measure_theory.function.conditional_expectation.condexp_L2 ⟷ Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

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

@@ -560,32 +560,32 @@ theorem condexpIndSMul_empty {x : G} :
 #align measure_theory.condexp_ind_smul_empty MeasureTheory.condexpIndSMul_empty
 -/
 
-#print MeasureTheory.set_integral_condexpL2_indicator /-
-theorem set_integral_condexpL2_indicator (hs : measurable_set[m] s) (ht : MeasurableSet t)
+#print MeasureTheory.setIntegral_condexpL2_indicator /-
+theorem setIntegral_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 • 1 := (setIntegral_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
+#align measure_theory.set_integral_condexp_L2_indicator MeasureTheory.setIntegral_condexpL2_indicator
 -/
 
-#print MeasureTheory.set_integral_condexpIndSMul /-
-theorem set_integral_condexpIndSMul (hs : measurable_set[m] s) (ht : MeasurableSet t)
-    (hμs : μ s ≠ ∞) (hμt : μ t ≠ ∞) (x : G') :
+#print MeasureTheory.setIntegral_condexpIndSMul /-
+theorem setIntegral_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)
+      setIntegral_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
+#align measure_theory.set_integral_condexp_ind_smul MeasureTheory.setIntegral_condexpIndSMul
 -/
 
 #print MeasureTheory.condexpL2_indicator_nonneg /-

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

@@ -42,7 +42,7 @@ open scoped ENNReal Topology MeasureTheory
 
 namespace MeasureTheory
 
-variable {α E E' F G G' 𝕜 : Type _} {p : ℝ≥0∞} [IsROrC 𝕜]
+variable {α E E' F G G' 𝕜 : Type _} {p : ℝ≥0∞} [RCLike 𝕜]
   -- 𝕜 for ℝ or ℂ
   -- E for an inner product space
   [NormedAddCommGroup E]
@@ -319,7 +319,7 @@ theorem integral_condexpL2_eq (hm : m ≤ m0) (f : Lp E' 2 μ) (hs : measurable_
 #align measure_theory.integral_condexp_L2_eq MeasureTheory.integral_condexpL2_eq
 -/
 
-variable {E'' 𝕜' : Type _} [IsROrC 𝕜'] [NormedAddCommGroup E''] [InnerProductSpace 𝕜' E'']
+variable {E'' 𝕜' : Type _} [RCLike 𝕜'] [NormedAddCommGroup E''] [InnerProductSpace 𝕜' E'']
   [CompleteSpace E''] [NormedSpace ℝ E'']
 
 variable (𝕜 𝕜')

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

@@ -220,11 +220,11 @@ 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 
+    dsimp only at hx
     rw [Pi.zero_apply] at hx ⊢
-    · rwa [ENNReal.coe_eq_zero, nnnorm_eq_zero] 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
@@ -343,7 +343,7 @@ 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
@@ -365,7 +365,7 @@ 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
@@ -383,7 +383,7 @@ 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

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

@@ -253,6 +253,8 @@ 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
   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

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

@@ -253,8 +253,6 @@ 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
   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

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 -/
-import Mathbin.Analysis.InnerProductSpace.Projection
-import Mathbin.MeasureTheory.Function.ConditionalExpectation.Unique
+import Analysis.InnerProductSpace.Projection
+import MeasureTheory.Function.ConditionalExpectation.Unique
 
 #align_import measure_theory.function.conditional_expectation.condexp_L2 from "leanprover-community/mathlib"@"e160cefedc932ce41c7049bf0c4b0f061d06216e"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module measure_theory.function.conditional_expectation.condexp_L2
-! 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.Analysis.InnerProductSpace.Projection
 import Mathbin.MeasureTheory.Function.ConditionalExpectation.Unique
 
+#align_import measure_theory.function.conditional_expectation.condexp_L2 from "leanprover-community/mathlib"@"e160cefedc932ce41c7049bf0c4b0f061d06216e"
+
 /-! # Conditional expectation in L2
 
 > 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_L2
-! 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.
 -/
@@ -13,6 +13,9 @@ import Mathbin.MeasureTheory.Function.ConditionalExpectation.Unique
 
 /-! # Conditional expectation in L2
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file contains one step 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

@@ -67,40 +67,53 @@ local notation "⟪" x ", " y "⟫₂" => @inner 𝕜 (α →₂[μ] E) _ x y
 
 variable (𝕜)
 
