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

@@ -118,7 +118,7 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
     exact hr.le
   refine' lt_of_le_of_lt (set_lintegral_mono (by measurability) (by measurability) h_int) _
   refine' integrable_on.set_lintegral_lt_top _
-  rw [← intervalIntegrable_iff_integrable_Ioc_of_le zero_le_one]
+  rw [← intervalIntegrable_iff_integrableOn_Ioc_of_le zero_le_one]
   apply intervalIntegral.intervalIntegrable_rpow'
   rwa [neg_lt_neg_iff, inv_mul_lt_iff' hr, one_mul]
 #align finite_integral_rpow_sub_one_pow_aux finite_integral_rpow_sub_one_pow_aux

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

@@ -38,7 +38,7 @@ variable {E : Type _} [NormedAddCommGroup E]
 #print sqrt_one_add_norm_sq_le /-
 theorem sqrt_one_add_norm_sq_le (x : E) : Real.sqrt (1 + ‖x‖ ^ 2) ≤ 1 + ‖x‖ :=
   by
-  refine' le_of_pow_le_pow 2 (by positivity) two_pos _
+  refine' le_of_pow_le_pow_left 2 (by positivity) two_pos _
   simp [sq_sqrt (zero_lt_one_add_norm_sq x).le, add_pow_two]
 #align sqrt_one_add_norm_sq_le sqrt_one_add_norm_sq_le
 -/
@@ -48,7 +48,7 @@ theorem one_add_norm_le_sqrt_two_mul_sqrt (x : E) : 1 + ‖x‖ ≤ Real.sqrt 2
   by
   suffices (sqrt 2 * sqrt (1 + ‖x‖ ^ 2)) ^ 2 - (1 + ‖x‖) ^ 2 = (1 - ‖x‖) ^ 2
     by
-    refine' le_of_pow_le_pow 2 (by positivity) (by norm_num) _
+    refine' le_of_pow_le_pow_left 2 (by positivity) (by norm_num) _
     rw [← sub_nonneg, this]
     positivity
   rw [mul_pow, sq_sqrt (zero_lt_one_add_norm_sq x).le, add_pow_two, sub_pow_two]
@@ -111,7 +111,7 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
     have hxr : 0 ≤ x ^ (-r⁻¹) := rpow_nonneg_of_nonneg hx.1.le _
     apply ENNReal.ofReal_le_ofReal
     rw [← neg_mul, rpow_mul hx.1.le, rpow_nat_cast]
-    refine' pow_le_pow_of_le_left _ (by simp only [sub_le_self_iff, zero_le_one]) n
+    refine' pow_le_pow_left _ (by simp only [sub_le_self_iff, zero_le_one]) n
     rw [le_sub_iff_add_le', add_zero]
     refine' Real.one_le_rpow_of_pos_of_le_one_of_nonpos hx.1 hx.2 _
     rw [Right.neg_nonpos_iff, inv_nonneg]

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 -/
-import Mathbin.MeasureTheory.Measure.Lebesgue.EqHaar
-import Mathbin.MeasureTheory.Integral.Layercake
+import MeasureTheory.Measure.Lebesgue.EqHaar
+import MeasureTheory.Integral.Layercake
 
 #align_import analysis.special_functions.japanese_bracket from "leanprover-community/mathlib"@"d07a9c875ed7139abfde6a333b2be205c5bd404e"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
-
-! This file was ported from Lean 3 source module analysis.special_functions.japanese_bracket
-! leanprover-community/mathlib commit d07a9c875ed7139abfde6a333b2be205c5bd404e
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Measure.Lebesgue.EqHaar
 import Mathbin.MeasureTheory.Integral.Layercake
 
+#align_import analysis.special_functions.japanese_bracket from "leanprover-community/mathlib"@"d07a9c875ed7139abfde6a333b2be205c5bd404e"
+
 /-!
 # Japanese Bracket
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9f55d0d4363ae59948c33864cbc52e0b12e0e8ce

