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

@@ -150,7 +150,7 @@ theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x
   have h : ∀ x, ‖⟪f x, g x⟫‖ ≤ ‖‖f x‖ ^ (2 : ℝ) + ‖g x‖ ^ (2 : ℝ)‖ :=
     by
     intro x
-    rw [← @Nat.cast_two ℝ, Real.rpow_nat_cast, Real.rpow_nat_cast]
+    rw [← @Nat.cast_two ℝ, Real.rpow_natCast, Real.rpow_natCast]
     calc
       ‖⟪f x, g x⟫‖ ≤ ‖f x‖ * ‖g x‖ := norm_inner_le_norm _ _
       _ ≤ 2 * ‖f x‖ * ‖g x‖ :=
@@ -191,8 +191,8 @@ theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
   congr
   ext1 x
   have h_two : (2 : ℝ) = ((2 : ℕ) : ℝ) := by simp
-  rw [← Real.rpow_nat_cast _ 2, ← h_two, ←
-    ENNReal.ofReal_rpow_of_nonneg (norm_nonneg _) zero_le_two, ofReal_norm_eq_coe_nnnorm]
+  rw [← Real.rpow_natCast _ 2, ← h_two, ← ENNReal.ofReal_rpow_of_nonneg (norm_nonneg _) zero_le_two,
+    ofReal_norm_eq_coe_nnnorm]
   norm_cast
 #align measure_theory.L2.integral_inner_eq_sq_snorm MeasureTheory.L2.integral_inner_eq_sq_snorm
 -/
@@ -202,7 +202,7 @@ private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = RCLike.r
   have h_two : (2 : ℝ≥0∞).toReal = 2 := by simp
   rw [inner_def, integral_inner_eq_sq_snorm, norm_def, ← ENNReal.toReal_pow, RCLike.ofReal_re,
     ENNReal.toReal_eq_toReal (ENNReal.pow_ne_top (Lp.snorm_ne_top f)) _]
-  · rw [← ENNReal.rpow_nat_cast, snorm_eq_snorm' two_ne_zero ENNReal.two_ne_top, snorm', ←
+  · rw [← ENNReal.rpow_natCast, snorm_eq_snorm' two_ne_zero ENNReal.two_ne_top, snorm', ←
       ENNReal.rpow_mul, one_div, h_two]
     simp
   · refine' (lintegral_rpow_nnnorm_lt_top_of_snorm'_lt_top zero_lt_two _).Ne
@@ -259,10 +259,10 @@ section IndicatorConstLp
 
 variable (𝕜) {s : Set α}
 
-#print MeasureTheory.L2.inner_indicatorConstLp_eq_set_integral_inner /-
+#print MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner /-
 /-- The inner product in `L2` of the indicator of a set `indicator_const_Lp 2 hs hμs c` and `f` is
 equal to the integral of the inner product over `s`: `∫ x in s, ⟪c, f x⟫ ∂μ`. -/
-theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : MeasurableSet s) (c : E)
+theorem inner_indicatorConstLp_eq_setIntegral_inner (f : Lp E 2 μ) (hs : MeasurableSet s) (c : E)
     (hμs : μ s ≠ ∞) : (⟪indicatorConstLp 2 hs hμs c, f⟫ : 𝕜) = ∫ x in s, ⟪c, f x⟫ ∂μ :=
   by
   rw [inner_def, ← integral_add_compl hs (L2.integrable_inner _ f)]
@@ -290,18 +290,18 @@ theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : Measu
     rw [hx hxs]
     exact inner_zero_left _
   rw [h_left, h_right, add_zero]
-#align measure_theory.L2.inner_indicator_const_Lp_eq_set_integral_inner MeasureTheory.L2.inner_indicatorConstLp_eq_set_integral_inner
+#align measure_theory.L2.inner_indicator_const_Lp_eq_set_integral_inner MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner
 -/
 
-#print MeasureTheory.L2.inner_indicatorConstLp_eq_inner_set_integral /-
+#print MeasureTheory.L2.inner_indicatorConstLp_eq_inner_setIntegral /-
 /-- The inner product in `L2` of the indicator of a set `indicator_const_Lp 2 hs hμs c` and `f` is
 equal to the inner product of the constant `c` and the integral of `f` over `s`. -/
-theorem inner_indicatorConstLp_eq_inner_set_integral [CompleteSpace E] [NormedSpace ℝ E]
+theorem inner_indicatorConstLp_eq_inner_setIntegral [CompleteSpace E] [NormedSpace ℝ E]
     (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (c : E) (f : Lp E 2 μ) :
     (⟪indicatorConstLp 2 hs hμs c, f⟫ : 𝕜) = ⟪c, ∫ x in s, f x ∂μ⟫ := by
   rw [← integral_inner (integrable_on_Lp_of_measure_ne_top f fact_one_le_two_ennreal.elim hμs),
     L2.inner_indicator_const_Lp_eq_set_integral_inner]
-#align measure_theory.L2.inner_indicator_const_Lp_eq_inner_set_integral MeasureTheory.L2.inner_indicatorConstLp_eq_inner_set_integral
+#align measure_theory.L2.inner_indicator_const_Lp_eq_inner_set_integral MeasureTheory.L2.inner_indicatorConstLp_eq_inner_setIntegral
 -/
 
 variable {𝕜}

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

@@ -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 Data.IsROrC.Lemmas
+import Analysis.RCLike.Lemmas
 import MeasureTheory.Function.StronglyMeasurable.Inner
 import MeasureTheory.Integral.SetIntegral
 
@@ -73,7 +73,7 @@ section InnerProductSpace
 
 variable {α : Type _} {m : MeasurableSpace α} {p : ℝ≥0∞} {μ : Measure α}
 
-variable {E 𝕜 : Type _} [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
+variable {E 𝕜 : Type _} [RCLike 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 
@@ -130,7 +130,7 @@ end InnerProductSpace
 
 namespace L2
 
-variable {α E F 𝕜 : Type _} [IsROrC 𝕜] [MeasurableSpace α] {μ : Measure α} [NormedAddCommGroup E]
+variable {α E F 𝕜 : Type _} [RCLike 𝕜] [MeasurableSpace α] {μ : Measure α} [NormedAddCommGroup E]
   [InnerProductSpace 𝕜 E] [NormedAddCommGroup F]
 
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
@@ -197,10 +197,10 @@ theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
 #align measure_theory.L2.integral_inner_eq_sq_snorm MeasureTheory.L2.integral_inner_eq_sq_snorm
 -/
 
-private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = IsROrC.re ⟪f, f⟫ :=
+private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = RCLike.re ⟪f, f⟫ :=
   by
   have h_two : (2 : ℝ≥0∞).toReal = 2 := by simp
-  rw [inner_def, integral_inner_eq_sq_snorm, norm_def, ← ENNReal.toReal_pow, IsROrC.ofReal_re,
+  rw [inner_def, integral_inner_eq_sq_snorm, norm_def, ← ENNReal.toReal_pow, RCLike.ofReal_re,
     ENNReal.toReal_eq_toReal (ENNReal.pow_ne_top (Lp.snorm_ne_top f)) _]
   · rw [← ENNReal.rpow_nat_cast, snorm_eq_snorm' two_ne_zero ENNReal.two_ne_top, snorm', ←
       ENNReal.rpow_mul, one_div, h_two]
@@ -321,7 +321,7 @@ end L2
 
 section InnerContinuous
 
-variable {α : Type _} [TopologicalSpace α] [MeasureSpace α] [BorelSpace α] {𝕜 : Type _} [IsROrC 𝕜]
+variable {α : Type _} [TopologicalSpace α] [MeasureSpace α] [BorelSpace α] {𝕜 : Type _} [RCLike 𝕜]
 
 variable (μ : Measure α) [IsFiniteMeasure μ]
 

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

@@ -122,7 +122,7 @@ local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 #print integral_eq_zero_of_forall_integral_inner_eq_zero /-
 theorem integral_eq_zero_of_forall_integral_inner_eq_zero (f : α → E) (hf : Integrable f μ)
     (hf_int : ∀ c : E, ∫ x, ⟪c, f x⟫ ∂μ = 0) : ∫ x, f x ∂μ = 0 := by
-  specialize hf_int (∫ x, f x ∂μ); rwa [integral_inner hf, inner_self_eq_zero] at hf_int 
+  specialize hf_int (∫ x, f x ∂μ); rwa [integral_inner hf, inner_self_eq_zero] at hf_int
 #align integral_eq_zero_of_forall_integral_inner_eq_zero integral_eq_zero_of_forall_integral_inner_eq_zero
 -/
 
@@ -233,7 +233,7 @@ private theorem add_left' (f f' g : α →₂[μ] E) : ⟪f + f', g⟫ = inner f
     inner_add_left]
   refine' integral_congr_ae ((coe_fn_add f f').mono fun x hx => _)
   congr
-  rwa [Pi.add_apply] at hx 
+  rwa [Pi.add_apply] at hx
 
 private theorem smul_left' (f g : α →₂[μ] E) (r : 𝕜) : ⟪r • f, g⟫ = conj r * inner f g :=
   by
@@ -241,7 +241,7 @@ private theorem smul_left' (f g : α →₂[μ] E) (r : 𝕜) : ⟪r • f, g⟫
   refine' integral_congr_ae ((coe_fn_smul r f).mono fun x hx => _)
   rw [smul_eq_mul, ← inner_smul_left]
   congr
-  rwa [Pi.smul_apply] at hx 
+  rwa [Pi.smul_apply] at hx
 
 #print MeasureTheory.L2.innerProductSpace /-
 instance innerProductSpace : InnerProductSpace 𝕜 (α →₂[μ] E)
@@ -278,7 +278,7 @@ theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : Measu
   have h_right : ∫ x in sᶜ, ⟪(indicator_const_Lp 2 hs hμs c) x, f x⟫ ∂μ = 0 :=
     by
     suffices h_ae_eq : ∀ᵐ x ∂μ, x ∉ s → ⟪indicator_const_Lp 2 hs hμs c x, f x⟫ = 0
-    · simp_rw [← Set.mem_compl_iff] at h_ae_eq 
+    · simp_rw [← Set.mem_compl_iff] at h_ae_eq
       suffices h_int_zero :
         ∫ x in sᶜ, inner (indicator_const_Lp 2 hs hμs c x) (f x) ∂μ = ∫ x in sᶜ, (0 : 𝕜) ∂μ
       · rw [h_int_zero]

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

@@ -3,9 +3,9 @@ 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.Data.IsROrC.Lemmas
-import Mathbin.MeasureTheory.Function.StronglyMeasurable.Inner
-import Mathbin.MeasureTheory.Integral.SetIntegral
+import Data.IsROrC.Lemmas
+import MeasureTheory.Function.StronglyMeasurable.Inner
+import MeasureTheory.Integral.SetIntegral
 
 #align_import measure_theory.function.l2_space from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
 

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

@@ -2,16 +2,13 @@
 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.l2_space
-! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.IsROrC.Lemmas
 import Mathbin.MeasureTheory.Function.StronglyMeasurable.Inner
 import Mathbin.MeasureTheory.Integral.SetIntegral
 
+#align_import measure_theory.function.l2_space from "leanprover-community/mathlib"@"7e5137f579de09a059a5ce98f364a04e221aabf0"
+
 /-! # `L^2` space
 
 > THIS FILE IS SYNCHRONIZED WITH MATHLIB4.

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

@@ -43,10 +43,13 @@ section
 
 variable {α F : Type _} {m : MeasurableSpace α} {μ : Measure α} [NormedAddCommGroup F]
 
+#print MeasureTheory.Memℒp.integrable_sq /-
 theorem Memℒp.integrable_sq {f : α → ℝ} (h : Memℒp f 2 μ) : Integrable (fun x => f x ^ 2) μ := by
   simpa [← mem_ℒp_one_iff_integrable] using h.norm_rpow two_ne_zero ENNReal.two_ne_top
 #align measure_theory.mem_ℒp.integrable_sq MeasureTheory.Memℒp.integrable_sq
+-/
 
+#print MeasureTheory.memℒp_two_iff_integrable_sq_norm /-
 theorem memℒp_two_iff_integrable_sq_norm {f : α → F} (hf : AEStronglyMeasurable f μ) :
     Memℒp f 2 μ ↔ Integrable (fun x => ‖f x‖ ^ 2) μ :=
   by
@@ -55,7 +58,9 @@ theorem memℒp_two_iff_integrable_sq_norm {f : α → F} (hf : AEStronglyMeasur
   · simp
   · rw [div_eq_mul_inv, ENNReal.mul_inv_cancel two_ne_zero ENNReal.two_ne_top]
 #align measure_theory.mem_ℒp_two_iff_integrable_sq_norm MeasureTheory.memℒp_two_iff_integrable_sq_norm
+-/
 
+#print MeasureTheory.memℒp_two_iff_integrable_sq /-
 theorem memℒp_two_iff_integrable_sq {f : α → ℝ} (hf : AEStronglyMeasurable f μ) :
     Memℒp f 2 μ ↔ Integrable (fun x => f x ^ 2) μ :=
   by
@@ -63,6 +68,7 @@ theorem memℒp_two_iff_integrable_sq {f : α → ℝ} (hf : AEStronglyMeasurabl
   ext x
   simp
 #align measure_theory.mem_ℒp_two_iff_integrable_sq MeasureTheory.memℒp_two_iff_integrable_sq
+-/
 
 end
 
@@ -72,46 +78,56 @@ variable {α : Type _} {m : MeasurableSpace α} {p : ℝ≥0∞} {μ : Measure 
 
 variable {E 𝕜 : Type _} [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
--- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 
+#print MeasureTheory.Memℒp.const_inner /-
 theorem Memℒp.const_inner (c : E) {f : α → E} (hf : Memℒp f p μ) : Memℒp (fun a => ⟪c, f a⟫) p μ :=
   hf.of_le_mul (AEStronglyMeasurable.inner aestronglyMeasurable_const hf.1)
     (eventually_of_forall fun x => norm_inner_le_norm _ _)
 #align measure_theory.mem_ℒp.const_inner MeasureTheory.Memℒp.const_inner
+-/
 