+#print MeasureTheory.condexpL2 /-
 /-- Conditional expectation of a function in L2 with respect to a sigma-algebra -/
 noncomputable 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) :
+#print MeasureTheory.aeStronglyMeasurable'_condexpL2 /-
+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
+-/
 
+#print MeasureTheory.integrableOn_condexpL2_of_measure_ne_top /-
 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
+-/
 
+#print MeasureTheory.integrable_condexpL2_of_isFiniteMeasure /-
 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
+-/
 
+#print MeasureTheory.norm_condexpL2_le_one /-
 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
+-/
 
+#print MeasureTheory.norm_condexpL2_le /-
 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
+-/
 
+#print MeasureTheory.snorm_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
@@ -108,7 +121,9 @@ theorem snorm_condexpL2_le (hm : m ≤ m0) (f : α →₂[μ] E) :
     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
+-/
 
+#print MeasureTheory.norm_condexpL2_coe_le /-
 theorem norm_condexpL2_coe_le (hm : m ≤ m0) (f : α →₂[μ] E) :
     ‖(condexpL2 𝕜 hm f : α →₂[μ] E)‖ ≤ ‖f‖ :=
   by
@@ -116,13 +131,17 @@ theorem norm_condexpL2_coe_le (hm : m ≤ m0) (f : α →₂[μ] E) :
   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
+-/
 
+#print MeasureTheory.inner_condexpL2_left_eq_right /-
 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
+-/
 
+#print MeasureTheory.condexpL2_indicator_of_measurable /-
 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) =
@@ -137,7 +156,9 @@ theorem condexpL2_indicator_of_measurable (hm : m ≤ m0) (hs : measurable_set[m
   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
+-/
 
+#print MeasureTheory.inner_condexpL2_eq_inner_fun /-
 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
@@ -145,11 +166,13 @@ theorem inner_condexpL2_eq_inner_fun (hm : m ≤ m0) (f g : α →₂[μ] E)
   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}
 
+#print MeasureTheory.integral_condexpL2_eq_of_fin_meas_real /-
 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
@@ -162,7 +185,9 @@ theorem integral_condexpL2_eq_of_fin_meas_real (f : Lp 𝕜 2 μ) (hs : measurab
     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
+-/
 
+#print MeasureTheory.lintegral_nnnorm_condexpL2_le /-
 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
@@ -188,7 +213,9 @@ theorem lintegral_nnnorm_condexpL2_le (hs : measurable_set[m] s) (hμs : μ s 
     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
+-/
 
+#print MeasureTheory.condexpL2_ae_eq_zero_of_ae_eq_zero /-
 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
@@ -210,7 +237,9 @@ theorem condexpL2_ae_eq_zero_of_ae_eq_zero (hs : measurable_set[m] s) (hμs : μ
     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
+-/
 
+#print MeasureTheory.lintegral_nnnorm_condexpL2_indicator_le_real /-
 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) :=
@@ -229,9 +258,11 @@ theorem lintegral_nnnorm_condexpL2_indicator_le_real (hs : MeasurableSet s) (hμ
   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
 
+#print MeasureTheory.condexpL2_const_inner /-
 /-- `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. -/
@@ -262,7 +293,9 @@ theorem condexpL2_const_inner (hm : m ≤ m0) (f : Lp E 2 μ) (c : E) :
   · 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
+-/
 
+#print MeasureTheory.integral_condexpL2_eq /-
 /-- `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 :=
@@ -284,12 +317,14 @@ theorem integral_condexpL2_eq (hm : m ≤ m0) (f : Lp E' 2 μ) (hs : measurable_
     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')
 
+#print MeasureTheory.condexpL2_comp_continuousLinearMap /-
 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
@@ -312,6 +347,7 @@ theorem condexpL2_comp_continuousLinearMap (hm : m ≤ m0) (T : E' →L[ℝ] E''
     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'}
 
@@ -319,6 +355,7 @@ section CondexpL2Indicator
 
 variable (𝕜)
 
+#print MeasureTheory.condexpL2_indicator_ae_eq_smul /-
 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 =>
@@ -332,7 +369,9 @@ theorem condexpL2_indicator_ae_eq_smul (hm : m ≤ m0) (hs : MeasurableSet s) (h
   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
+-/
 
