μ : Measure α} {hm : m ≤ m0} [SigmaFinite (μ.trim hm)]
   {f g : α → F'} {s : Set α}
 
--- Porting note: `F'` is not automatically inferred in `condexpL1Clm` in Lean 4;
+-- Porting note: `F'` is not automatically inferred in `condexpL1CLM` in Lean 4;
 -- to avoid repeatedly typing `(F' := ...)` it is made explicit.
 variable (F')
 
 /-- 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)] :
+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
+#align measure_theory.condexp_L1_clm MeasureTheory.condexpL1CLM
 
 variable {F'}
 
-theorem condexpL1Clm_smul (c : 𝕜) (f : α →₁[μ] F') :
-    condexpL1Clm F' hm μ (c • f) = c • condexpL1Clm F' hm μ f := by
+theorem condexpL1CLM_smul (c : 𝕜) (f : α →₁[μ] F') :
+    condexpL1CLM F' hm μ (c • f) = c • condexpL1CLM F' hm μ f := by
   refine' L1.setToL1_smul (dominatedFinMeasAdditive_condexpInd F' hm μ) _ c f
   exact fun c s x => condexpInd_smul' c x
-#align measure_theory.condexp_L1_clm_smul MeasureTheory.condexpL1Clm_smul
+#align measure_theory.condexp_L1_clm_smul MeasureTheory.condexpL1CLM_smul
 
-theorem condexpL1Clm_indicatorConstLp (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : F') :
-    (condexpL1Clm F' hm μ) (indicatorConstLp 1 hs hμs x) = condexpInd F' hm μ s x :=
+theorem condexpL1CLM_indicatorConstLp (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : F') :
+    (condexpL1CLM F' hm μ) (indicatorConstLp 1 hs hμs x) = condexpInd F' 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
+#align measure_theory.condexp_L1_clm_indicator_const_Lp MeasureTheory.condexpL1CLM_indicatorConstLp
 
-theorem condexpL1Clm_indicatorConst (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : F') :
-    (condexpL1Clm F' hm μ) ↑(simpleFunc.indicatorConst 1 hs hμs x) = condexpInd F' hm μ s x := by
-  rw [Lp.simpleFunc.coe_indicatorConst]; exact condexpL1Clm_indicatorConstLp hs hμs x
-#align measure_theory.condexp_L1_clm_indicator_const MeasureTheory.condexpL1Clm_indicatorConst
+theorem condexpL1CLM_indicatorConst (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : F') :
+    (condexpL1CLM F' hm μ) ↑(simpleFunc.indicatorConst 1 hs hμs x) = condexpInd F' hm μ s x := by
+  rw [Lp.simpleFunc.coe_indicatorConst]; exact condexpL1CLM_indicatorConstLp hs hμs x
+#align measure_theory.condexp_L1_clm_indicator_const MeasureTheory.condexpL1CLM_indicatorConst
 