+#print MeasureTheory.Memℒp.inner_const /-
 theorem Memℒp.inner_const {f : α → E} (hf : Memℒp f p μ) (c : E) : Memℒp (fun a => ⟪f a, c⟫) p μ :=
   hf.of_le_mul (AEStronglyMeasurable.inner hf.1 aestronglyMeasurable_const)
     (eventually_of_forall fun x => by rw [mul_comm]; exact norm_inner_le_norm _ _)
 #align measure_theory.mem_ℒp.inner_const MeasureTheory.Memℒp.inner_const
+-/
 
 variable {f : α → E}
 
+#print MeasureTheory.Integrable.const_inner /-
 theorem Integrable.const_inner (c : E) (hf : Integrable f μ) : Integrable (fun x => ⟪c, f x⟫) μ :=
   by rw [← mem_ℒp_one_iff_integrable] at hf ⊢; exact hf.const_inner c
 #align measure_theory.integrable.const_inner MeasureTheory.Integrable.const_inner
+-/
 
+#print MeasureTheory.Integrable.inner_const /-
 theorem Integrable.inner_const (hf : Integrable f μ) (c : E) : Integrable (fun x => ⟪f x, c⟫) μ :=
   by rw [← mem_ℒp_one_iff_integrable] at hf ⊢; exact hf.inner_const c
 #align measure_theory.integrable.inner_const MeasureTheory.Integrable.inner_const
+-/
 
 variable [CompleteSpace E] [NormedSpace ℝ E]
 
+#print integral_inner /-
 theorem integral_inner {f : α → E} (hf : Integrable f μ) (c : E) :
     ∫ x, ⟪c, f x⟫ ∂μ = ⟪c, ∫ x, f x ∂μ⟫ :=
   ((innerSL 𝕜 c).restrictScalars ℝ).integral_comp_comm hf
 #align integral_inner integral_inner
+-/
 
 variable (𝕜)
 
--- mathport name: inner_with_explicit
 -- variable binder update doesn't work for lemmas which refer to `𝕜` only via the notation
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 
+#print integral_eq_zero_of_forall_integral_inner_eq_zero /-
 theorem integral_eq_zero_of_forall_integral_inner_eq_zero (f : α → E) (hf : Integrable f μ)
     (hf_int : ∀ c : E, ∫ x, ⟪c, f x⟫ ∂μ = 0) : ∫ x, f x ∂μ = 0 := by
   specialize hf_int (∫ x, f x ∂μ); rwa [integral_inner hf, inner_self_eq_zero] at hf_int 
 #align integral_eq_zero_of_forall_integral_inner_eq_zero integral_eq_zero_of_forall_integral_inner_eq_zero
+-/
 
 end InnerProductSpace
 
@@ -120,16 +136,18 @@ namespace L2
 variable {α E F 𝕜 : Type _} [IsROrC 𝕜] [MeasurableSpace α] {μ : Measure α} [NormedAddCommGroup E]
   [InnerProductSpace 𝕜 E] [NormedAddCommGroup F]
 
--- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
 
+#print MeasureTheory.L2.snorm_rpow_two_norm_lt_top /-
 theorem snorm_rpow_two_norm_lt_top (f : Lp F 2 μ) : snorm (fun x => ‖f x‖ ^ (2 : ℝ)) 1 μ < ∞ :=
   by
   have h_two : ENNReal.ofReal (2 : ℝ) = 2 := by simp [zero_le_one]
   rw [snorm_norm_rpow f zero_lt_two, one_mul, h_two]
   exact ENNReal.rpow_lt_top_of_nonneg zero_le_two (Lp.snorm_ne_top f)
 #align measure_theory.L2.snorm_rpow_two_norm_lt_top MeasureTheory.L2.snorm_rpow_two_norm_lt_top
+-/
 
+#print MeasureTheory.L2.snorm_inner_lt_top /-
 theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x, g x⟫) 1 μ < ∞ :=
   by
   have h : ∀ x, ‖⟪f x, g x⟫‖ ≤ ‖‖f x‖ ^ (2 : ℝ) + ‖g x‖ ^ (2 : ℝ)‖ :=
@@ -148,20 +166,22 @@ theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x
   rw [ENNReal.add_lt_top]
   exact ⟨snorm_rpow_two_norm_lt_top f, snorm_rpow_two_norm_lt_top g⟩
 #align measure_theory.L2.snorm_inner_lt_top MeasureTheory.L2.snorm_inner_lt_top
+-/
 
 section InnerProductSpace
 
 open scoped ComplexConjugate
 
-include 𝕜
-
 instance : Inner 𝕜 (α →₂[μ] E) :=
   ⟨fun f g => ∫ a, ⟪f a, g a⟫ ∂μ⟩
 
+#print MeasureTheory.L2.inner_def /-
 theorem inner_def (f g : α →₂[μ] E) : ⟪f, g⟫ = ∫ a : α, ⟪f a, g a⟫ ∂μ :=
   rfl
 #align measure_theory.L2.inner_def MeasureTheory.L2.inner_def
+-/
 
+#print MeasureTheory.L2.integral_inner_eq_sq_snorm /-
 theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
     ∫ a, ⟪f a, f a⟫ ∂μ = ENNReal.toReal (∫⁻ a, (‖f a‖₊ : ℝ≥0∞) ^ (2 : ℝ) ∂μ) :=
   by
@@ -178,6 +198,7 @@ theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
     ENNReal.ofReal_rpow_of_nonneg (norm_nonneg _) zero_le_two, ofReal_norm_eq_coe_nnnorm]
   norm_cast
 #align measure_theory.L2.integral_inner_eq_sq_snorm MeasureTheory.L2.integral_inner_eq_sq_snorm
+-/
 
 private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = IsROrC.re ⟪f, f⟫ :=
   by
@@ -191,19 +212,23 @@ private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = IsROrC.r
     rw [← h_two, ← snorm_eq_snorm' two_ne_zero ENNReal.two_ne_top]
     exact Lp.snorm_lt_top f
 
+#print MeasureTheory.L2.mem_L1_inner /-
 theorem mem_L1_inner (f g : α →₂[μ] E) :
     AEEqFun.mk (fun x => ⟪f x, g x⟫)
         ((Lp.aestronglyMeasurable f).inner (Lp.aestronglyMeasurable g)) ∈
       Lp 𝕜 1 μ :=
   by simp_rw [mem_Lp_iff_snorm_lt_top, snorm_ae_eq_fun]; exact snorm_inner_lt_top f g
 #align measure_theory.L2.mem_L1_inner MeasureTheory.L2.mem_L1_inner
+-/
 
+#print MeasureTheory.L2.integrable_inner /-
 theorem integrable_inner (f g : α →₂[μ] E) : Integrable (fun x : α => ⟪f x, g x⟫) μ :=
   (integrable_congr
         (AEEqFun.coeFn_mk (fun x => ⟪f x, g x⟫)
           ((Lp.aestronglyMeasurable f).inner (Lp.aestronglyMeasurable g)))).mp
     (AEEqFun.integrable_iff_mem_L1.mpr (mem_L1_inner f g))
 #align measure_theory.L2.integrable_inner MeasureTheory.L2.integrable_inner
+-/
 
 private theorem add_left' (f f' g : α →₂[μ] E) : ⟪f + f', g⟫ = inner f g + inner f' g :=
   by
@@ -221,6 +246,7 @@ private theorem smul_left' (f g : α →₂[μ] E) (r : 𝕜) : ⟪r • f, g⟫
   congr
   rwa [Pi.smul_apply] at hx 
 
+#print MeasureTheory.L2.innerProductSpace /-
 instance innerProductSpace : InnerProductSpace 𝕜 (α →₂[μ] E)
     where
   norm_sq_eq_inner := norm_sq_eq_inner'
@@ -228,6 +254,7 @@ instance innerProductSpace : InnerProductSpace 𝕜 (α →₂[μ] E)
   addLeft := add_left'
   smul_left := smul_left'
 #align measure_theory.L2.inner_product_space MeasureTheory.L2.innerProductSpace
+-/
 
 end InnerProductSpace
 
@@ -235,6 +262,7 @@ section IndicatorConstLp
 
 variable (𝕜) {s : Set α}
 
+#print MeasureTheory.L2.inner_indicatorConstLp_eq_set_integral_inner /-
 /-- The inner product in `L2` of the indicator of a set `indicator_const_Lp 2 hs hμs c` and `f` is
 equal to the integral of the inner product over `s`: `∫ x in s, ⟪c, f x⟫ ∂μ`. -/
 theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : MeasurableSet s) (c : E)
@@ -266,7 +294,9 @@ theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : Measu
     exact inner_zero_left _
   rw [h_left, h_right, add_zero]
 #align measure_theory.L2.inner_indicator_const_Lp_eq_set_integral_inner MeasureTheory.L2.inner_indicatorConstLp_eq_set_integral_inner
+-/
 
+#print MeasureTheory.L2.inner_indicatorConstLp_eq_inner_set_integral /-
 /-- The inner product in `L2` of the indicator of a set `indicator_const_Lp 2 hs hμs c` and `f` is
 equal to the inner product of the constant `c` and the integral of `f` over `s`. -/
 theorem inner_indicatorConstLp_eq_inner_set_integral [CompleteSpace E] [NormedSpace ℝ E]
@@ -275,15 +305,18 @@ theorem inner_indicatorConstLp_eq_inner_set_integral [CompleteSpace E] [NormedSp
   rw [← integral_inner (integrable_on_Lp_of_measure_ne_top f fact_one_le_two_ennreal.elim hμs),
     L2.inner_indicator_const_Lp_eq_set_integral_inner]
 #align measure_theory.L2.inner_indicator_const_Lp_eq_inner_set_integral MeasureTheory.L2.inner_indicatorConstLp_eq_inner_set_integral
+-/
 
 variable {𝕜}
 
+#print MeasureTheory.L2.inner_indicatorConstLp_one /-
 /-- The inner product in `L2` of the indicator of a set `indicator_const_Lp 2 hs hμs (1 : 𝕜)` and
 a real or complex function `f` is equal to the integral of `f` over `s`. -/
 theorem inner_indicatorConstLp_one (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (f : Lp 𝕜 2 μ) :
     ⟪indicatorConstLp 2 hs hμs (1 : 𝕜), f⟫ = ∫ x in s, f x ∂μ := by
   rw [L2.inner_indicator_const_Lp_eq_inner_set_integral 𝕜 hs hμs (1 : 𝕜) f]; simp
 #align measure_theory.L2.inner_indicator_const_Lp_one MeasureTheory.L2.inner_indicatorConstLp_one
+-/
 
 end IndicatorConstLp
 
@@ -297,9 +330,9 @@ variable (μ : Measure α) [IsFiniteMeasure μ]
 
 open scoped BoundedContinuousFunction ComplexConjugate
 
--- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 (α →₂[μ] 𝕜) _ x y
 
+#print MeasureTheory.BoundedContinuousFunction.inner_toLp /-
 /-- For bounded continuous functions `f`, `g` on a finite-measure topological space `α`, the L^2
 inner product is the integral of their pointwise inner product. -/
 theorem BoundedContinuousFunction.inner_toLp (f g : α →ᵇ 𝕜) :
@@ -313,9 +346,11 @@ theorem BoundedContinuousFunction.inner_toLp (f g : α →ᵇ 𝕜) :
   rw [hf, hg]
   simp
 #align measure_theory.bounded_continuous_function.inner_to_Lp MeasureTheory.BoundedContinuousFunction.inner_toLp
+-/
 
 variable [CompactSpace α]
 
+#print MeasureTheory.ContinuousMap.inner_toLp /-
 /-- For continuous functions `f`, `g` on a compact, finite-measure topological space `α`, the L^2
 inner product is the integral of their pointwise inner product. -/
 theorem ContinuousMap.inner_toLp (f g : C(α, 𝕜)) :
@@ -328,6 +363,7 @@ theorem ContinuousMap.inner_toLp (f g : C(α, 𝕜)) :
   rw [hf, hg]
   simp
 #align measure_theory.continuous_map.inner_to_Lp MeasureTheory.ContinuousMap.inner_toLp
+-/
 
 end InnerContinuous
 

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

@@ -98,7 +98,7 @@ theorem Integrable.inner_const (hf : Integrable f μ) (c : E) : Integrable (fun
 variable [CompleteSpace E] [NormedSpace ℝ E]
 
 theorem integral_inner {f : α → E} (hf : Integrable f μ) (c : E) :
-    (∫ x, ⟪c, f x⟫ ∂μ) = ⟪c, ∫ x, f x ∂μ⟫ :=
+    ∫ x, ⟪c, f x⟫ ∂μ = ⟪c, ∫ x, f x ∂μ⟫ :=
   ((innerSL 𝕜 c).restrictScalars ℝ).integral_comp_comm hf
 #align integral_inner integral_inner
 
@@ -109,7 +109,7 @@ variable (𝕜)
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 
 theorem integral_eq_zero_of_forall_integral_inner_eq_zero (f : α → E) (hf : Integrable f μ)
-    (hf_int : ∀ c : E, (∫ x, ⟪c, f x⟫ ∂μ) = 0) : (∫ x, f x ∂μ) = 0 := by
+    (hf_int : ∀ c : E, ∫ x, ⟪c, f x⟫ ∂μ = 0) : ∫ x, f x ∂μ = 0 := by
   specialize hf_int (∫ x, f x ∂μ); rwa [integral_inner hf, inner_self_eq_zero] at hf_int 
 #align integral_eq_zero_of_forall_integral_inner_eq_zero integral_eq_zero_of_forall_integral_inner_eq_zero
 