+#print MeasureTheory.condexpL2_indicator_eq_toSpanSingleton_comp /-
 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') =
@@ -349,9 +388,11 @@ theorem condexpL2_indicator_eq_toSpanSingleton_comp (hm : m ≤ m0) (hs : Measur
   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}
 
+#print MeasureTheory.set_lintegral_nnnorm_condexpL2_indicator_le /-
 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‖₊ :=
@@ -368,7 +409,9 @@ theorem set_lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : Measur
     _ ≤ 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
+-/
 
+#print MeasureTheory.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‖₊ :=
@@ -379,7 +422,9 @@ theorem lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : Measurable
   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
+-/
 
+#print MeasureTheory.integrable_condexpL2_indicator /-
 /-- 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)]
@@ -394,6 +439,7 @@ theorem integrable_condexpL2_indicator (hm : m ≤ m0) [SigmaFinite (μ.trim hm)
       (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
 
@@ -401,14 +447,17 @@ section CondexpIndSmul
 
 variable [NormedSpace ℝ G] {hm : m ≤ m0}
 
+#print MeasureTheory.condexpIndSMul /-
 /-- Conditional expectation of the indicator of a measurable set with finite measure, in L2. -/
-noncomputable def condexpIndSmul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (x : G) :
+noncomputable 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
+#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 :=
+#print MeasureTheory.aeStronglyMeasurable'_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 _ _
@@ -421,39 +470,49 @@ 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 := by
+#print MeasureTheory.condexpIndSMul_add /-
+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
+#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
+#print MeasureTheory.condexpIndSMul_smul /-
+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
+#align measure_theory.condexp_ind_smul_smul MeasureTheory.condexpIndSMul_smul
+-/
 
-theorem condexpIndSmul_smul' [NormedSpace ℝ F] [SMulCommClass ℝ 𝕜 F] (hs : MeasurableSet s)
+#print 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
+    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'
+#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 =>
+#print MeasureTheory.condexpIndSMul_ae_eq_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
+#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 ≠ ∞)
+#print MeasureTheory.set_lintegral_nnnorm_condexpIndSMul_le /-
+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])
+        ((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]
@@ -461,21 +520,25 @@ 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
+#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‖₊ :=
+#print MeasureTheory.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
+#align measure_theory.lintegral_nnnorm_condexp_ind_smul_le MeasureTheory.lintegral_nnnorm_condexpIndSMul_le
+-/
 
+#print MeasureTheory.integrable_condexpIndSMul /-
 /-- 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 :=
+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) _
@@ -483,17 +546,21 @@ theorem integrable_condexpIndSmul (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.integrable_condexpIndSmul
+#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
+#print MeasureTheory.condexpIndSMul_empty /-
+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
+#align measure_theory.condexp_ind_smul_empty MeasureTheory.condexpIndSMul_empty
+-/
 
+#print MeasureTheory.set_integral_condexpL2_indicator /-
 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 :=
@@ -504,20 +571,24 @@ theorem set_integral_condexpL2_indicator (hs : measurable_set[m] s) (ht : Measur
     _ = (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)
+#print MeasureTheory.set_integral_condexpIndSMul /-
+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)
+        ((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
+#align measure_theory.set_integral_condexp_ind_smul MeasureTheory.set_integral_condexpIndSMul
+-/
 
+#print MeasureTheory.condexpL2_indicator_nonneg /-
 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
@@ -543,15 +614,18 @@ theorem condexpL2_indicator_nonneg (hm : m ≤ m0) (hs : MeasurableSet s) (hμs
       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]
+#print MeasureTheory.condexpIndSMul_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 :=
+    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
+#align measure_theory.condexp_ind_smul_nonneg MeasureTheory.condexpIndSMul_nonneg
+-/
 
 end CondexpIndSmul
 

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

@@ -61,10 +61,8 @@ variable {α E E' F G G' 𝕜 : Type _} {p : ℝ≥0∞} [IsROrC 𝕜]
 
 variable {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)

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

@@ -78,10 +78,10 @@ noncomputable def condexpL2 (hm : m ≤ m0) : (α →₂[μ] E) →L[𝕜] lpMea
 
 variable {𝕜}
 
-theorem aeStronglyMeasurable'_condexpL2 (hm : m ≤ m0) (f : α →₂[μ] E) :
-    AeStronglyMeasurable' m (condexpL2 𝕜 hm f) μ :=
+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 integrableOn_condexpL2_of_measure_ne_top (hm : m ≤ m0) (hμs : μ s ≠ ∞) (f : α →₂[μ] E) :
     IntegrableOn (condexpL2 𝕜 hm f) s μ :=
@@ -141,7 +141,7 @@ theorem condexpL2_indicator_of_measurable (hm : m ≤ m0) (hs : measurable_set[m
 #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 :=
+    (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]
@@ -409,8 +409,8 @@ noncomputable def condexpIndSmul (hm : m ≤ m0) (hs : MeasurableSet s) (hμs :
   (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 :=
+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 _ _
@@ -423,7 +423,7 @@ 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 := by

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

A PR accompanying #12339.