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 
 ! This file was ported from Lean 3 source module analysis.special_functions.japanese_bracket
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
+! leanprover-community/mathlib commit d07a9c875ed7139abfde6a333b2be205c5bd404e
 ! 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.Layercake
 /-!
 # Japanese Bracket
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file, we show that Japanese bracket $(1 + \|x\|^2)^{1/2}$ can be estimated from above
 and below by $1 + \|x\|$.
 The functions $(1 + \|x\|^2)^{-r/2}$ and $(1 + |x|)^{-r}$ are integrable provided that `r` is larger

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

@@ -35,12 +35,15 @@ open Asymptotics Filter Set Real MeasureTheory FiniteDimensional
 
 variable {E : Type _} [NormedAddCommGroup E]
 
+#print sqrt_one_add_norm_sq_le /-
 theorem sqrt_one_add_norm_sq_le (x : E) : Real.sqrt (1 + ‖x‖ ^ 2) ≤ 1 + ‖x‖ :=
   by
   refine' le_of_pow_le_pow 2 (by positivity) two_pos _
   simp [sq_sqrt (zero_lt_one_add_norm_sq x).le, add_pow_two]
 #align sqrt_one_add_norm_sq_le sqrt_one_add_norm_sq_le
+-/
 
+#print one_add_norm_le_sqrt_two_mul_sqrt /-
 theorem one_add_norm_le_sqrt_two_mul_sqrt (x : E) : 1 + ‖x‖ ≤ Real.sqrt 2 * sqrt (1 + ‖x‖ ^ 2) :=
   by
   suffices (sqrt 2 * sqrt (1 + ‖x‖ ^ 2)) ^ 2 - (1 + ‖x‖) ^ 2 = (1 - ‖x‖) ^ 2
@@ -52,7 +55,9 @@ theorem one_add_norm_le_sqrt_two_mul_sqrt (x : E) : 1 + ‖x‖ ≤ Real.sqrt 2
   norm_num
   ring
 #align one_add_norm_le_sqrt_two_mul_sqrt one_add_norm_le_sqrt_two_mul_sqrt
+-/
 
+#print rpow_neg_one_add_norm_sq_le /-
 theorem rpow_neg_one_add_norm_sq_le {r : ℝ} (x : E) (hr : 0 < r) :
     (1 + ‖x‖ ^ 2) ^ (-r / 2) ≤ 2 ^ (r / 2) * (1 + ‖x‖) ^ (-r) :=
   by
@@ -67,27 +72,33 @@ theorem rpow_neg_one_add_norm_sq_le {r : ℝ} (x : E) (hr : 0 < r) :
     rpow_le_rpow_iff h4.le h6.le hr]
   exact one_add_norm_le_sqrt_two_mul_sqrt _
 #align rpow_neg_one_add_norm_sq_le rpow_neg_one_add_norm_sq_le
+-/
 
+#print le_rpow_one_add_norm_iff_norm_le /-
 theorem le_rpow_one_add_norm_iff_norm_le {r t : ℝ} (hr : 0 < r) (ht : 0 < t) (x : E) :
     t ≤ (1 + ‖x‖) ^ (-r) ↔ ‖x‖ ≤ t ^ (-r⁻¹) - 1 :=
   by
   rw [le_sub_iff_add_le', neg_inv]
   exact (Real.le_rpow_inv_iff_of_neg (by positivity) ht (neg_lt_zero.mpr hr)).symm
 #align le_rpow_one_add_norm_iff_norm_le le_rpow_one_add_norm_iff_norm_le
+-/
 
 variable (E)
 