@@ -163,7 +163,7 @@ theorem inner_def (f g : α →₂[μ] E) : ⟪f, g⟫ = ∫ a : α, ⟪f a, g a
 #align measure_theory.L2.inner_def MeasureTheory.L2.inner_def
 
 theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
-    (∫ a, ⟪f a, f a⟫ ∂μ) = ENNReal.toReal (∫⁻ a, (‖f a‖₊ : ℝ≥0∞) ^ (2 : ℝ) ∂μ) :=
+    ∫ a, ⟪f a, f a⟫ ∂μ = ENNReal.toReal (∫⁻ a, (‖f a‖₊ : ℝ≥0∞) ^ (2 : ℝ) ∂μ) :=
   by
   simp_rw [inner_self_eq_norm_sq_to_K]
   norm_cast
@@ -241,7 +241,7 @@ theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : Measu
     (hμs : μ s ≠ ∞) : (⟪indicatorConstLp 2 hs hμs c, f⟫ : 𝕜) = ∫ x in s, ⟪c, f x⟫ ∂μ :=
   by
   rw [inner_def, ← integral_add_compl hs (L2.integrable_inner _ f)]
-  have h_left : (∫ x in s, ⟪(indicator_const_Lp 2 hs hμs c) x, f x⟫ ∂μ) = ∫ x in s, ⟪c, f x⟫ ∂μ :=
+  have h_left : ∫ x in s, ⟪(indicator_const_Lp 2 hs hμs c) x, f x⟫ ∂μ = ∫ x in s, ⟪c, f x⟫ ∂μ :=
     by
     suffices h_ae_eq : ∀ᵐ x ∂μ, x ∈ s → ⟪indicator_const_Lp 2 hs hμs c x, f x⟫ = ⟪c, f x⟫
     exact set_integral_congr_ae hs h_ae_eq
@@ -250,12 +250,12 @@ theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : Measu
     refine' h_indicator.mono fun x hx hxs => _
     congr
     exact hx hxs
-  have h_right : (∫ x in sᶜ, ⟪(indicator_const_Lp 2 hs hμs c) x, f x⟫ ∂μ) = 0 :=
+  have h_right : ∫ x in sᶜ, ⟪(indicator_const_Lp 2 hs hμs c) x, f x⟫ ∂μ = 0 :=
     by
     suffices h_ae_eq : ∀ᵐ x ∂μ, x ∉ s → ⟪indicator_const_Lp 2 hs hμs c x, f x⟫ = 0
     · simp_rw [← Set.mem_compl_iff] at h_ae_eq 
       suffices h_int_zero :
-        (∫ x in sᶜ, inner (indicator_const_Lp 2 hs hμs c x) (f x) ∂μ) = ∫ x in sᶜ, (0 : 𝕜) ∂μ
+        ∫ x in sᶜ, inner (indicator_const_Lp 2 hs hμs c x) (f x) ∂μ = ∫ x in sᶜ, (0 : 𝕜) ∂μ
       · rw [h_int_zero]
         simp
       exact set_integral_congr_ae hs.compl h_ae_eq

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

@@ -142,7 +142,6 @@ theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x
         (mul_le_mul_of_nonneg_right (le_mul_of_one_le_left (norm_nonneg _) one_le_two)
           (norm_nonneg _))
       _ ≤ ‖‖f x‖ ^ 2 + ‖g x‖ ^ 2‖ := (two_mul_le_add_sq _ _).trans (le_abs_self _)
-      
   refine' (snorm_mono_ae (ae_of_all _ h)).trans_lt ((snorm_add_le _ _ le_rfl).trans_lt _)
   · exact ((Lp.ae_strongly_measurable f).norm.AEMeasurable.pow_const _).AEStronglyMeasurable
   · exact ((Lp.ae_strongly_measurable g).norm.AEMeasurable.pow_const _).AEStronglyMeasurable

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

@@ -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.l2_space
-! leanprover-community/mathlib commit 83a66c8775fa14ee5180c85cab98e970956401ad
+! leanprover-community/mathlib commit 7e5137f579de09a059a5ce98f364a04e221aabf0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.MeasureTheory.Integral.SetIntegral
 
 /-! # `L^2` space
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 If `E` is an inner product space over `𝕜` (`ℝ` or `ℂ`), then `Lp E 2 μ` (defined in `lp_space.lean`)
 is also an inner product space, with inner product defined as `inner f g = ∫ a, ⟪f a, g a⟫ ∂μ`.
 

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

@@ -48,7 +48,7 @@ theorem memℒp_two_iff_integrable_sq_norm {f : α → F} (hf : AEStronglyMeasur
     Memℒp f 2 μ ↔ Integrable (fun x => ‖f x‖ ^ 2) μ :=
   by
   rw [← mem_ℒp_one_iff_integrable]
-  convert(mem_ℒp_norm_rpow_iff hf two_ne_zero ENNReal.two_ne_top).symm
+  convert (mem_ℒp_norm_rpow_iff hf two_ne_zero ENNReal.two_ne_top).symm
   · simp
   · rw [div_eq_mul_inv, ENNReal.mul_inv_cancel two_ne_zero ENNReal.two_ne_top]
 #align measure_theory.mem_ℒp_two_iff_integrable_sq_norm MeasureTheory.memℒp_two_iff_integrable_sq_norm
@@ -291,7 +291,7 @@ section InnerContinuous
 
 variable {α : Type _} [TopologicalSpace α] [MeasureSpace α] [BorelSpace α] {𝕜 : Type _} [IsROrC 𝕜]
 
-variable (μ : Measure α) [FiniteMeasure μ]
+variable (μ : Measure α) [IsFiniteMeasure μ]
 
 open scoped BoundedContinuousFunction ComplexConjugate
 
@@ -307,7 +307,7 @@ theorem BoundedContinuousFunction.inner_toLp (f g : α →ᵇ 𝕜) :
   apply integral_congr_ae
   have hf_ae := f.coe_fn_to_Lp 2 μ 𝕜
   have hg_ae := g.coe_fn_to_Lp 2 μ 𝕜
-  filter_upwards [hf_ae, hg_ae]with _ hf hg
+  filter_upwards [hf_ae, hg_ae] with _ hf hg
   rw [hf, hg]
   simp
 #align measure_theory.bounded_continuous_function.inner_to_Lp MeasureTheory.BoundedContinuousFunction.inner_toLp
@@ -322,7 +322,7 @@ theorem ContinuousMap.inner_toLp (f g : C(α, 𝕜)) :
   apply integral_congr_ae
   have hf_ae := f.coe_fn_to_Lp μ
   have hg_ae := g.coe_fn_to_Lp μ
-  filter_upwards [hf_ae, hg_ae]with _ hf hg
+  filter_upwards [hf_ae, hg_ae] with _ hf hg
   rw [hf, hg]
   simp
 #align measure_theory.continuous_map.inner_to_Lp MeasureTheory.ContinuousMap.inner_toLp

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

@@ -85,11 +85,11 @@ theorem Memℒp.inner_const {f : α → E} (hf : Memℒp f p μ) (c : E) : Mem
 variable {f : α → E}
 
 theorem Integrable.const_inner (c : E) (hf : Integrable f μ) : Integrable (fun x => ⟪c, f x⟫) μ :=
-  by rw [← mem_ℒp_one_iff_integrable] at hf⊢; exact hf.const_inner c
+  by rw [← mem_ℒp_one_iff_integrable] at hf ⊢; exact hf.const_inner c
 #align measure_theory.integrable.const_inner MeasureTheory.Integrable.const_inner
 
 theorem Integrable.inner_const (hf : Integrable f μ) (c : E) : Integrable (fun x => ⟪f x, c⟫) μ :=
-  by rw [← mem_ℒp_one_iff_integrable] at hf⊢; exact hf.inner_const c
+  by rw [← mem_ℒp_one_iff_integrable] at hf ⊢; exact hf.inner_const c
 #align measure_theory.integrable.inner_const MeasureTheory.Integrable.inner_const
 
 variable [CompleteSpace E] [NormedSpace ℝ E]
@@ -107,7 +107,7 @@ local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 
 theorem integral_eq_zero_of_forall_integral_inner_eq_zero (f : α → E) (hf : Integrable f μ)
     (hf_int : ∀ c : E, (∫ x, ⟪c, f x⟫ ∂μ) = 0) : (∫ x, f x ∂μ) = 0 := by
-  specialize hf_int (∫ x, f x ∂μ); rwa [integral_inner hf, inner_self_eq_zero] at hf_int
+  specialize hf_int (∫ x, f x ∂μ); rwa [integral_inner hf, inner_self_eq_zero] at hf_int 
 #align integral_eq_zero_of_forall_integral_inner_eq_zero integral_eq_zero_of_forall_integral_inner_eq_zero
 
 end InnerProductSpace
@@ -209,7 +209,7 @@ private theorem add_left' (f f' g : α →₂[μ] E) : ⟪f + f', g⟫ = inner f
     inner_add_left]
   refine' integral_congr_ae ((coe_fn_add f f').mono fun x hx => _)
   congr
-  rwa [Pi.add_apply] at hx
+  rwa [Pi.add_apply] at hx 
 
 private theorem smul_left' (f g : α →₂[μ] E) (r : 𝕜) : ⟪r • f, g⟫ = conj r * inner f g :=
   by
@@ -217,7 +217,7 @@ private theorem smul_left' (f g : α →₂[μ] E) (r : 𝕜) : ⟪r • f, g⟫
   refine' integral_congr_ae ((coe_fn_smul r f).mono fun x hx => _)
   rw [smul_eq_mul, ← inner_smul_left]
   congr
-  rwa [Pi.smul_apply] at hx
+  rwa [Pi.smul_apply] at hx 
 
 instance innerProductSpace : InnerProductSpace 𝕜 (α →₂[μ] E)
     where
@@ -251,7 +251,7 @@ theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : Measu
   have h_right : (∫ x in sᶜ, ⟪(indicator_const_Lp 2 hs hμs c) x, f x⟫ ∂μ) = 0 :=
     by
     suffices h_ae_eq : ∀ᵐ x ∂μ, x ∉ s → ⟪indicator_const_Lp 2 hs hμs c x, f x⟫ = 0
-    · simp_rw [← Set.mem_compl_iff] at h_ae_eq
+    · simp_rw [← Set.mem_compl_iff] at h_ae_eq 
       suffices h_int_zero :
         (∫ x in sᶜ, inner (indicator_const_Lp 2 hs hμs c x) (f x) ∂μ) = ∫ x in sᶜ, (0 : 𝕜) ∂μ
       · rw [h_int_zero]

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

@@ -30,7 +30,7 @@ is also an inner product space, with inner product defined as `inner f g = ∫ a
 
 noncomputable section
 
-open TopologicalSpace MeasureTheory MeasureTheory.lp Filter
+open TopologicalSpace MeasureTheory MeasureTheory.Lp Filter
 
 open scoped NNReal ENNReal MeasureTheory
 
@@ -120,7 +120,7 @@ variable {α E F 𝕜 : Type _} [IsROrC 𝕜] [MeasurableSpace α] {μ : Measure
 -- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
 
-theorem snorm_rpow_two_norm_lt_top (f : lp F 2 μ) : snorm (fun x => ‖f x‖ ^ (2 : ℝ)) 1 μ < ∞ :=
+theorem snorm_rpow_two_norm_lt_top (f : Lp F 2 μ) : snorm (fun x => ‖f x‖ ^ (2 : ℝ)) 1 μ < ∞ :=
   by
   have h_two : ENNReal.ofReal (2 : ℝ) = 2 := by simp [zero_le_one]
   rw [snorm_norm_rpow f zero_lt_two, one_mul, h_two]
@@ -191,15 +191,15 @@ private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = IsROrC.r
 
 theorem mem_L1_inner (f g : α →₂[μ] E) :
     AEEqFun.mk (fun x => ⟪f x, g x⟫)
-        ((lp.aEStronglyMeasurable f).inner (lp.aEStronglyMeasurable g)) ∈
-      lp 𝕜 1 μ :=
+        ((Lp.aestronglyMeasurable f).inner (Lp.aestronglyMeasurable g)) ∈
+      Lp 𝕜 1 μ :=
   by simp_rw [mem_Lp_iff_snorm_lt_top, snorm_ae_eq_fun]; exact snorm_inner_lt_top f g
 #align measure_theory.L2.mem_L1_inner MeasureTheory.L2.mem_L1_inner
 
 theorem integrable_inner (f g : α →₂[μ] E) : Integrable (fun x : α => ⟪f x, g x⟫) μ :=
   (integrable_congr
         (AEEqFun.coeFn_mk (fun x => ⟪f x, g x⟫)
-          ((lp.aEStronglyMeasurable f).inner (lp.aEStronglyMeasurable g)))).mp
+          ((Lp.aestronglyMeasurable f).inner (Lp.aestronglyMeasurable g)))).mp
     (AEEqFun.integrable_iff_mem_L1.mpr (mem_L1_inner f g))
 #align measure_theory.L2.integrable_inner MeasureTheory.L2.integrable_inner
 
@@ -235,7 +235,7 @@ variable (𝕜) {s : Set α}
 
 /-- The inner product in `L2` of the indicator of a set `indicator_const_Lp 2 hs hμs c` and `f` is
 equal to the integral of the inner product over `s`: `∫ x in s, ⟪c, f x⟫ ∂μ`. -/
-theorem inner_indicatorConstLp_eq_set_integral_inner (f : lp E 2 μ) (hs : MeasurableSet s) (c : E)
+theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : MeasurableSet s) (c : E)
     (hμs : μ s ≠ ∞) : (⟪indicatorConstLp 2 hs hμs c, f⟫ : 𝕜) = ∫ x in s, ⟪c, f x⟫ ∂μ :=
   by
   rw [inner_def, ← integral_add_compl hs (L2.integrable_inner _ f)]
@@ -268,7 +268,7 @@ theorem inner_indicatorConstLp_eq_set_integral_inner (f : lp E 2 μ) (hs : Measu
 /-- The inner product in `L2` of the indicator of a set `indicator_const_Lp 2 hs hμs c` and `f` is
 equal to the inner product of the constant `c` and the integral of `f` over `s`. -/
 theorem inner_indicatorConstLp_eq_inner_set_integral [CompleteSpace E] [NormedSpace ℝ E]
-    (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (c : E) (f : lp E 2 μ) :
+    (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (c : E) (f : Lp E 2 μ) :
     (⟪indicatorConstLp 2 hs hμs c, f⟫ : 𝕜) = ⟪c, ∫ x in s, f x ∂μ⟫ := by
   rw [← integral_inner (integrable_on_Lp_of_measure_ne_top f fact_one_le_two_ennreal.elim hμs),
     L2.inner_indicator_const_Lp_eq_set_integral_inner]
@@ -278,7 +278,7 @@ variable {𝕜}
 