Zulip discussion

@@ -186,10 +186,10 @@ theorem condexpL2_ae_eq_zero_of_ae_eq_zero (hs : MeasurableSet[m] s) (hμs : μ
     (hf : f =ᵐ[μ.restrict s] 0) : condexpL2 ℝ ℝ hm f =ᵐ[μ.restrict s] (0 : α → ℝ) := by
   suffices h_nnnorm_eq_zero : ∫⁻ x in s, ‖(condexpL2 ℝ ℝ hm f : α → ℝ) x‖₊ ∂μ = 0 by
     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' 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 [lpMeas_coe]
       exact (Lp.stronglyMeasurable _).measurable

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

@@ -179,7 +179,7 @@ theorem lintegral_nnnorm_condexpL2_le (hs : MeasurableSet[m] s) (hμs : μ s ≠
     exact integrableOn_condexpL2_of_measure_ne_top hm hμs f
   · intro t ht hμt
     rw [← integral_condexpL2_eq_of_fin_meas_real f ht hμt.ne]
-    exact set_integral_congr_ae (hm t ht) (hg_eq.mono fun x hx _ => hx)
+    exact setIntegral_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 : MeasurableSet[m] s) (hμs : μ s ≠ ∞) {f : Lp ℝ 2 μ}
@@ -235,7 +235,7 @@ theorem condexpL2_const_inner (hm : m ≤ m0) (f : Lp E 2 μ) (c : E) :
   have h_eq : h_mem_Lp.toLp _ =ᵐ[μ] fun a => ⟪c, (condexpL2 E 𝕜 hm f : α → E) a⟫ :=
     h_mem_Lp.coeFn_toLp
   refine' EventuallyEq.trans _ h_eq
-  refine' Lp.ae_eq_of_forall_set_integral_eq' 𝕜 hm _ _ two_ne_zero ENNReal.coe_ne_top
+  refine' Lp.ae_eq_of_forall_setIntegral_eq' 𝕜 hm _ _ two_ne_zero ENNReal.coe_ne_top
     (fun s _ hμs => integrableOn_condexpL2_of_measure_ne_top hm hμs.ne _) _ _ _ _
   · intro s _ hμs
     rw [IntegrableOn, integrable_congr (ae_restrict_of_ae h_eq)]
@@ -243,10 +243,10 @@ theorem condexpL2_const_inner (hm : m ≤ m0) (f : Lp E 2 μ) (c : E) :
   · intro s hs hμs
     rw [← lpMeas_coe, integral_condexpL2_eq_of_fin_meas_real _ hs hμs.ne,
       integral_congr_ae (ae_restrict_of_ae h_eq), lpMeas_coe, ←
-      L2.inner_indicatorConstLp_eq_set_integral_inner 𝕜 (↑(condexpL2 E 𝕜 hm f)) (hm s hs) c hμs.ne,
+      L2.inner_indicatorConstLp_eq_setIntegral_inner 𝕜 (↑(condexpL2 E 𝕜 hm f)) (hm s hs) c hμs.ne,
       ← inner_condexpL2_left_eq_right, condexpL2_indicator_of_measurable _ hs,
-      L2.inner_indicatorConstLp_eq_set_integral_inner 𝕜 f (hm s hs) c hμs.ne,
-      set_integral_congr_ae (hm s hs)
+      L2.inner_indicatorConstLp_eq_setIntegral_inner 𝕜 f (hm s hs) c hμs.ne,
+      setIntegral_congr_ae (hm s hs)
         ((Memℒp.coeFn_toLp ((Lp.memℒp f).const_inner c)).mono fun x hx _ => hx)]
   · rw [← lpMeas_coe]; exact lpMeas.aeStronglyMeasurable' _
   · refine' AEStronglyMeasurable'.congr _ h_eq.symm
@@ -269,8 +269,8 @@ theorem integral_condexpL2_eq (hm : m ≤ m0) (f : Lp E' 2 μ) (hs : MeasurableS
       ((integrableOn_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs).const_inner c)]
   have h_ae_eq_f := Memℒp.coeFn_toLp (E := 𝕜) ((Lp.memℒp f).const_inner c)
   rw [← lpMeas_coe, sub_eq_zero, ←
-    set_integral_congr_ae (hm s hs) ((condexpL2_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)]
+    setIntegral_congr_ae (hm s hs) ((condexpL2_const_inner hm f c).mono fun x hx _ => hx), ←
+    setIntegral_congr_ae (hm s hs) (h_ae_eq_f.mono fun x hx _ => hx)]
   exact integral_condexpL2_eq_of_fin_meas_real _ hs hμs
 #align measure_theory.integral_condexp_L2_eq MeasureTheory.integral_condexpL2_eq
 