-/-- Auxiliary lemma used in the proof of `set_integral_condexpL1Clm`. -/
-theorem set_integral_condexpL1Clm_of_measure_ne_top (f : α →₁[μ] F') (hs : MeasurableSet[m] s)
-    (hμs : μ s ≠ ∞) : ∫ x in s, condexpL1Clm F' hm μ f x ∂μ = ∫ x in s, f x ∂μ := by
+/-- Auxiliary lemma used in the proof of `set_integral_condexpL1CLM`. -/
+theorem set_integral_condexpL1CLM_of_measure_ne_top (f : α →₁[μ] F') (hs : MeasurableSet[m] s)
+    (hμs : μ s ≠ ∞) : ∫ x in s, condexpL1CLM F' 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, condexpL1Clm F' hm μ f x ∂μ = ∫ x in s, f x ∂μ) _ _
+    (fun f : α →₁[μ] F' => ∫ x in s, condexpL1CLM F' hm μ f x ∂μ = ∫ x in s, f x ∂μ) _ _
     (isClosed_eq _ _) f
   · intro x t ht hμt
-    simp_rw [condexpL1Clm_indicatorConst ht hμt.ne x]
+    simp_rw [condexpL1CLM_indicatorConst ht hμt.ne x]
     rw [Lp.simpleFunc.coe_indicatorConst, set_integral_indicatorConstLp (hm _ hs)]
     exact set_integral_condexpInd hs ht hμs hμt.ne x
   · intro f g hf_Lp hg_Lp _ hf hg
-    simp_rw [(condexpL1Clm F' hm μ).map_add]
-    rw [set_integral_congr_ae (hm s hs) ((Lp.coeFn_add (condexpL1Clm F' hm μ (hf_Lp.toLp f))
-      (condexpL1Clm F' hm μ (hg_Lp.toLp g))).mono fun x hx _ => hx)]
+    simp_rw [(condexpL1CLM F' hm μ).map_add]
+    rw [set_integral_congr_ae (hm s hs) ((Lp.coeFn_add (condexpL1CLM F' hm μ (hf_Lp.toLp f))
+      (condexpL1CLM F' hm μ (hg_Lp.toLp g))).mono fun x hx _ => hx)]
     rw [set_integral_congr_ae (hm s hs)
       ((Lp.coeFn_add (hf_Lp.toLp f) (hg_Lp.toLp g)).mono fun x hx _ => hx)]
     simp_rw [Pi.add_apply]
     rw [integral_add (L1.integrable_coeFn _).integrableOn (L1.integrable_coeFn _).integrableOn,
       integral_add (L1.integrable_coeFn _).integrableOn (L1.integrable_coeFn _).integrableOn, hf,
       hg]
-  · exact (continuous_set_integral s).comp (condexpL1Clm F' hm μ).continuous
+  · exact (continuous_set_integral s).comp (condexpL1CLM F' 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
+#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 `condexpL1Clm` over an `m`-measurable set is equal
+/-- The integral of the conditional expectation `condexpL1CLM` 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 : MeasurableSet[m] s) :
-    ∫ x in s, condexpL1Clm F' hm μ f x ∂μ = ∫ x in s, f x ∂μ := by
+theorem set_integral_condexpL1CLM (f : α →₁[μ] F') (hs : MeasurableSet[m] s) :
+    ∫ x in s, condexpL1CLM F' hm μ f x ∂μ = ∫ x in s, f x ∂μ := by
   let S := spanningSets (μ.trim hm)
   have hS_meas : ∀ i, MeasurableSet[m] (S i) := measurable_spanningSets (μ.trim hm)
   have hS_meas0 : ∀ i, MeasurableSet (S i) := fun i => hm _ (hS_meas i)
@@ -444,70 +444,70 @@ theorem set_integral_condexpL1Clm (f : α →₁[μ] F') (hs : MeasurableSet[m]
     simp_rw [Set.mem_inter_iff]
     exact fun h => ⟨monotone_spanningSets (μ.trim hm) hij h.1, h.2⟩
   have h_eq_forall :
-    (fun i => ∫ x in S i ∩ s, condexpL1Clm F' hm μ f x ∂μ) = fun i => ∫ x in S i ∩ s, f x ∂μ :=
+    (fun i => ∫ x in S i ∩ s, condexpL1CLM F' hm μ f x ∂μ) = fun i => ∫ x in S i ∩ s, f x ∂μ :=
     funext fun i =>
-      set_integral_condexpL1Clm_of_measure_ne_top f (@MeasurableSet.inter α m _ _ (hS_meas i) hs)
+      set_integral_condexpL1CLM_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) atTop (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_coeFn f).integrableOn
     rwa [← hs_eq] at h
-  have h_left : Tendsto (fun i => ∫ x in S i ∩ s, condexpL1Clm F' hm μ f x ∂μ) atTop
-      (𝓝 (∫ x in s, condexpL1Clm F' hm μ f x ∂μ)) := by
+  have h_left : Tendsto (fun i => ∫ x in S i ∩ s, condexpL1CLM F' hm μ f x ∂μ) atTop
+      (𝓝 (∫ x in s, condexpL1CLM F' 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_coeFn (condexpL1Clm F' hm μ f)).integrableOn
+      (L1.integrable_coeFn (condexpL1CLM F' 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
+#align measure_theory.set_integral_condexp_L1_clm MeasureTheory.set_integral_condexpL1CLM
 