 /-- The inner product in `L2` of the indicator of a set `indicator_const_Lp 2 hs hμs (1 : 𝕜)` and
 a real or complex function `f` is equal to the integral of `f` over `s`. -/
-theorem inner_indicatorConstLp_one (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (f : lp 𝕜 2 μ) :
+theorem inner_indicatorConstLp_one (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (f : Lp 𝕜 2 μ) :
     ⟪indicatorConstLp 2 hs hμs (1 : 𝕜), f⟫ = ∫ x in s, f x ∂μ := by
   rw [L2.inner_indicator_const_Lp_eq_inner_set_integral 𝕜 hs hμs (1 : 𝕜) f]; simp
 #align measure_theory.L2.inner_indicator_const_Lp_one MeasureTheory.L2.inner_indicatorConstLp_one

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

@@ -32,7 +32,7 @@ noncomputable section
 
 open TopologicalSpace MeasureTheory MeasureTheory.lp Filter
 
-open NNReal ENNReal MeasureTheory
+open scoped NNReal ENNReal MeasureTheory
 
 namespace MeasureTheory
 
@@ -149,7 +149,7 @@ theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x
 
 section InnerProductSpace
 
-open ComplexConjugate
+open scoped ComplexConjugate
 
 include 𝕜
 
@@ -293,7 +293,7 @@ variable {α : Type _} [TopologicalSpace α] [MeasureSpace α] [BorelSpace α] {
 
 variable (μ : Measure α) [FiniteMeasure μ]
 
-open BoundedContinuousFunction ComplexConjugate
+open scoped BoundedContinuousFunction ComplexConjugate
 
 -- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 (α →₂[μ] 𝕜) _ x y

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

@@ -79,23 +79,17 @@ theorem Memℒp.const_inner (c : E) {f : α → E} (hf : Memℒp f p μ) : Mem
 
 theorem Memℒp.inner_const {f : α → E} (hf : Memℒp f p μ) (c : E) : Memℒp (fun a => ⟪f a, c⟫) p μ :=
   hf.of_le_mul (AEStronglyMeasurable.inner hf.1 aestronglyMeasurable_const)
-    (eventually_of_forall fun x => by
-      rw [mul_comm]
-      exact norm_inner_le_norm _ _)
+    (eventually_of_forall fun x => by rw [mul_comm]; exact norm_inner_le_norm _ _)
 #align measure_theory.mem_ℒp.inner_const MeasureTheory.Memℒp.inner_const
 
 variable {f : α → E}
 
 theorem Integrable.const_inner (c : E) (hf : Integrable f μ) : Integrable (fun x => ⟪c, f x⟫) μ :=
-  by
-  rw [← mem_ℒp_one_iff_integrable] at hf⊢
-  exact hf.const_inner c
+  by rw [← mem_ℒp_one_iff_integrable] at hf⊢; exact hf.const_inner c
 #align measure_theory.integrable.const_inner MeasureTheory.Integrable.const_inner
 
 theorem Integrable.inner_const (hf : Integrable f μ) (c : E) : Integrable (fun x => ⟪f x, c⟫) μ :=
-  by
-  rw [← mem_ℒp_one_iff_integrable] at hf⊢
-  exact hf.inner_const c
+  by rw [← mem_ℒp_one_iff_integrable] at hf⊢; exact hf.inner_const c
 #align measure_theory.integrable.inner_const MeasureTheory.Integrable.inner_const
 
 variable [CompleteSpace E] [NormedSpace ℝ E]
@@ -112,10 +106,8 @@ variable (𝕜)
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 
 theorem integral_eq_zero_of_forall_integral_inner_eq_zero (f : α → E) (hf : Integrable f μ)
-    (hf_int : ∀ c : E, (∫ x, ⟪c, f x⟫ ∂μ) = 0) : (∫ x, f x ∂μ) = 0 :=
-  by
-  specialize hf_int (∫ x, f x ∂μ)
-  rwa [integral_inner hf, inner_self_eq_zero] at hf_int
+    (hf_int : ∀ c : E, (∫ x, ⟪c, f x⟫ ∂μ) = 0) : (∫ x, f x ∂μ) = 0 := by
+  specialize hf_int (∫ x, f x ∂μ); rwa [integral_inner hf, inner_self_eq_zero] at hf_int
 #align integral_eq_zero_of_forall_integral_inner_eq_zero integral_eq_zero_of_forall_integral_inner_eq_zero
 
 end InnerProductSpace
@@ -201,9 +193,7 @@ theorem mem_L1_inner (f g : α →₂[μ] E) :
     AEEqFun.mk (fun x => ⟪f x, g x⟫)
         ((lp.aEStronglyMeasurable f).inner (lp.aEStronglyMeasurable g)) ∈
       lp 𝕜 1 μ :=
-  by
-  simp_rw [mem_Lp_iff_snorm_lt_top, snorm_ae_eq_fun]
-  exact snorm_inner_lt_top f g
+  by simp_rw [mem_Lp_iff_snorm_lt_top, snorm_ae_eq_fun]; exact snorm_inner_lt_top f g
 #align measure_theory.L2.mem_L1_inner MeasureTheory.L2.mem_L1_inner
 
 theorem integrable_inner (f g : α →₂[μ] E) : Integrable (fun x : α => ⟪f x, g x⟫) μ :=
@@ -289,10 +279,8 @@ variable {𝕜}
 /-- The inner product in `L2` of the indicator of a set `indicator_const_Lp 2 hs hμs (1 : 𝕜)` and
 a real or complex function `f` is equal to the integral of `f` over `s`. -/
 theorem inner_indicatorConstLp_one (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (f : lp 𝕜 2 μ) :
-    ⟪indicatorConstLp 2 hs hμs (1 : 𝕜), f⟫ = ∫ x in s, f x ∂μ :=
-  by
-  rw [L2.inner_indicator_const_Lp_eq_inner_set_integral 𝕜 hs hμs (1 : 𝕜) f]
-  simp
+    ⟪indicatorConstLp 2 hs hμs (1 : 𝕜), f⟫ = ∫ x in s, f x ∂μ := by
+  rw [L2.inner_indicator_const_Lp_eq_inner_set_integral 𝕜 hs hμs (1 : 𝕜) f]; simp
 #align measure_theory.L2.inner_indicator_const_Lp_one MeasureTheory.L2.inner_indicatorConstLp_one
 
 end IndicatorConstLp

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

@@ -196,7 +196,6 @@ private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = IsROrC.r
   · refine' (lintegral_rpow_nnnorm_lt_top_of_snorm'_lt_top zero_lt_two _).Ne
     rw [← h_two, ← snorm_eq_snorm' two_ne_zero ENNReal.two_ne_top]
     exact Lp.snorm_lt_top f
-#align measure_theory.L2.norm_sq_eq_inner' measure_theory.L2.norm_sq_eq_inner'
 
 theorem mem_L1_inner (f g : α →₂[μ] E) :
     AEEqFun.mk (fun x => ⟪f x, g x⟫)
@@ -221,7 +220,6 @@ private theorem add_left' (f f' g : α →₂[μ] E) : ⟪f + f', g⟫ = inner f
   refine' integral_congr_ae ((coe_fn_add f f').mono fun x hx => _)
   congr
   rwa [Pi.add_apply] at hx
-#align measure_theory.L2.add_left' measure_theory.L2.add_left'
 
 private theorem smul_left' (f g : α →₂[μ] E) (r : 𝕜) : ⟪r • f, g⟫ = conj r * inner f g :=
   by
@@ -230,7 +228,6 @@ private theorem smul_left' (f g : α →₂[μ] E) (r : 𝕜) : ⟪r • f, g⟫
   rw [smul_eq_mul, ← inner_smul_left]
   congr
   rwa [Pi.smul_apply] at hx
-#align measure_theory.L2.smul_left' measure_theory.L2.smul_left'
 
 instance innerProductSpace : InnerProductSpace 𝕜 (α →₂[μ] E)
     where

mathlib commit https://github.com/leanprover-community/mathlib/commit/ef95945cd48c932c9e034872bd25c3c220d9c946

@@ -161,7 +161,7 @@ open ComplexConjugate
 
 include 𝕜
 
-instance : HasInner 𝕜 (α →₂[μ] E) :=
+instance : Inner 𝕜 (α →₂[μ] E) :=
   ⟨fun f g => ∫ a, ⟪f a, g a⟫ ∂μ⟩
 
 theorem inner_def (f g : α →₂[μ] E) : ⟪f, g⟫ = ∫ a : α, ⟪f a, g a⟫ ∂μ :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -199,7 +199,7 @@ private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = IsROrC.r
 #align measure_theory.L2.norm_sq_eq_inner' measure_theory.L2.norm_sq_eq_inner'
 
 theorem mem_L1_inner (f g : α →₂[μ] E) :
-    AeEqFun.mk (fun x => ⟪f x, g x⟫)
+    AEEqFun.mk (fun x => ⟪f x, g x⟫)
         ((lp.aEStronglyMeasurable f).inner (lp.aEStronglyMeasurable g)) ∈
       lp 𝕜 1 μ :=
   by
@@ -209,9 +209,9 @@ theorem mem_L1_inner (f g : α →₂[μ] E) :
 
 theorem integrable_inner (f g : α →₂[μ] E) : Integrable (fun x : α => ⟪f x, g x⟫) μ :=
   (integrable_congr
-        (AeEqFun.coeFn_mk (fun x => ⟪f x, g x⟫)
+        (AEEqFun.coeFn_mk (fun x => ⟪f x, g x⟫)
           ((lp.aEStronglyMeasurable f).inner (lp.aEStronglyMeasurable g)))).mp
-    (AeEqFun.integrable_iff_mem_L1.mpr (mem_L1_inner f g))
+    (AEEqFun.integrable_iff_mem_L1.mpr (mem_L1_inner f g))
 #align measure_theory.L2.integrable_inner MeasureTheory.L2.integrable_inner
 
 private theorem add_left' (f f' g : α →₂[μ] E) : ⟪f + f', g⟫ = inner f g + inner f' g :=

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

@@ -44,7 +44,7 @@ theorem Memℒp.integrable_sq {f : α → ℝ} (h : Memℒp f 2 μ) : Integrable
   simpa [← mem_ℒp_one_iff_integrable] using h.norm_rpow two_ne_zero ENNReal.two_ne_top
 #align measure_theory.mem_ℒp.integrable_sq MeasureTheory.Memℒp.integrable_sq
 
-theorem memℒp_two_iff_integrable_sq_norm {f : α → F} (hf : AeStronglyMeasurable f μ) :
+theorem memℒp_two_iff_integrable_sq_norm {f : α → F} (hf : AEStronglyMeasurable f μ) :
     Memℒp f 2 μ ↔ Integrable (fun x => ‖f x‖ ^ 2) μ :=
   by
   rw [← mem_ℒp_one_iff_integrable]
@@ -53,7 +53,7 @@ theorem memℒp_two_iff_integrable_sq_norm {f : α → F} (hf : AeStronglyMeasur
   · rw [div_eq_mul_inv, ENNReal.mul_inv_cancel two_ne_zero ENNReal.two_ne_top]
 #align measure_theory.mem_ℒp_two_iff_integrable_sq_norm MeasureTheory.memℒp_two_iff_integrable_sq_norm
 
-theorem memℒp_two_iff_integrable_sq {f : α → ℝ} (hf : AeStronglyMeasurable f μ) :
+theorem memℒp_two_iff_integrable_sq {f : α → ℝ} (hf : AEStronglyMeasurable f μ) :
     Memℒp f 2 μ ↔ Integrable (fun x => f x ^ 2) μ :=
   by
   convert mem_ℒp_two_iff_integrable_sq_norm hf
@@ -73,12 +73,12 @@ variable {E 𝕜 : Type _} [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpa
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 
 theorem Memℒp.const_inner (c : E) {f : α → E} (hf : Memℒp f p μ) : Memℒp (fun a => ⟪c, f a⟫) p μ :=
-  hf.of_le_mul (AeStronglyMeasurable.inner aeStronglyMeasurable_const hf.1)
+  hf.of_le_mul (AEStronglyMeasurable.inner aestronglyMeasurable_const hf.1)
     (eventually_of_forall fun x => norm_inner_le_norm _ _)
 #align measure_theory.mem_ℒp.const_inner MeasureTheory.Memℒp.const_inner
 
 theorem Memℒp.inner_const {f : α → E} (hf : Memℒp f p μ) (c : E) : Memℒp (fun a => ⟪f a, c⟫) p μ :=
-  hf.of_le_mul (AeStronglyMeasurable.inner hf.1 aeStronglyMeasurable_const)
+  hf.of_le_mul (AEStronglyMeasurable.inner hf.1 aestronglyMeasurable_const)
     (eventually_of_forall fun x => by
       rw [mul_comm]
       exact norm_inner_le_norm _ _)
@@ -149,8 +149,8 @@ theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x
       _ ≤ ‖‖f x‖ ^ 2 + ‖g x‖ ^ 2‖ := (two_mul_le_add_sq _ _).trans (le_abs_self _)
       