@@ -282,15 +282,15 @@ variable (𝕜 𝕜')
 theorem condexpL2_comp_continuousLinearMap (hm : m ≤ m0) (T : E' →L[ℝ] E'') (f : α →₂[μ] E') :
     (condexpL2 E'' 𝕜' hm (T.compLp f) : α →₂[μ] E'') =ᵐ[μ]
     T.compLp (condexpL2 E' 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
+  refine' Lp.ae_eq_of_forall_setIntegral_eq' 𝕜' hm _ _ two_ne_zero ENNReal.coe_ne_top
     (fun s _ hμs => integrableOn_condexpL2_of_measure_ne_top hm hμs.ne _) (fun s _ hμs =>
       integrableOn_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs.ne) _ _ _
   · intro s hs hμs
-    rw [T.set_integral_compLp _ (hm s hs),
+    rw [T.setIntegral_compLp _ (hm s hs),
       T.integral_comp_comm
         (integrableOn_Lp_of_measure_ne_top _ fact_one_le_two_ennreal.elim hμs.ne),
       ← lpMeas_coe, ← lpMeas_coe, integral_condexpL2_eq hm f hs hμs.ne,
-      integral_condexpL2_eq hm (T.compLp f) hs hμs.ne, T.set_integral_compLp _ (hm s hs),
+      integral_condexpL2_eq hm (T.compLp f) hs hμs.ne, T.setIntegral_compLp _ (hm s hs),
       T.integral_comp_comm
         (integrableOn_Lp_of_measure_ne_top f fact_one_le_two_ennreal.elim hμs.ne)]
   · rw [← lpMeas_coe]; exact lpMeas.aeStronglyMeasurable' _
@@ -468,29 +468,37 @@ theorem condexpIndSMul_empty {x : G} : condexpIndSMul hm MeasurableSet.empty
   simp only [Submodule.coe_zero, ContinuousLinearMap.map_zero]
 #align measure_theory.condexp_ind_smul_empty MeasureTheory.condexpIndSMul_empty
 
-theorem set_integral_condexpL2_indicator (hs : MeasurableSet[m] s) (ht : MeasurableSet t)
+theorem setIntegral_condexpL2_indicator (hs : MeasurableSet[m] s) (ht : MeasurableSet t)
     (hμs : μ s ≠ ∞) (hμt : μ t ≠ ∞) :
     ∫ x in s, (condexpL2 ℝ ℝ hm (indicatorConstLp 2 ht hμt 1) : α → ℝ) x ∂μ = (μ (t ∩ s)).toReal :=
   calc
     ∫ x in s, (condexpL2 ℝ ℝ hm (indicatorConstLp 2 ht hμt 1) : α → 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 : ℝ) := set_integral_indicatorConstLp (hm s hs) ht hμt 1
+    _ = (μ (t ∩ s)).toReal • (1 : ℝ) := setIntegral_indicatorConstLp (hm s hs) ht hμt 1
     _ = (μ (t ∩ s)).toReal := by rw [smul_eq_mul, mul_one]
-#align measure_theory.set_integral_condexp_L2_indicator MeasureTheory.set_integral_condexpL2_indicator
+#align measure_theory.set_integral_condexp_L2_indicator MeasureTheory.setIntegral_condexpL2_indicator
 