-theorem aestronglyMeasurable'_condexpL1Clm (f : α →₁[μ] F') :
-    AEStronglyMeasurable' m (condexpL1Clm F' hm μ f) μ := by
+theorem aestronglyMeasurable'_condexpL1CLM (f : α →₁[μ] F') :
+    AEStronglyMeasurable' m (condexpL1CLM F' hm μ f) μ := by
   refine' @Lp.induction _ _ _ _ _ _ _ ENNReal.one_ne_top
-    (fun f : α →₁[μ] F' => AEStronglyMeasurable' m (condexpL1Clm F' hm μ f) μ) _ _ _ f
+    (fun f : α →₁[μ] F' => AEStronglyMeasurable' m (condexpL1CLM F' hm μ f) μ) _ _ _ f
   · intro c s hs hμs
-    rw [condexpL1Clm_indicatorConst hs hμs.ne c]
+    rw [condexpL1CLM_indicatorConst hs hμs.ne c]
     exact aestronglyMeasurable'_condexpInd hs hμs.ne c
   · intro f g hf hg _ hfm hgm
-    rw [(condexpL1Clm F' hm μ).map_add]
+    rw [(condexpL1CLM F' hm μ).map_add]
     refine' AEStronglyMeasurable'.congr _ (coeFn_add _ _).symm
     exact AEStronglyMeasurable'.add hfm hgm
-  · have : {f : Lp F' 1 μ | AEStronglyMeasurable' m (condexpL1Clm F' hm μ f) μ} =
-        condexpL1Clm F' hm μ ⁻¹' {f | AEStronglyMeasurable' m f μ} := rfl
+  · have : {f : Lp F' 1 μ | AEStronglyMeasurable' m (condexpL1CLM F' hm μ f) μ} =
+        condexpL1CLM F' hm μ ⁻¹' {f | AEStronglyMeasurable' m f μ} := rfl
     rw [this]
-    refine' IsClosed.preimage (condexpL1Clm F' hm μ).continuous _
+    refine' IsClosed.preimage (condexpL1CLM F' hm μ).continuous _
     exact isClosed_aeStronglyMeasurable' 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 F' hm μ (f : α →₁[μ] F') = ↑f := by
+theorem condexpL1CLM_lpMeas (f : lpMeas F' ℝ m 1 μ) :
+    condexpL1CLM F' hm μ (f : α →₁[μ] F') = ↑f := by
   let g := lpMeasToLpTrimLie F' ℝ 1 μ hm f
   have hfg : f = (lpMeasToLpTrimLie 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' =>
-    condexpL1Clm F' hm μ ((lpMeasToLpTrimLie F' ℝ 1 μ hm).symm g : α →₁[μ] F') =
+    condexpL1CLM F' hm μ ((lpMeasToLpTrimLie F' ℝ 1 μ hm).symm g : α →₁[μ] F') =
     ↑((lpMeasToLpTrimLie F' ℝ 1 μ hm).symm g)) _ _ _ g
   · intro c s hs hμs
     rw [@Lp.simpleFunc.coe_indicatorConst _ _ m, lpMeasToLpTrimLie_symm_indicator hs hμs.ne c,
-      condexpL1Clm_indicatorConstLp]
+      condexpL1CLM_indicatorConstLp]
     exact condexpInd_of_measurable hs ((le_trim hm).trans_lt hμs).ne c
   · intro f g hf hg _ hf_eq hg_eq
     rw [LinearIsometryEquiv.map_add]
     push_cast
     rw [map_add, hf_eq, hg_eq]
   · refine' isClosed_eq _ _
-    · refine' (condexpL1Clm F' hm μ).continuous.comp (continuous_induced_dom.comp _)
+    · refine' (condexpL1CLM F' 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
+#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 F' 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'
+theorem condexpL1CLM_of_aestronglyMeasurable' (f : α →₁[μ] F') (hfm : AEStronglyMeasurable' m f μ) :
+    condexpL1CLM F' 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. -/
@@ -519,7 +519,7 @@ 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 F' hm μ (hf.toL1 f) :=
+theorem condexpL1_eq (hf : Integrable f μ) : condexpL1 hm μ f = condexpL1CLM F' hm μ (hf.toL1 f) :=
   setToFun_eq (dominatedFinMeasAdditive_condexpInd F' hm μ) hf
 #align measure_theory.condexp_L1_eq MeasureTheory.condexpL1_eq
 