   refine' (snorm_mono_ae (ae_of_all _ h)).trans_lt ((snorm_add_le _ _ le_rfl).trans_lt _)
-  · exact ((Lp.ae_strongly_measurable f).norm.AEMeasurable.pow_const _).AeStronglyMeasurable
-  · exact ((Lp.ae_strongly_measurable g).norm.AEMeasurable.pow_const _).AeStronglyMeasurable
+  · exact ((Lp.ae_strongly_measurable f).norm.AEMeasurable.pow_const _).AEStronglyMeasurable
+  · exact ((Lp.ae_strongly_measurable g).norm.AEMeasurable.pow_const _).AEStronglyMeasurable
   rw [ENNReal.add_lt_top]
   exact ⟨snorm_rpow_two_norm_lt_top f, snorm_rpow_two_norm_lt_top g⟩
 #align measure_theory.L2.snorm_inner_lt_top MeasureTheory.L2.snorm_inner_lt_top
@@ -176,7 +176,7 @@ theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
   rw [integral_eq_lintegral_of_nonneg_ae]
   rotate_left
   · exact Filter.eventually_of_forall fun x => sq_nonneg _
-  · exact ((Lp.ae_strongly_measurable f).norm.AEMeasurable.pow_const _).AeStronglyMeasurable
+  · exact ((Lp.ae_strongly_measurable f).norm.AEMeasurable.pow_const _).AEStronglyMeasurable
   congr
   ext1 x
   have h_two : (2 : ℝ) = ((2 : ℕ) : ℝ) := by simp
@@ -200,7 +200,7 @@ private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = IsROrC.r
 
 theorem mem_L1_inner (f g : α →₂[μ] E) :
     AeEqFun.mk (fun x => ⟪f x, g x⟫)
-        ((lp.aeStronglyMeasurable f).inner (lp.aeStronglyMeasurable g)) ∈
+        ((lp.aEStronglyMeasurable f).inner (lp.aEStronglyMeasurable g)) ∈
       lp 𝕜 1 μ :=
   by
   simp_rw [mem_Lp_iff_snorm_lt_top, snorm_ae_eq_fun]
@@ -210,7 +210,7 @@ theorem mem_L1_inner (f g : α →₂[μ] E) :
 theorem integrable_inner (f g : α →₂[μ] E) : Integrable (fun x : α => ⟪f x, g x⟫) μ :=
   (integrable_congr
         (AeEqFun.coeFn_mk (fun x => ⟪f x, g x⟫)
-          ((lp.aeStronglyMeasurable f).inner (lp.aeStronglyMeasurable g)))).mp
+          ((lp.aEStronglyMeasurable f).inner (lp.aEStronglyMeasurable g)))).mp
     (AeEqFun.integrable_iff_mem_L1.mpr (mem_L1_inner f g))
 #align measure_theory.L2.integrable_inner MeasureTheory.L2.integrable_inner
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 
 ! This file was ported from Lean 3 source module measure_theory.function.l2_space
-! leanprover-community/mathlib commit 24e0c85412ff6adbeca08022c25ba4876eedf37a
+! leanprover-community/mathlib commit 83a66c8775fa14ee5180c85cab98e970956401ad
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
+import Mathbin.Data.IsROrC.Lemmas
 import Mathbin.MeasureTheory.Function.StronglyMeasurable.Inner
 import Mathbin.MeasureTheory.Integral.SetIntegral
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 
 ! This file was ported from Lean 3 source module measure_theory.function.l2_space
-! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
+! leanprover-community/mathlib commit 24e0c85412ff6adbeca08022c25ba4876eedf37a
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.InnerProductSpace.Basic
+import Mathbin.MeasureTheory.Function.StronglyMeasurable.Inner
 import Mathbin.MeasureTheory.Integral.SetIntegral
 
 /-! # `L^2` space
@@ -29,7 +29,7 @@ is also an inner product space, with inner product defined as `inner f g = ∫ a
 
 noncomputable section
 
-open TopologicalSpace MeasureTheory MeasureTheory.lp
+open TopologicalSpace MeasureTheory MeasureTheory.lp Filter
 
 open NNReal ENNReal MeasureTheory
 
@@ -62,6 +62,63 @@ theorem memℒp_two_iff_integrable_sq {f : α → ℝ} (hf : AeStronglyMeasurabl
 
 end
 
+section InnerProductSpace
+
+variable {α : Type _} {m : MeasurableSpace α} {p : ℝ≥0∞} {μ : Measure α}
+
+variable {E 𝕜 : Type _} [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
+
+-- mathport name: «expr⟪ , ⟫»
+local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
+
+theorem Memℒp.const_inner (c : E) {f : α → E} (hf : Memℒp f p μ) : Memℒp (fun a => ⟪c, f a⟫) p μ :=
+  hf.of_le_mul (AeStronglyMeasurable.inner aeStronglyMeasurable_const hf.1)
+    (eventually_of_forall fun x => norm_inner_le_norm _ _)
+#align measure_theory.mem_ℒp.const_inner MeasureTheory.Memℒp.const_inner
+
+theorem Memℒp.inner_const {f : α → E} (hf : Memℒp f p μ) (c : E) : Memℒp (fun a => ⟪f a, c⟫) p μ :=
+  hf.of_le_mul (AeStronglyMeasurable.inner hf.1 aeStronglyMeasurable_const)
+    (eventually_of_forall fun x => by
+      rw [mul_comm]
+      exact norm_inner_le_norm _ _)
+#align measure_theory.mem_ℒp.inner_const MeasureTheory.Memℒp.inner_const
+
+variable {f : α → E}
+
+theorem Integrable.const_inner (c : E) (hf : Integrable f μ) : Integrable (fun x => ⟪c, f x⟫) μ :=
+  by
+  rw [← mem_ℒp_one_iff_integrable] at hf⊢
+  exact hf.const_inner c
+#align measure_theory.integrable.const_inner MeasureTheory.Integrable.const_inner
+
+theorem Integrable.inner_const (hf : Integrable f μ) (c : E) : Integrable (fun x => ⟪f x, c⟫) μ :=
+  by
+  rw [← mem_ℒp_one_iff_integrable] at hf⊢
+  exact hf.inner_const c
+#align measure_theory.integrable.inner_const MeasureTheory.Integrable.inner_const
+
+variable [CompleteSpace E] [NormedSpace ℝ E]
+
+theorem integral_inner {f : α → E} (hf : Integrable f μ) (c : E) :
+    (∫ x, ⟪c, f x⟫ ∂μ) = ⟪c, ∫ x, f x ∂μ⟫ :=
+  ((innerSL 𝕜 c).restrictScalars ℝ).integral_comp_comm hf
+#align integral_inner integral_inner
+
+variable (𝕜)
+
+-- mathport name: inner_with_explicit
+-- variable binder update doesn't work for lemmas which refer to `𝕜` only via the notation
+local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
+
+theorem integral_eq_zero_of_forall_integral_inner_eq_zero (f : α → E) (hf : Integrable f μ)
+    (hf_int : ∀ c : E, (∫ x, ⟪c, f x⟫ ∂μ) = 0) : (∫ x, f x ∂μ) = 0 :=
+  by
+  specialize hf_int (∫ x, f x ∂μ)
+  rwa [integral_inner hf, inner_self_eq_zero] at hf_int
+#align integral_eq_zero_of_forall_integral_inner_eq_zero integral_eq_zero_of_forall_integral_inner_eq_zero
+
+end InnerProductSpace
+
 namespace L2
 
 variable {α E F 𝕜 : Type _} [IsROrC 𝕜] [MeasurableSpace α] {μ : Measure α} [NormedAddCommGroup E]
@@ -178,7 +235,7 @@ instance innerProductSpace : InnerProductSpace 𝕜 (α →₂[μ] E)
     where
   norm_sq_eq_inner := norm_sq_eq_inner'
   conj_symm _ _ := by simp_rw [inner_def, ← integral_conj, inner_conj_symm]
-  add_left := add_left'
+  addLeft := add_left'
   smul_left := smul_left'
 #align measure_theory.L2.inner_product_space MeasureTheory.L2.innerProductSpace
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2f8347015b12b0864dfaf366ec4909eb70c78740

@@ -130,7 +130,7 @@ theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
 private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = IsROrC.re ⟪f, f⟫ :=
   by
   have h_two : (2 : ℝ≥0∞).toReal = 2 := by simp
-  rw [inner_def, integral_inner_eq_sq_snorm, norm_def, ← ENNReal.toReal_pow, IsROrC.of_real_re,
+  rw [inner_def, integral_inner_eq_sq_snorm, norm_def, ← ENNReal.toReal_pow, IsROrC.ofReal_re,
     ENNReal.toReal_eq_toReal (ENNReal.pow_ne_top (Lp.snorm_ne_top f)) _]
   · rw [← ENNReal.rpow_nat_cast, snorm_eq_snorm' two_ne_zero ENNReal.two_ne_top, snorm', ←
       ENNReal.rpow_mul, one_div, h_two]

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

@@ -248,7 +248,7 @@ section InnerContinuous
 
 variable {α : Type _} [TopologicalSpace α] [MeasureSpace α] [BorelSpace α] {𝕜 : Type _} [IsROrC 𝕜]
 
-variable (μ : Measure α) [IsFiniteMeasure μ]
+variable (μ : Measure α) [FiniteMeasure μ]
 
 open BoundedContinuousFunction ComplexConjugate
 

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

@@ -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.l2_space
-! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
+! leanprover-community/mathlib commit 3f655f5297b030a87d641ad4e825af8d9679eb0b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -79,21 +79,21 @@ theorem snorm_rpow_two_norm_lt_top (f : lp F 2 μ) : snorm (fun x => ‖f x‖ ^
 
 theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x, g x⟫) 1 μ < ∞ :=
   by
-  have h : ∀ x, IsROrC.abs ⟪f x, g x⟫ ≤ ‖f x‖ * ‖g x‖ := fun x => abs_inner_le_norm _ _
-  have h' : ∀ x, IsROrC.abs ⟪f x, g x⟫ ≤ IsROrC.abs (‖f x‖ ^ 2 + ‖g x‖ ^ 2) :=
+  have h : ∀ x, ‖⟪f x, g x⟫‖ ≤ ‖‖f x‖ ^ (2 : ℝ) + ‖g x‖ ^ (2 : ℝ)‖ :=
     by
-    refine' fun x => le_trans (h x) _
-    rw [IsROrC.abs_to_real, abs_eq_self.mpr]
-    swap
-    · exact add_nonneg (by simp) (by simp)
-    refine' le_trans _ (half_le_self (add_nonneg (sq_nonneg _) (sq_nonneg _)))
-    refine' (le_div_iff (zero_lt_two' ℝ)).mpr ((le_of_eq _).trans (two_mul_le_add_sq _ _))
-    ring
-  simp_rw [← IsROrC.norm_eq_abs, ← Real.rpow_nat_cast] at h'
-  refine' (snorm_mono_ae (ae_of_all _ h')).trans_lt ((snorm_add_le _ _ le_rfl).trans_lt _)
+    intro x
+    rw [← @Nat.cast_two ℝ, Real.rpow_nat_cast, Real.rpow_nat_cast]
+    calc
+      ‖⟪f x, g x⟫‖ ≤ ‖f x‖ * ‖g x‖ := norm_inner_le_norm _ _
+      _ ≤ 2 * ‖f x‖ * ‖g x‖ :=
+        (mul_le_mul_of_nonneg_right (le_mul_of_one_le_left (norm_nonneg _) one_le_two)
+          (norm_nonneg _))
+      _ ≤ ‖‖f x‖ ^ 2 + ‖g x‖ ^ 2‖ := (two_mul_le_add_sq _ _).trans (le_abs_self _)
+      
+  refine' (snorm_mono_ae (ae_of_all _ h)).trans_lt ((snorm_add_le _ _ le_rfl).trans_lt _)
   · exact ((Lp.ae_strongly_measurable f).norm.AEMeasurable.pow_const _).AeStronglyMeasurable
   · exact ((Lp.ae_strongly_measurable g).norm.AEMeasurable.pow_const _).AeStronglyMeasurable
-  simp only [Nat.cast_bit0, ENNReal.add_lt_top, Nat.cast_one]
+  rw [ENNReal.add_lt_top]
   exact ⟨snorm_rpow_two_norm_lt_top f, snorm_rpow_two_norm_lt_top g⟩
 #align measure_theory.L2.snorm_inner_lt_top MeasureTheory.L2.snorm_inner_lt_top
 

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

@@ -39,9 +39,9 @@ section
 
 variable {α F : Type _} {m : MeasurableSpace α} {μ : Measure α} [NormedAddCommGroup F]
 
-theorem Memℒp.integrableSq {f : α → ℝ} (h : Memℒp f 2 μ) : Integrable (fun x => f x ^ 2) μ := by
+theorem Memℒp.integrable_sq {f : α → ℝ} (h : Memℒp f 2 μ) : Integrable (fun x => f x ^ 2) μ := by
   simpa [← mem_ℒp_one_iff_integrable] using h.norm_rpow two_ne_zero ENNReal.two_ne_top
-#align measure_theory.mem_ℒp.integrable_sq MeasureTheory.Memℒp.integrableSq
+#align measure_theory.mem_ℒp.integrable_sq MeasureTheory.Memℒp.integrable_sq
 
 theorem memℒp_two_iff_integrable_sq_norm {f : α → F} (hf : AeStronglyMeasurable f μ) :
     Memℒp f 2 μ ↔ Integrable (fun x => ‖f x‖ ^ 2) μ :=
@@ -91,8 +91,8 @@ theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x
     ring
   simp_rw [← IsROrC.norm_eq_abs, ← Real.rpow_nat_cast] at h'
   refine' (snorm_mono_ae (ae_of_all _ h')).trans_lt ((snorm_add_le _ _ le_rfl).trans_lt _)
-  · exact ((Lp.ae_strongly_measurable f).norm.AeMeasurable.pow_const _).AeStronglyMeasurable
-  · exact ((Lp.ae_strongly_measurable g).norm.AeMeasurable.pow_const _).AeStronglyMeasurable
+  · exact ((Lp.ae_strongly_measurable f).norm.AEMeasurable.pow_const _).AeStronglyMeasurable
+  · exact ((Lp.ae_strongly_measurable g).norm.AEMeasurable.pow_const _).AeStronglyMeasurable
   simp only [Nat.cast_bit0, ENNReal.add_lt_top, Nat.cast_one]
   exact ⟨snorm_rpow_two_norm_lt_top f, snorm_rpow_two_norm_lt_top g⟩
 #align measure_theory.L2.snorm_inner_lt_top MeasureTheory.L2.snorm_inner_lt_top
@@ -118,7 +118,7 @@ theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
   rw [integral_eq_lintegral_of_nonneg_ae]
   rotate_left
   · exact Filter.eventually_of_forall fun x => sq_nonneg _
-  · exact ((Lp.ae_strongly_measurable f).norm.AeMeasurable.pow_const _).AeStronglyMeasurable
+  · exact ((Lp.ae_strongly_measurable f).norm.AEMeasurable.pow_const _).AeStronglyMeasurable
   congr
   ext1 x
   have h_two : (2 : ℝ) = ((2 : ℕ) : ℝ) := by simp
@@ -149,12 +149,12 @@ theorem mem_L1_inner (f g : α →₂[μ] E) :
   exact snorm_inner_lt_top f g
 #align measure_theory.L2.mem_L1_inner MeasureTheory.L2.mem_L1_inner
 