-theorem set_integral_condexpIndSMul (hs : MeasurableSet[m] s) (ht : MeasurableSet t)
+@[deprecated]
+alias set_integral_condexpL2_indicator :=
+  setIntegral_condexpL2_indicator -- deprecated on 2024-04-17
+
+theorem setIntegral_condexpIndSMul (hs : MeasurableSet[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 ℝ hm (indicatorConstLp 2 ht hμt 1) : α → ℝ) a • x ∂μ :=
-      set_integral_congr_ae (hm s hs)
+      setIntegral_congr_ae (hm s hs)
         ((condexpIndSMul_ae_eq_smul hm ht hμt x).mono fun x hx _ => hx)
     _ = (∫ a in s, (condexpL2 ℝ ℝ hm (indicatorConstLp 2 ht hμt 1) : α → ℝ) a ∂μ) • x :=
       (integral_smul_const _ x)
-    _ = (μ (t ∩ s)).toReal • x := by rw [set_integral_condexpL2_indicator hs ht hμs hμt]
-#align measure_theory.set_integral_condexp_ind_smul MeasureTheory.set_integral_condexpIndSMul
+    _ = (μ (t ∩ s)).toReal • x := by rw [setIntegral_condexpL2_indicator hs ht hμs hμt]
+#align measure_theory.set_integral_condexp_ind_smul MeasureTheory.setIntegral_condexpIndSMul
+
+@[deprecated]
+alias set_integral_condexpIndSMul :=
+  setIntegral_condexpIndSMul -- deprecated on 2024-04-17
 
 theorem condexpL2_indicator_nonneg (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ∞)
     [SigmaFinite (μ.trim hm)] : (0 : α → ℝ) ≤ᵐ[μ]
@@ -499,7 +507,7 @@ theorem condexpL2_indicator_nonneg (hm : m ≤ m0) (hs : MeasurableSet s) (hμs
     aeStronglyMeasurable'_condexpL2 _ _
   refine' EventuallyLE.trans_eq _ h.ae_eq_mk.symm
   refine' @ae_le_of_ae_le_trim _ _ _ _ _ _ hm (0 : α → ℝ) _ _
-  refine' ae_nonneg_of_forall_set_integral_nonneg_of_sigmaFinite _ _
+  refine' ae_nonneg_of_forall_setIntegral_nonneg_of_sigmaFinite _ _
   · rintro t - -
     refine @Integrable.integrableOn _ _ m _ _ _ _ ?_
     refine' Integrable.trim hm _ _
@@ -507,13 +515,13 @@ theorem condexpL2_indicator_nonneg (hm : m ≤ m0) (hs : MeasurableSet s) (hμs
       exact integrable_condexpL2_indicator hm hs hμs _
     · exact h.stronglyMeasurable_mk
   · intro t ht hμt
-    rw [← set_integral_trim hm h.stronglyMeasurable_mk ht]
+    rw [← setIntegral_trim hm h.stronglyMeasurable_mk ht]
     have h_ae :
       ∀ᵐ x ∂μ, x ∈ t → h.mk _ x = (condexpL2 ℝ ℝ hm (indicatorConstLp 2 hs hμs 1) : α → 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_condexpL2_indicator ht hs ((le_trim hm).trans_lt hμt).ne hμs]
+    rw [setIntegral_congr_ae (hm t ht) h_ae,
+      setIntegral_condexpL2_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
 

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

@@ -475,7 +475,7 @@ theorem set_integral_condexpL2_indicator (hs : MeasurableSet[m] s) (ht : Measura
     ∫ x in s, (condexpL2 ℝ ℝ hm (indicatorConstLp 2 ht hμt 1) : α → 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 : ℝ) := (set_integral_indicatorConstLp (hm s hs) ht hμt 1)
+    _ = (μ (t ∩ s)).toReal • (1 : ℝ) := set_integral_indicatorConstLp (hm s hs) ht hμt 1
     _ = (μ (t ∩ s)).toReal := by rw [smul_eq_mul, mul_one]
 #align measure_theory.set_integral_condexp_L2_indicator MeasureTheory.set_integral_condexpL2_indicator
 

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.