@@ -537,7 +537,7 @@ theorem aestronglyMeasurable'_condexpL1 {f : α → F'} :
     AEStronglyMeasurable' m (condexpL1 hm μ f) μ := by
   by_cases hf : Integrable f μ
   · rw [condexpL1_eq hf]
-    exact aestronglyMeasurable'_condexpL1Clm _
+    exact aestronglyMeasurable'_condexpL1CLM _
   · rw [condexpL1_undef hf]
     refine AEStronglyMeasurable'.congr ?_ (coeFn_zero _ _ _).symm
     exact StronglyMeasurable.aeStronglyMeasurable' (@stronglyMeasurable_zero _ _ m _ _)
@@ -558,7 +558,7 @@ the integral of `f` on that set. See also `set_integral_condexp`, the similar st
 theorem set_integral_condexpL1 (hf : Integrable f μ) (hs : MeasurableSet[m] s) :
     ∫ x in s, condexpL1 hm μ f x ∂μ = ∫ x in s, f x ∂μ := by
   simp_rw [condexpL1_eq hf]
-  rw [set_integral_condexpL1Clm (hf.toL1 f) hs]
+  rw [set_integral_condexpL1CLM (hf.toL1 f) hs]
   exact set_integral_congr_ae (hm s hs) (hf.coeFn_toL1.mono fun x hx _ => hx)
 #align measure_theory.set_integral_condexp_L1 MeasureTheory.set_integral_condexpL1
 
@@ -585,7 +585,7 @@ theorem condexpL1_of_aestronglyMeasurable' (hfm : AEStronglyMeasurable' m f μ)
     (hfi : Integrable f μ) : condexpL1 hm μ f =ᵐ[μ] f := by
   rw [condexpL1_eq hfi]
   refine' EventuallyEq.trans _ (Integrable.coeFn_toL1 hfi)
-  rw [condexpL1Clm_of_aestronglyMeasurable']
+  rw [condexpL1CLM_of_aestronglyMeasurable']
   exact AEStronglyMeasurable'.congr hfm (Integrable.coeFn_toL1 hfi).symm
 #align measure_theory.condexp_L1_of_ae_strongly_measurable' MeasureTheory.condexpL1_of_aestronglyMeasurable'
 

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

@@ -474,7 +474,7 @@ theorem aestronglyMeasurable'_condexpL1Clm (f : α →₁[μ] F') :
     refine' AEStronglyMeasurable'.congr _ (coeFn_add _ _).symm
     exact AEStronglyMeasurable'.add hfm hgm
   · have : {f : Lp F' 1 μ | AEStronglyMeasurable' m (condexpL1Clm F' hm μ f) μ} =
-        condexpL1Clm F' hm μ ⁻¹' {f | AEStronglyMeasurable' m f μ} := by rfl
+        condexpL1Clm F' hm μ ⁻¹' {f | AEStronglyMeasurable' m f μ} := rfl
     rw [this]
     refine' IsClosed.preimage (condexpL1Clm F' hm μ).continuous _
     exact isClosed_aeStronglyMeasurable' hm

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

This has nice performance benefits.

@@ -37,7 +37,7 @@ open scoped NNReal ENNReal Topology BigOperators MeasureTheory
 
 namespace MeasureTheory
 
-variable {α β F F' G G' 𝕜 : Type _} {p : ℝ≥0∞} [IsROrC 𝕜]
+variable {α β F F' G G' 𝕜 : Type*} {p : ℝ≥0∞} [IsROrC 𝕜]
   -- 𝕜 for ℝ or ℂ
   -- F for a Lp submodule
   [NormedAddCommGroup F]

• 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.condexp_L1
-! 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.CondexpL2
 
+#align_import measure_theory.function.conditional_expectation.condexp_L1 from "leanprover-community/mathlib"@"d8bbb04e2d2a44596798a9207ceefc0fb236e41e"
+
 /-! # Conditional expectation in L1
 
 This file contains two more steps of the construction of the conditional expectation, which is