-theorem integrableInner (f g : α →₂[μ] E) : Integrable (fun x : α => ⟪f x, g x⟫) μ :=
+theorem integrable_inner (f g : α →₂[μ] E) : Integrable (fun x : α => ⟪f x, g x⟫) μ :=
   (integrable_congr
         (AeEqFun.coeFn_mk (fun x => ⟪f x, g x⟫)
           ((lp.aeStronglyMeasurable f).inner (lp.aeStronglyMeasurable g)))).mp
     (AeEqFun.integrable_iff_mem_L1.mpr (mem_L1_inner f g))
-#align measure_theory.L2.integrable_inner MeasureTheory.L2.integrableInner
+#align measure_theory.L2.integrable_inner MeasureTheory.L2.integrable_inner
 
 private theorem add_left' (f f' g : α →₂[μ] E) : ⟪f + f', g⟫ = inner f g + inner f' g :=
   by

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 
 ! This file was ported from Lean 3 source module measure_theory.function.l2_space
-! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
+! leanprover-community/mathlib commit 46b633fd842bef9469441c0209906f6dddd2b4f5
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -64,8 +64,8 @@ end
 
 namespace L2
 
-variable {α E F 𝕜 : Type _} [IsROrC 𝕜] [MeasurableSpace α] {μ : Measure α} [InnerProductSpace 𝕜 E]
-  [NormedAddCommGroup F]
+variable {α E F 𝕜 : Type _} [IsROrC 𝕜] [MeasurableSpace α] {μ : Measure α} [NormedAddCommGroup E]
+  [InnerProductSpace 𝕜 E] [NormedAddCommGroup F]
 
 -- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -47,7 +47,7 @@ theorem memℒp_two_iff_integrable_sq_norm {f : α → F} (hf : AeStronglyMeasur
     Memℒp f 2 μ ↔ Integrable (fun x => ‖f x‖ ^ 2) μ :=
   by
   rw [← mem_ℒp_one_iff_integrable]
-  convert (mem_ℒp_norm_rpow_iff hf two_ne_zero ENNReal.two_ne_top).symm
+  convert(mem_ℒp_norm_rpow_iff hf two_ne_zero ENNReal.two_ne_top).symm
   · simp
   · rw [div_eq_mul_inv, ENNReal.mul_inv_cancel two_ne_zero ENNReal.two_ne_top]
 #align measure_theory.mem_ℒp_two_iff_integrable_sq_norm MeasureTheory.memℒp_two_iff_integrable_sq_norm

mathlib commit https://github.com/leanprover-community/mathlib/commit/1a313d8bba1bad05faba71a4a4e9742ab5bd9efd

@@ -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.l2_space
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
+! leanprover-community/mathlib commit 3fc0b254310908f70a1a75f01147d52e53e9f8a2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -177,7 +177,7 @@ private theorem smul_left' (f g : α →₂[μ] E) (r : 𝕜) : ⟪r • f, g⟫
 instance innerProductSpace : InnerProductSpace 𝕜 (α →₂[μ] E)
     where
   norm_sq_eq_inner := norm_sq_eq_inner'
-  conj_sym _ _ := by simp_rw [inner_def, ← integral_conj, inner_conj_sym]
+  conj_symm _ _ := by simp_rw [inner_def, ← integral_conj, inner_conj_symm]
   add_left := add_left'
   smul_left := smul_left'
 #align measure_theory.L2.inner_product_space MeasureTheory.L2.innerProductSpace
@@ -216,7 +216,7 @@ theorem inner_indicatorConstLp_eq_set_integral_inner (f : lp E 2 μ) (hs : Measu
       indicator_const_Lp_coe_fn_nmem
     refine' h_indicator.mono fun x hx hxs => _
     rw [hx hxs]
-    exact inner_zero_left
+    exact inner_zero_left _
   rw [h_left, h_right, add_zero]
 #align measure_theory.L2.inner_indicator_const_Lp_eq_set_integral_inner MeasureTheory.L2.inner_indicatorConstLp_eq_set_integral_inner
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 
 ! This file was ported from Lean 3 source module measure_theory.function.l2_space
-! leanprover-community/mathlib commit 247a102b14f3cebfee126293341af5f6bed00237
+! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -40,16 +40,16 @@ section
 variable {α F : Type _} {m : MeasurableSpace α} {μ : Measure α} [NormedAddCommGroup F]
 
 theorem Memℒp.integrableSq {f : α → ℝ} (h : Memℒp f 2 μ) : Integrable (fun x => f x ^ 2) μ := by
-  simpa [← mem_ℒp_one_iff_integrable] using h.norm_rpow ENNReal.two_ne_zero ENNReal.two_ne_top
+  simpa [← mem_ℒp_one_iff_integrable] using h.norm_rpow two_ne_zero ENNReal.two_ne_top
 #align measure_theory.mem_ℒp.integrable_sq MeasureTheory.Memℒp.integrableSq
 
 theorem memℒp_two_iff_integrable_sq_norm {f : α → F} (hf : AeStronglyMeasurable f μ) :
     Memℒp f 2 μ ↔ Integrable (fun x => ‖f x‖ ^ 2) μ :=
   by
   rw [← mem_ℒp_one_iff_integrable]
-  convert (mem_ℒp_norm_rpow_iff hf ENNReal.two_ne_zero ENNReal.two_ne_top).symm
+  convert (mem_ℒp_norm_rpow_iff hf two_ne_zero ENNReal.two_ne_top).symm
   · simp
-  · rw [div_eq_mul_inv, ENNReal.mul_inv_cancel ENNReal.two_ne_zero ENNReal.two_ne_top]
+  · rw [div_eq_mul_inv, ENNReal.mul_inv_cancel two_ne_zero ENNReal.two_ne_top]
 #align measure_theory.mem_ℒp_two_iff_integrable_sq_norm MeasureTheory.memℒp_two_iff_integrable_sq_norm
 
 theorem memℒp_two_iff_integrable_sq {f : α → ℝ} (hf : AeStronglyMeasurable f μ) :
@@ -132,11 +132,11 @@ private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = IsROrC.r
   have h_two : (2 : ℝ≥0∞).toReal = 2 := by simp
   rw [inner_def, integral_inner_eq_sq_snorm, norm_def, ← ENNReal.toReal_pow, IsROrC.of_real_re,
     ENNReal.toReal_eq_toReal (ENNReal.pow_ne_top (Lp.snorm_ne_top f)) _]
-  · rw [← ENNReal.rpow_nat_cast, snorm_eq_snorm' ENNReal.two_ne_zero ENNReal.two_ne_top, snorm', ←
+  · rw [← ENNReal.rpow_nat_cast, snorm_eq_snorm' two_ne_zero ENNReal.two_ne_top, snorm', ←
       ENNReal.rpow_mul, one_div, h_two]
     simp
   · refine' (lintegral_rpow_nnnorm_lt_top_of_snorm'_lt_top zero_lt_two _).Ne
-    rw [← h_two, ← snorm_eq_snorm' ENNReal.two_ne_zero ENNReal.two_ne_top]
+    rw [← h_two, ← snorm_eq_snorm' two_ne_zero ENNReal.two_ne_top]
     exact Lp.snorm_lt_top f
 #align measure_theory.L2.norm_sq_eq_inner' measure_theory.L2.norm_sq_eq_inner'
 

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

@@ -31,7 +31,7 @@ noncomputable section
 
 open TopologicalSpace MeasureTheory MeasureTheory.lp
 
-open NNReal Ennreal MeasureTheory
+open NNReal ENNReal MeasureTheory
 
 namespace MeasureTheory
 
@@ -40,16 +40,16 @@ section
 variable {α F : Type _} {m : MeasurableSpace α} {μ : Measure α} [NormedAddCommGroup F]
 
 theorem Memℒp.integrableSq {f : α → ℝ} (h : Memℒp f 2 μ) : Integrable (fun x => f x ^ 2) μ := by
-  simpa [← mem_ℒp_one_iff_integrable] using h.norm_rpow Ennreal.two_ne_zero Ennreal.two_ne_top
+  simpa [← mem_ℒp_one_iff_integrable] using h.norm_rpow ENNReal.two_ne_zero ENNReal.two_ne_top
 #align measure_theory.mem_ℒp.integrable_sq MeasureTheory.Memℒp.integrableSq
 
 theorem memℒp_two_iff_integrable_sq_norm {f : α → F} (hf : AeStronglyMeasurable f μ) :
     Memℒp f 2 μ ↔ Integrable (fun x => ‖f x‖ ^ 2) μ :=
   by
   rw [← mem_ℒp_one_iff_integrable]
-  convert (mem_ℒp_norm_rpow_iff hf Ennreal.two_ne_zero Ennreal.two_ne_top).symm
+  convert (mem_ℒp_norm_rpow_iff hf ENNReal.two_ne_zero ENNReal.two_ne_top).symm
   · simp
-  · rw [div_eq_mul_inv, Ennreal.mul_inv_cancel Ennreal.two_ne_zero Ennreal.two_ne_top]
+  · rw [div_eq_mul_inv, ENNReal.mul_inv_cancel ENNReal.two_ne_zero ENNReal.two_ne_top]
 #align measure_theory.mem_ℒp_two_iff_integrable_sq_norm MeasureTheory.memℒp_two_iff_integrable_sq_norm
 
 theorem memℒp_two_iff_integrable_sq {f : α → ℝ} (hf : AeStronglyMeasurable f μ) :
@@ -72,9 +72,9 @@ local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
 
 theorem snorm_rpow_two_norm_lt_top (f : lp F 2 μ) : snorm (fun x => ‖f x‖ ^ (2 : ℝ)) 1 μ < ∞ :=
   by
-  have h_two : Ennreal.ofReal (2 : ℝ) = 2 := by simp [zero_le_one]
+  have h_two : ENNReal.ofReal (2 : ℝ) = 2 := by simp [zero_le_one]
   rw [snorm_norm_rpow f zero_lt_two, one_mul, h_two]
-  exact Ennreal.rpow_lt_top_of_nonneg zero_le_two (Lp.snorm_ne_top f)
+  exact ENNReal.rpow_lt_top_of_nonneg zero_le_two (Lp.snorm_ne_top f)
 #align measure_theory.L2.snorm_rpow_two_norm_lt_top MeasureTheory.L2.snorm_rpow_two_norm_lt_top
 
 theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x, g x⟫) 1 μ < ∞ :=
@@ -93,7 +93,7 @@ theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x
   refine' (snorm_mono_ae (ae_of_all _ h')).trans_lt ((snorm_add_le _ _ le_rfl).trans_lt _)
   · exact ((Lp.ae_strongly_measurable f).norm.AeMeasurable.pow_const _).AeStronglyMeasurable
   · exact ((Lp.ae_strongly_measurable g).norm.AeMeasurable.pow_const _).AeStronglyMeasurable
-  simp only [Nat.cast_bit0, Ennreal.add_lt_top, Nat.cast_one]
+  simp only [Nat.cast_bit0, ENNReal.add_lt_top, Nat.cast_one]
   exact ⟨snorm_rpow_two_norm_lt_top f, snorm_rpow_two_norm_lt_top g⟩
 #align measure_theory.L2.snorm_inner_lt_top MeasureTheory.L2.snorm_inner_lt_top
 
@@ -111,7 +111,7 @@ theorem inner_def (f g : α →₂[μ] E) : ⟪f, g⟫ = ∫ a : α, ⟪f a, g a
 #align measure_theory.L2.inner_def MeasureTheory.L2.inner_def
 
 theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
-    (∫ a, ⟪f a, f a⟫ ∂μ) = Ennreal.toReal (∫⁻ a, (‖f a‖₊ : ℝ≥0∞) ^ (2 : ℝ) ∂μ) :=
+    (∫ a, ⟪f a, f a⟫ ∂μ) = ENNReal.toReal (∫⁻ a, (‖f a‖₊ : ℝ≥0∞) ^ (2 : ℝ) ∂μ) :=
   by
   simp_rw [inner_self_eq_norm_sq_to_K]
   norm_cast
@@ -123,20 +123,20 @@ theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
   ext1 x
   have h_two : (2 : ℝ) = ((2 : ℕ) : ℝ) := by simp
   rw [← Real.rpow_nat_cast _ 2, ← h_two, ←
-    Ennreal.ofReal_rpow_of_nonneg (norm_nonneg _) zero_le_two, ofReal_norm_eq_coe_nnnorm]
+    ENNReal.ofReal_rpow_of_nonneg (norm_nonneg _) zero_le_two, ofReal_norm_eq_coe_nnnorm]
   norm_cast
 #align measure_theory.L2.integral_inner_eq_sq_snorm MeasureTheory.L2.integral_inner_eq_sq_snorm
 
 private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = IsROrC.re ⟪f, f⟫ :=
   by
   have h_two : (2 : ℝ≥0∞).toReal = 2 := by simp
-  rw [inner_def, integral_inner_eq_sq_snorm, norm_def, ← Ennreal.toReal_pow, IsROrC.of_real_re,
-    Ennreal.toReal_eq_toReal (Ennreal.pow_ne_top (Lp.snorm_ne_top f)) _]
-  · rw [← Ennreal.rpow_nat_cast, snorm_eq_snorm' Ennreal.two_ne_zero Ennreal.two_ne_top, snorm', ←
-      Ennreal.rpow_mul, one_div, h_two]
+  rw [inner_def, integral_inner_eq_sq_snorm, norm_def, ← ENNReal.toReal_pow, IsROrC.of_real_re,
+    ENNReal.toReal_eq_toReal (ENNReal.pow_ne_top (Lp.snorm_ne_top f)) _]
+  · rw [← ENNReal.rpow_nat_cast, snorm_eq_snorm' ENNReal.two_ne_zero ENNReal.two_ne_top, snorm', ←
+      ENNReal.rpow_mul, one_div, h_two]
     simp
   · refine' (lintegral_rpow_nnnorm_lt_top_of_snorm'_lt_top zero_lt_two _).Ne
-    rw [← h_two, ← snorm_eq_snorm' Ennreal.two_ne_zero Ennreal.two_ne_top]
+    rw [← h_two, ← snorm_eq_snorm' ENNReal.two_ne_zero ENNReal.two_ne_top]
     exact Lp.snorm_lt_top f
 #align measure_theory.L2.norm_sq_eq_inner' measure_theory.L2.norm_sq_eq_inner'
 

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

@@ -12,7 +12,7 @@ import Mathlib.MeasureTheory.Integral.SetIntegral
 /-! # `L^2` space
 
 If `E` is an inner product space over `𝕜` (`ℝ` or `ℂ`), then `Lp E 2 μ`
-(defined in `MeasureTheory.Function.LpSpace`)
+(defined in `Mathlib.MeasureTheory.Function.LpSpace`)
 is also an inner product space, with inner product defined as `inner f g = ∫ a, ⟪f a, g a⟫ ∂μ`.
 