@@ -26,7 +26,7 @@ the orthogonal projection on the subspace `lpMeas`.
 ## Implementation notes
 
 Most of the results in this file are valid for a complete real normed space `F`.
-However, some lemmas also use `𝕜 : IsROrC`:
+However, some lemmas also use `𝕜 : RCLike`:
 * `condexpL2` is defined only for an `InnerProductSpace` 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 `NormedSpace 𝕜 F`.
@@ -41,7 +41,7 @@ open scoped ENNReal Topology MeasureTheory
 
 namespace MeasureTheory
 
-variable {α E E' F G G' 𝕜 : Type*} {p : ℝ≥0∞} [IsROrC 𝕜]
+variable {α E E' F G G' 𝕜 : Type*} {p : ℝ≥0∞} [RCLike 𝕜]
   -- 𝕜 for ℝ or ℂ
   -- E for an inner product space
   [NormedAddCommGroup E]
@@ -274,7 +274,7 @@ theorem integral_condexpL2_eq (hm : m ≤ m0) (f : Lp E' 2 μ) (hs : MeasurableS
   exact integral_condexpL2_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'']
+variable {E'' 𝕜' : Type*} [RCLike 𝕜'] [NormedAddCommGroup E''] [InnerProductSpace 𝕜' E'']
   [CompleteSpace E''] [NormedSpace ℝ E'']
 
 variable (𝕜 𝕜')

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.

@@ -329,8 +329,7 @@ theorem condexpL2_indicator_eq_toSpanSingleton_comp (hm : m ≤ m0) (hs : Measur
     (condexpL2 ℝ ℝ hm (indicatorConstLp 2 hs hμs 1) : α →₂[μ] ℝ)
   rw [← EventuallyEq] at h_comp
   refine' EventuallyEq.trans _ h_comp.symm
-  refine' eventually_of_forall fun y => _
-  rfl
+  filter_upwards with y using rfl
 #align measure_theory.condexp_L2_indicator_eq_to_span_singleton_comp MeasureTheory.condexpL2_indicator_eq_toSpanSingleton_comp
 
 variable {𝕜}

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

This follows on from #6964.

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

@@ -184,8 +184,8 @@ theorem lintegral_nnnorm_condexpL2_le (hs : MeasurableSet[m] s) (hμs : μ s ≠
 
 theorem condexpL2_ae_eq_zero_of_ae_eq_zero (hs : MeasurableSet[m] s) (hμs : μ s ≠ ∞) {f : Lp ℝ 2 μ}
     (hf : f =ᵐ[μ.restrict s] 0) : condexpL2 ℝ ℝ hm f =ᵐ[μ.restrict s] (0 : α → ℝ) := by
-  suffices h_nnnorm_eq_zero : ∫⁻ x in s, ‖(condexpL2 ℝ ℝ hm f : α → ℝ) x‖₊ ∂μ = 0
-  · rw [lintegral_eq_zero_iff] at h_nnnorm_eq_zero
+  suffices h_nnnorm_eq_zero : ∫⁻ x in s, ‖(condexpL2 ℝ ℝ hm f : α → ℝ) x‖₊ ∂μ = 0 by
+    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 ⊢

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

@@ -99,7 +99,7 @@ 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 E 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
 

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -5,6 +5,7 @@ Authors: Rémy Degenne
 -/
 import Mathlib.Analysis.InnerProductSpace.Projection
 import Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique
+import Mathlib.MeasureTheory.Function.L2Space
 
 #align_import measure_theory.function.conditional_expectation.condexp_L2 from "leanprover-community/mathlib"@"d8bbb04e2d2a44596798a9207ceefc0fb236e41e"
 

Following on from previous gcongr golfing PRs #4702 and #4784.

This is a replacement for #7901: this round of golfs, first introduced there, there exposed some performance issues in gcongr, hopefully fixed by #8731, and I am opening a new PR so that the performance can be checked against current master rather than master at the time of #7901.

@@ -358,7 +358,8 @@ theorem lintegral_nnnorm_condexpL2_indicator_le (hm : m ≤ m0) (hs : Measurable
   · rw [lpMeas_coe]
     exact (Lp.aestronglyMeasurable _).ennnorm
   refine' (set_lintegral_nnnorm_condexpL2_indicator_le hm hs hμs x ht hμt).trans _
-  exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
+  gcongr
+  apply 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
@@ -371,7 +372,8 @@ theorem integrable_condexpL2_indicator (hm : m ≤ m0) [SigmaFinite (μ.trim hm)
   · rw [lpMeas_coe]; exact Lp.aestronglyMeasurable _
   · refine' fun t ht hμt =>
       (set_lintegral_nnnorm_condexpL2_indicator_le hm hs hμs x ht hμt).trans _
-    exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
+    gcongr
+    apply Set.inter_subset_left
 #align measure_theory.integrable_condexp_L2_indicator MeasureTheory.integrable_condexpL2_indicator
 