 ### Main results

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

@@ -226,12 +226,12 @@ variable (𝕜) {s : Set α}
 
 /-- The inner product in `L2` of the indicator of a set `indicatorConstLp 2 hs hμs c` and `f` is
 equal to the integral of the inner product over `s`: `∫ x in s, ⟪c, f x⟫ ∂μ`. -/
-theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : MeasurableSet s) (c : E)
+theorem inner_indicatorConstLp_eq_setIntegral_inner (f : Lp E 2 μ) (hs : MeasurableSet s) (c : E)
     (hμs : μ s ≠ ∞) : (⟪indicatorConstLp 2 hs hμs c, f⟫ : 𝕜) = ∫ x in s, ⟪c, f x⟫ ∂μ := by
   rw [inner_def, ← integral_add_compl hs (L2.integrable_inner _ f)]
   have h_left : (∫ x in s, ⟪(indicatorConstLp 2 hs hμs c) x, f x⟫ ∂μ) = ∫ x in s, ⟪c, f x⟫ ∂μ := by
     suffices h_ae_eq : ∀ᵐ x ∂μ, x ∈ s → ⟪indicatorConstLp 2 hs hμs c x, f x⟫ = ⟪c, f x⟫ from
-      set_integral_congr_ae hs h_ae_eq
+      setIntegral_congr_ae hs h_ae_eq
     have h_indicator : ∀ᵐ x : α ∂μ, x ∈ s → indicatorConstLp 2 hs hμs c x = c :=
       indicatorConstLp_coeFn_mem
     refine' h_indicator.mono fun x hx hxs => _
@@ -244,23 +244,31 @@ theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : Measu
           (∫ x in sᶜ, inner (indicatorConstLp 2 hs hμs c x) (f x) ∂μ) = ∫ _ in sᶜ, (0 : 𝕜) ∂μ by
         rw [h_int_zero]
         simp
-      exact set_integral_congr_ae hs.compl h_ae_eq
+      exact setIntegral_congr_ae hs.compl h_ae_eq
     have h_indicator : ∀ᵐ x : α ∂μ, x ∉ s → indicatorConstLp 2 hs hμs c x = 0 :=
       indicatorConstLp_coeFn_nmem
     refine' h_indicator.mono fun x hx hxs => _
     rw [hx hxs]
     exact inner_zero_left _
   rw [h_left, h_right, add_zero]
-#align measure_theory.L2.inner_indicator_const_Lp_eq_set_integral_inner MeasureTheory.L2.inner_indicatorConstLp_eq_set_integral_inner
+#align measure_theory.L2.inner_indicator_const_Lp_eq_set_integral_inner MeasureTheory.L2.inner_indicatorConstLp_eq_setIntegral_inner
+
+@[deprecated]
+alias inner_indicatorConstLp_eq_set_integral_inner :=
+  inner_indicatorConstLp_eq_setIntegral_inner -- deprecated on 2024-04-17
 
 /-- The inner product in `L2` of the indicator of a set `indicatorConstLp 2 hs hμs c` and `f` is
 equal to the inner product of the constant `c` and the integral of `f` over `s`. -/
-theorem inner_indicatorConstLp_eq_inner_set_integral [CompleteSpace E] [NormedSpace ℝ E]
+theorem inner_indicatorConstLp_eq_inner_setIntegral [CompleteSpace E] [NormedSpace ℝ E]
     (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (c : E) (f : Lp E 2 μ) :
     (⟪indicatorConstLp 2 hs hμs c, f⟫ : 𝕜) = ⟪c, ∫ x in s, f x ∂μ⟫ := by
   rw [← integral_inner (integrableOn_Lp_of_measure_ne_top f fact_one_le_two_ennreal.elim hμs),
-    L2.inner_indicatorConstLp_eq_set_integral_inner]
-#align measure_theory.L2.inner_indicator_const_Lp_eq_inner_set_integral MeasureTheory.L2.inner_indicatorConstLp_eq_inner_set_integral
+    L2.inner_indicatorConstLp_eq_setIntegral_inner]
+#align measure_theory.L2.inner_indicator_const_Lp_eq_inner_set_integral MeasureTheory.L2.inner_indicatorConstLp_eq_inner_setIntegral
+
+@[deprecated]
+alias inner_indicatorConstLp_eq_inner_set_integral :=
+  inner_indicatorConstLp_eq_inner_setIntegral -- deprecated on 2024-04-17
 
 variable {𝕜}
 
@@ -268,7 +276,7 @@ variable {𝕜}
 a real or complex function `f` is equal to the integral of `f` over `s`. -/
 theorem inner_indicatorConstLp_one (hs : MeasurableSet s) (hμs : μ s ≠ ∞) (f : Lp 𝕜 2 μ) :
     ⟪indicatorConstLp 2 hs hμs (1 : 𝕜), f⟫ = ∫ x in s, f x ∂μ := by
-  rw [L2.inner_indicatorConstLp_eq_inner_set_integral 𝕜 hs hμs (1 : 𝕜) f]; simp
+  rw [L2.inner_indicatorConstLp_eq_inner_setIntegral 𝕜 hs hμs (1 : 𝕜) f]; simp
 #align measure_theory.L2.inner_indicator_const_Lp_one MeasureTheory.L2.inner_indicatorConstLp_one
 
 end IndicatorConstLp

Now that I am defining NNRat.cast, I want a definitive answer to this naming issue. Plenty of lemmas in mathlib already use natCast/intCast/ratCast over nat_cast/int_cast/rat_cast, and this matches with the general expectation that underscore-separated name parts correspond to a single declaration.

@@ -122,7 +122,7 @@ theorem snorm_rpow_two_norm_lt_top (f : Lp F 2 μ) : snorm (fun x => ‖f x‖ ^
 theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x, g x⟫) 1 μ < ∞ := by
   have h : ∀ x, ‖⟪f x, g x⟫‖ ≤ ‖‖f x‖ ^ (2 : ℝ) + ‖g x‖ ^ (2 : ℝ)‖ := by
     intro x
-    rw [← @Nat.cast_two ℝ, Real.rpow_nat_cast, Real.rpow_nat_cast]
+    rw [← @Nat.cast_two ℝ, Real.rpow_natCast, Real.rpow_natCast]
     calc
       ‖⟪f x, g x⟫‖ ≤ ‖f x‖ * ‖g x‖ := norm_inner_le_norm _ _
       _ ≤ 2 * ‖f x‖ * ‖g x‖ :=
@@ -160,7 +160,7 @@ theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
   congr
   ext1 x
   have h_two : (2 : ℝ) = ((2 : ℕ) : ℝ) := by simp
-  rw [← Real.rpow_nat_cast _ 2, ← h_two, ←
+  rw [← Real.rpow_natCast _ 2, ← h_two, ←
     ENNReal.ofReal_rpow_of_nonneg (norm_nonneg _) zero_le_two, ofReal_norm_eq_coe_nnnorm]
   norm_cast
 #align measure_theory.L2.integral_inner_eq_sq_snorm MeasureTheory.L2.integral_inner_eq_sq_snorm
@@ -169,7 +169,7 @@ private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = RCLike.r
   have h_two : (2 : ℝ≥0∞).toReal = 2 := by simp
   rw [inner_def, integral_inner_eq_sq_snorm, norm_def, ← ENNReal.toReal_pow, RCLike.ofReal_re,
     ENNReal.toReal_eq_toReal (ENNReal.pow_ne_top (Lp.snorm_ne_top f)) _]
-  · rw [← ENNReal.rpow_nat_cast, snorm_eq_snorm' two_ne_zero ENNReal.two_ne_top, snorm', ←
+  · rw [← ENNReal.rpow_natCast, snorm_eq_snorm' two_ne_zero ENNReal.two_ne_top, snorm', ←
       ENNReal.rpow_mul, one_div, h_two]
     simp
   · refine' (lintegral_rpow_nnnorm_lt_top_of_snorm'_lt_top zero_lt_two _).ne

@@ -11,7 +11,8 @@ import Mathlib.MeasureTheory.Integral.SetIntegral
 
 /-! # `L^2` space
 
-If `E` is an inner product space over `𝕜` (`ℝ` or `ℂ`), then `Lp E 2 μ` (defined in `lp_space.lean`)
+If `E` is an inner product space over `𝕜` (`ℝ` or `ℂ`), then `Lp E 2 μ`
+(defined in `MeasureTheory.Function.LpSpace`)
 is also an inner product space, with inner product defined as `inner f g = ∫ a, ⟪f a, g a⟫ ∂μ`.
 
 ### Main results
@@ -20,7 +21,7 @@ is also an inner product space, with inner product defined as `inner f g = ∫ a
   belongs to `Lp 𝕜 1 μ`.
 * `integrable_inner` : for `f` and `g` in `Lp E 2 μ`, the pointwise inner product
  `fun x ↦ ⟪f x, g x⟫` is integrable.
-* `L2.inner_product_space` : `Lp E 2 μ` is an inner product space.
+* `L2.innerProductSpace` : `Lp E 2 μ` is an inner product space.
 
 -/
 

Quoting [@digama0](https://github.com/digama0):

These were actually never meant to go in the file, they are basically debugging information and only useful on significantly broken mathport files. You can safely remove all of them.

@@ -63,7 +63,6 @@ section InnerProductSpace
 variable {α : Type*} {m : MeasurableSpace α} {p : ℝ≥0∞} {μ : Measure α}
 variable {E 𝕜 : Type*} [RCLike 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
--- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 
 theorem Memℒp.const_inner (c : E) {f : α → E} (hf : Memℒp f p μ) : Memℒp (fun a => ⟪c, f a⟫) p μ :=
@@ -95,7 +94,6 @@ theorem _root_.integral_inner {f : α → E} (hf : Integrable f μ) (c : E) :
 
 variable (𝕜)
 
--- mathport name: inner_with_explicit
 -- variable binder update doesn't work for lemmas which refer to `𝕜` only via the notation
 -- Porting note: removed because it causes ambiguity in the lemma below
 -- local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
@@ -112,7 +110,6 @@ namespace L2
 variable {α E F 𝕜 : Type*} [RCLike 𝕜] [MeasurableSpace α] {μ : Measure α} [NormedAddCommGroup E]
   [InnerProductSpace 𝕜 E] [NormedAddCommGroup F]
 
--- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 _ _ x y
 
 theorem snorm_rpow_two_norm_lt_top (f : Lp F 2 μ) : snorm (fun x => ‖f x‖ ^ (2 : ℝ)) 1 μ < ∞ := by
@@ -284,7 +281,6 @@ variable (μ : Measure α) [IsFiniteMeasure μ]
 
 open scoped BoundedContinuousFunction ComplexConjugate
 
--- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 (α →₂[μ] 𝕜) _ x y
 
 -- Porting note: added `(E := 𝕜)`

RCLike is an analytic typeclass, hence should be under Analysis

@@ -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 Mathlib.Data.RCLike.Lemmas
+import Mathlib.Analysis.RCLike.Lemmas
 import Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner
 import Mathlib.MeasureTheory.Integral.SetIntegral
 

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.

@@ -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 Mathlib.Data.IsROrC.Lemmas
+import Mathlib.Data.RCLike.Lemmas
 import Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner
 import Mathlib.MeasureTheory.Integral.SetIntegral
 
@@ -61,7 +61,7 @@ end
 section InnerProductSpace
 
 variable {α : Type*} {m : MeasurableSpace α} {p : ℝ≥0∞} {μ : Measure α}
-variable {E 𝕜 : Type*} [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
+variable {E 𝕜 : Type*} [RCLike 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
 -- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
@@ -109,7 +109,7 @@ end InnerProductSpace
 
 namespace L2
 
-variable {α E F 𝕜 : Type*} [IsROrC 𝕜] [MeasurableSpace α] {μ : Measure α} [NormedAddCommGroup E]
+variable {α E F 𝕜 : Type*} [RCLike 𝕜] [MeasurableSpace α] {μ : Measure α} [NormedAddCommGroup E]
   [InnerProductSpace 𝕜 E] [NormedAddCommGroup F]
 
 -- mathport name: «expr⟪ , ⟫»
@@ -167,9 +167,9 @@ theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
   norm_cast
 #align measure_theory.L2.integral_inner_eq_sq_snorm MeasureTheory.L2.integral_inner_eq_sq_snorm
 
-private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = IsROrC.re ⟪f, f⟫ := by
+private theorem norm_sq_eq_inner' (f : α →₂[μ] E) : ‖f‖ ^ 2 = RCLike.re ⟪f, f⟫ := by
   have h_two : (2 : ℝ≥0∞).toReal = 2 := by simp
-  rw [inner_def, integral_inner_eq_sq_snorm, norm_def, ← ENNReal.toReal_pow, IsROrC.ofReal_re,
+  rw [inner_def, integral_inner_eq_sq_snorm, norm_def, ← ENNReal.toReal_pow, RCLike.ofReal_re,
     ENNReal.toReal_eq_toReal (ENNReal.pow_ne_top (Lp.snorm_ne_top f)) _]
   · rw [← ENNReal.rpow_nat_cast, snorm_eq_snorm' two_ne_zero ENNReal.two_ne_top, snorm', ←
       ENNReal.rpow_mul, one_div, h_two]
@@ -279,7 +279,7 @@ end L2
 
 section InnerContinuous
 
-variable {α : Type*} [TopologicalSpace α] [MeasurableSpace α] [BorelSpace α] {𝕜 : Type*} [IsROrC 𝕜]
+variable {α 𝕜 : Type*} [TopologicalSpace α] [MeasurableSpace α] [BorelSpace α] [RCLike 𝕜]
 variable (μ : Measure α) [IsFiniteMeasure μ]
 
 open scoped BoundedContinuousFunction ComplexConjugate

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -61,7 +61,6 @@ end
 section InnerProductSpace
 
 variable {α : Type*} {m : MeasurableSpace α} {p : ℝ≥0∞} {μ : Measure α}
-
 variable {E 𝕜 : Type*} [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
 -- mathport name: «expr⟪ , ⟫»
@@ -281,7 +280,6 @@ end L2
 section InnerContinuous
 
 variable {α : Type*} [TopologicalSpace α] [MeasurableSpace α] [BorelSpace α] {𝕜 : Type*} [IsROrC 𝕜]
-
 variable (μ : Measure α) [IsFiniteMeasure μ]
 
 open scoped BoundedContinuousFunction ComplexConjugate

Use Lean 4 syntax fun x ↦ instead, matching the style guide. This is close to exhaustive for doc comments; mathlib has about 460 remaining uses of λ (not all in Lean 3 syntax).

@@ -18,8 +18,8 @@ is also an inner product space, with inner product defined as `inner f g = ∫ a
 
 * `mem_L1_inner` : for `f` and `g` in `Lp E 2 μ`, the pointwise inner product `fun x ↦ ⟪f x, g x⟫`
   belongs to `Lp 𝕜 1 μ`.
-* `integrable_inner` : for `f` and `g` in `Lp E 2 μ`, the pointwise inner product `λ x, ⟪f x, g x⟫`
-  is integrable.
+* `integrable_inner` : for `f` and `g` in `Lp E 2 μ`, the pointwise inner product
+ `fun x ↦ ⟪f x, g x⟫` is integrable.
 * `L2.inner_product_space` : `Lp E 2 μ` is an inner product space.
 
 -/

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>

@@ -233,19 +233,19 @@ theorem inner_indicatorConstLp_eq_set_integral_inner (f : Lp E 2 μ) (hs : Measu
     (hμs : μ s ≠ ∞) : (⟪indicatorConstLp 2 hs hμs c, f⟫ : 𝕜) = ∫ x in s, ⟪c, f x⟫ ∂μ := by
   rw [inner_def, ← integral_add_compl hs (L2.integrable_inner _ f)]
   have h_left : (∫ x in s, ⟪(indicatorConstLp 2 hs hμs c) x, f x⟫ ∂μ) = ∫ x in s, ⟪c, f x⟫ ∂μ := by
-    suffices h_ae_eq : ∀ᵐ x ∂μ, x ∈ s → ⟪indicatorConstLp 2 hs hμs c x, f x⟫ = ⟪c, f x⟫
-    exact set_integral_congr_ae hs h_ae_eq
+    suffices h_ae_eq : ∀ᵐ x ∂μ, x ∈ s → ⟪indicatorConstLp 2 hs hμs c x, f x⟫ = ⟪c, f x⟫ from
+      set_integral_congr_ae hs h_ae_eq
     have h_indicator : ∀ᵐ x : α ∂μ, x ∈ s → indicatorConstLp 2 hs hμs c x = c :=
       indicatorConstLp_coeFn_mem
     refine' h_indicator.mono fun x hx hxs => _
     congr
     exact hx hxs
   have h_right : (∫ x in sᶜ, ⟪(indicatorConstLp 2 hs hμs c) x, f x⟫ ∂μ) = 0 := by
-    suffices h_ae_eq : ∀ᵐ x ∂μ, x ∉ s → ⟪indicatorConstLp 2 hs hμs c x, f x⟫ = 0
-    · simp_rw [← Set.mem_compl_iff] at h_ae_eq
+    suffices h_ae_eq : ∀ᵐ x ∂μ, x ∉ s → ⟪indicatorConstLp 2 hs hμs c x, f x⟫ = 0 by
+      simp_rw [← Set.mem_compl_iff] at h_ae_eq
       suffices h_int_zero :
-        (∫ x in sᶜ, inner (indicatorConstLp 2 hs hμs c x) (f x) ∂μ) = ∫ _ in sᶜ, (0 : 𝕜) ∂μ
-      · rw [h_int_zero]
+          (∫ x in sᶜ, inner (indicatorConstLp 2 hs hμs c x) (f x) ∂μ) = ∫ _ in sᶜ, (0 : 𝕜) ∂μ by
+        rw [h_int_zero]
         simp
       exact set_integral_congr_ae hs.compl h_ae_eq
     have h_indicator : ∀ᵐ x : α ∂μ, x ∉ s → indicatorConstLp 2 hs hμs c x = 0 :=

This fixes a tiny glitch in the instance arguments in the L2Space file: if you invoke some of these lemmas with @ then you find you need to give a measure twice over, once for the [MeasureSpace α] instance and once for the explicit argument.

@@ -280,7 +280,7 @@ end L2
 
 section InnerContinuous
 
-variable {α : Type*} [TopologicalSpace α] [MeasureSpace α] [BorelSpace α] {𝕜 : Type*} [IsROrC 𝕜]
+variable {α : Type*} [TopologicalSpace α] [MeasurableSpace α] [BorelSpace α] {𝕜 : Type*} [IsROrC 𝕜]
 
 variable (μ : Measure α) [IsFiniteMeasure μ]
 

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -24,9 +24,6 @@ is also an inner product space, with inner product defined as `inner f g = ∫ a
 
 -/
 
-
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 set_option linter.uppercaseLean3 false
 
 noncomputable section
@@ -134,7 +131,8 @@ theorem snorm_inner_lt_top (f g : α →₂[μ] E) : snorm (fun x : α => ⟪f x
       _ ≤ 2 * ‖f x‖ * ‖g x‖ :=
         (mul_le_mul_of_nonneg_right (le_mul_of_one_le_left (norm_nonneg _) one_le_two)
           (norm_nonneg _))
-      _ ≤ ‖‖f x‖ ^ 2 + ‖g x‖ ^ 2‖ := (two_mul_le_add_sq _ _).trans (le_abs_self _)
+      -- TODO(kmill): the type ascription is getting around an elaboration error
+      _ ≤ ‖(‖f x‖ ^ 2 + ‖g x‖ ^ 2 : ℝ)‖ := (two_mul_le_add_sq _ _).trans (le_abs_self _)
 
   refine' (snorm_mono_ae (ae_of_all _ h)).trans_lt ((snorm_add_le _ _ le_rfl).trans_lt _)
   · exact ((Lp.aestronglyMeasurable f).norm.aemeasurable.pow_const _).aestronglyMeasurable

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

This has nice performance benefits.

@@ -39,7 +39,7 @@ namespace MeasureTheory
 
 section
 
-variable {α F : Type _} {m : MeasurableSpace α} {μ : Measure α} [NormedAddCommGroup F]
+variable {α F : Type*} {m : MeasurableSpace α} {μ : Measure α} [NormedAddCommGroup F]
 
 theorem Memℒp.integrable_sq {f : α → ℝ} (h : Memℒp f 2 μ) : Integrable (fun x => f x ^ 2) μ := by
   simpa [← memℒp_one_iff_integrable] using h.norm_rpow two_ne_zero ENNReal.two_ne_top
@@ -63,9 +63,9 @@ end
 
 section InnerProductSpace
 
-variable {α : Type _} {m : MeasurableSpace α} {p : ℝ≥0∞} {μ : Measure α}
+variable {α : Type*} {m : MeasurableSpace α} {p : ℝ≥0∞} {μ : Measure α}
 
-variable {E 𝕜 : Type _} [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
+variable {E 𝕜 : Type*} [IsROrC 𝕜] [NormedAddCommGroup E] [InnerProductSpace 𝕜 E]
 
 -- mathport name: «expr⟪ , ⟫»
 local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
@@ -113,7 +113,7 @@ end InnerProductSpace
 
 namespace L2
 
-variable {α E F 𝕜 : Type _} [IsROrC 𝕜] [MeasurableSpace α] {μ : Measure α} [NormedAddCommGroup E]
+variable {α E F 𝕜 : Type*} [IsROrC 𝕜] [MeasurableSpace α] {μ : Measure α} [NormedAddCommGroup E]
   [InnerProductSpace 𝕜 E] [NormedAddCommGroup F]
 
 -- mathport name: «expr⟪ , ⟫»
@@ -282,7 +282,7 @@ end L2
 
 section InnerContinuous
 
-variable {α : Type _} [TopologicalSpace α] [MeasureSpace α] [BorelSpace α] {𝕜 : Type _} [IsROrC 𝕜]
+variable {α : Type*} [TopologicalSpace α] [MeasureSpace α] [BorelSpace α] {𝕜 : Type*} [IsROrC 𝕜]
 
 variable (μ : Measure α) [IsFiniteMeasure μ]
 

@@ -25,7 +25,7 @@ is also an inner product space, with inner product defined as `inner f g = ∫ a
 -/
 
 
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 set_option linter.uppercaseLean3 false
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 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.l2_space
-! leanprover-community/mathlib commit 83a66c8775fa14ee5180c85cab98e970956401ad
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.IsROrC.Lemmas
 import Mathlib.MeasureTheory.Function.StronglyMeasurable.Inner
 import Mathlib.MeasureTheory.Integral.SetIntegral
 
+#align_import measure_theory.function.l2_space from "leanprover-community/mathlib"@"83a66c8775fa14ee5180c85cab98e970956401ad"
+
 /-! # `L^2` space
 
 If `E` is an inner product space over `𝕜` (`ℝ` or `ℂ`), then `Lp E 2 μ` (defined in `lp_space.lean`)

@@ -96,7 +96,7 @@ theorem Integrable.inner_const (hf : Integrable f μ) (c : E) : Integrable (fun
 variable [CompleteSpace E] [NormedSpace ℝ E]
 
 theorem _root_.integral_inner {f : α → E} (hf : Integrable f μ) (c : E) :
-    (∫ x, ⟪c, f x⟫ ∂μ) = ⟪c, ∫ x, f x ∂μ⟫ :=
+    ∫ x, ⟪c, f x⟫ ∂μ = ⟪c, ∫ x, f x ∂μ⟫ :=
   ((innerSL 𝕜 c).restrictScalars ℝ).integral_comp_comm hf
 #align integral_inner integral_inner
 
@@ -108,7 +108,7 @@ variable (𝕜)
 -- local notation "⟪" x ", " y "⟫" => @inner 𝕜 E _ x y
 
 theorem _root_.integral_eq_zero_of_forall_integral_inner_eq_zero (f : α → E) (hf : Integrable f μ)
-    (hf_int : ∀ c : E, (∫ x, ⟪c, f x⟫ ∂μ) = 0) : (∫ x, f x ∂μ) = 0 := by
+    (hf_int : ∀ c : E, ∫ x, ⟪c, f x⟫ ∂μ = 0) : ∫ x, f x ∂μ = 0 := by
   specialize hf_int (∫ x, f x ∂μ); rwa [integral_inner hf, inner_self_eq_zero] at hf_int
 #align integral_eq_zero_of_forall_integral_inner_eq_zero integral_eq_zero_of_forall_integral_inner_eq_zero
 
@@ -158,7 +158,7 @@ theorem inner_def (f g : α →₂[μ] E) : ⟪f, g⟫ = ∫ a : α, ⟪f a, g a
 #align measure_theory.L2.inner_def MeasureTheory.L2.inner_def
 
 theorem integral_inner_eq_sq_snorm (f : α →₂[μ] E) :
-    (∫ a, ⟪f a, f a⟫ ∂μ) = ENNReal.toReal (∫⁻ a, (‖f a‖₊ : ℝ≥0∞) ^ (2 : ℝ) ∂μ) := by
+    ∫ a, ⟪f a, f a⟫ ∂μ = ENNReal.toReal (∫⁻ a, (‖f a‖₊ : ℝ≥0∞) ^ (2 : ℝ) ∂μ) := by
   simp_rw [inner_self_eq_norm_sq_to_K]
   norm_cast
   rw [integral_eq_lintegral_of_nonneg_ae]

Found with git grep -n "λ [a-zA-Z_ ]*,"

@@ -19,7 +19,7 @@ is also an inner product space, with inner product defined as `inner f g = ∫ a
 
 ### Main results
 
-* `mem_L1_inner` : for `f` and `g` in `Lp E 2 μ`, the pointwise inner product `λ x, ⟪f x, g x⟫`
+* `mem_L1_inner` : for `f` and `g` in `Lp E 2 μ`, the pointwise inner product `fun x ↦ ⟪f x, g x⟫`
   belongs to `Lp 𝕜 1 μ`.
 * `integrable_inner` : for `f` and `g` in `Lp E 2 μ`, the pointwise inner product `λ x, ⟪f x, g x⟫`
   is integrable.

Co-authored-by: Johan Commelin <johan@commelin.net>