 end CondexpL2Indicator
@@ -443,7 +445,8 @@ 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.aestronglyMeasurable _).ennnorm
   refine' (set_lintegral_nnnorm_condexpIndSMul_le hm hs hμs x ht hμt).trans _
-  exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
+  gcongr
+  apply 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
@@ -455,7 +458,8 @@ theorem integrable_condexpIndSMul (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hs
       _
   · exact Lp.aestronglyMeasurable _
   · refine' fun t ht hμt => (set_lintegral_nnnorm_condexpIndSMul_le hm hs hμs x ht hμt).trans _
-    exact mul_le_mul_right' (measure_mono (Set.inter_subset_left _ _)) _
+    gcongr
+    apply Set.inter_subset_left
 #align measure_theory.integrable_condexp_ind_smul MeasureTheory.integrable_condexpIndSMul
 
 theorem condexpIndSMul_empty {x : G} : condexpIndSMul hm MeasurableSet.empty

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

@@ -131,7 +131,7 @@ theorem condexpL2_indicator_of_measurable (hm : m ≤ m0) (hs : MeasurableSet[m]
   have h_mem : indicatorConstLp 2 (hm s hs) hμs c ∈ lpMeas E 𝕜 m 2 μ :=
     mem_lpMeas_indicatorConstLp hm hs hμs
   let ind := (⟨indicatorConstLp 2 (hm s hs) hμs c, h_mem⟩ : lpMeas E 𝕜 m 2 μ)
-  have h_coe_ind : (ind : α →₂[μ] E) = indicatorConstLp 2 (hm s hs) hμs c := by rfl
+  have h_coe_ind : (ind : α →₂[μ] E) = indicatorConstLp 2 (hm s hs) hμs c := 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

• Golf some proofs.
• Rename MeasureTheory.indicatorConst_empty to MeasureTheory.indicatorConstLp_empty.
• Change some linebreaks.

@@ -460,7 +460,7 @@ theorem integrable_condexpIndSMul (hm : m ≤ m0) [SigmaFinite (μ.trim hm)] (hs
 
 theorem condexpIndSMul_empty {x : G} : condexpIndSMul hm MeasurableSet.empty
     ((@measure_empty _ _ μ).le.trans_lt ENNReal.coe_lt_top).ne x = 0 := by
-  rw [condexpIndSMul, indicatorConst_empty]
+  rw [condexpIndSMul, indicatorConstLp_empty]
   simp only [Submodule.coe_zero, ContinuousLinearMap.map_zero]
 #align measure_theory.condexp_ind_smul_empty MeasureTheory.condexpIndSMul_empty
 

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

This has nice performance benefits.

@@ -40,7 +40,7 @@ open scoped ENNReal Topology MeasureTheory
 
 namespace MeasureTheory
 
-variable {α E E' F G G' 𝕜 : Type _} {p : ℝ≥0∞} [IsROrC 𝕜]
+variable {α E E' F G G' 𝕜 : Type*} {p : ℝ≥0∞} [IsROrC 𝕜]
   -- 𝕜 for ℝ or ℂ
   -- E for an inner product space
   [NormedAddCommGroup E]
@@ -273,7 +273,7 @@ theorem integral_condexpL2_eq (hm : m ≤ m0) (f : Lp E' 2 μ) (hs : MeasurableS
   exact integral_condexpL2_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'']
+variable {E'' 𝕜' : Type*} [IsROrC 𝕜'] [NormedAddCommGroup E''] [InnerProductSpace 𝕜' E'']
   [CompleteSpace E''] [NormedSpace ℝ E'']
 
 variable (𝕜 𝕜')

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module measure_theory.function.conditional_expectation.condexp_L2
-! 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.Analysis.InnerProductSpace.Projection
 import Mathlib.MeasureTheory.Function.ConditionalExpectation.Unique
 
+#align_import measure_theory.function.conditional_expectation.condexp_L2 from "leanprover-community/mathlib"@"d8bbb04e2d2a44596798a9207ceefc0fb236e41e"
+
 /-! # Conditional expectation in L2
 
 This file contains one step of the construction of the conditional expectation, which is completed

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Xavier-François Roblot <46200072+xroblot@users.noreply.github.com>