+#print closedBall_rpow_sub_one_eq_empty_aux /-
 theorem closedBall_rpow_sub_one_eq_empty_aux {r t : ℝ} (hr : 0 < r) (ht : 1 < t) :
     Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1) = ∅ :=
   by
   rw [Metric.closedBall_eq_empty, sub_neg]
   exact Real.rpow_lt_one_of_one_lt_of_neg ht (by simp only [hr, Right.neg_neg_iff, inv_pos])
 #align closed_ball_rpow_sub_one_eq_empty_aux closedBall_rpow_sub_one_eq_empty_aux
+-/
 
 variable [NormedSpace ℝ E] [FiniteDimensional ℝ E]
 
 variable {E}
 
+#print finite_integral_rpow_sub_one_pow_aux /-
 theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ) < r) :
     ∫⁻ x : ℝ in Ioc 0 1, ENNReal.ofReal ((x ^ (-r⁻¹) - 1) ^ n) < ∞ :=
   by
@@ -111,7 +122,9 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
   apply intervalIntegral.intervalIntegrable_rpow'
   rwa [neg_lt_neg_iff, inv_mul_lt_iff' hr, one_mul]
 #align finite_integral_rpow_sub_one_pow_aux finite_integral_rpow_sub_one_pow_aux
+-/
 
+#print finite_integral_one_add_norm /-
 theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
     [(@volume E _).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
     ∫⁻ x : E, ENNReal.ofReal ((1 + ‖x‖) ^ (-r)) < ∞ :=
@@ -166,7 +179,9 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
     MulZeroClass.zero_mul]
   exact WithTop.zero_lt_top
 #align finite_integral_one_add_norm finite_integral_one_add_norm
+-/
 
+#print integrable_one_add_norm /-
 theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).IsAddHaarMeasure]
     {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) : Integrable fun x : E => (1 + ‖x‖) ^ (-r) :=
   by
@@ -177,7 +192,9 @@ theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).I
   rw [has_finite_integral, this]
   exact finite_integral_one_add_norm hnr
 #align integrable_one_add_norm integrable_one_add_norm
+-/
 
+#print integrable_rpow_neg_one_add_norm_sq /-
 theorem integrable_rpow_neg_one_add_norm_sq [MeasureSpace E] [BorelSpace E]
     [(@volume E _).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
     Integrable fun x : E => (1 + ‖x‖ ^ 2) ^ (-r / 2) :=
@@ -192,4 +209,5 @@ theorem integrable_rpow_neg_one_add_norm_sq [MeasureSpace E] [BorelSpace E]
   simp_rw [norm_mul, norm_eq_abs, abs_of_nonneg h1, abs_of_nonneg h2, abs_of_nonneg h3]
   exact rpow_neg_one_add_norm_sq_le _ hr
 #align integrable_rpow_neg_one_add_norm_sq integrable_rpow_neg_one_add_norm_sq
+-/
 

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

@@ -89,7 +89,7 @@ variable [NormedSpace ℝ E] [FiniteDimensional ℝ E]
 variable {E}
 
 theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ) < r) :
-    (∫⁻ x : ℝ in Ioc 0 1, ENNReal.ofReal ((x ^ (-r⁻¹) - 1) ^ n)) < ∞ :=
+    ∫⁻ x : ℝ in Ioc 0 1, ENNReal.ofReal ((x ^ (-r⁻¹) - 1) ^ n) < ∞ :=
   by
   have hr : 0 < r := lt_of_le_of_lt n.cast_nonneg hnr
   have h_int :
@@ -114,7 +114,7 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
 
 theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
     [(@volume E _).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
-    (∫⁻ x : E, ENNReal.ofReal ((1 + ‖x‖) ^ (-r))) < ∞ :=
+    ∫⁻ x : E, ENNReal.ofReal ((1 + ‖x‖) ^ (-r)) < ∞ :=
   by
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   -- We start by applying the layer cake formula
@@ -172,7 +172,7 @@ theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).I
   by
   refine' ⟨by measurability, _⟩
   -- Lower Lebesgue integral
-  have : (∫⁻ a : E, ‖(1 + ‖a‖) ^ (-r)‖₊) = ∫⁻ a : E, ENNReal.ofReal ((1 + ‖a‖) ^ (-r)) :=
+  have : ∫⁻ a : E, ‖(1 + ‖a‖) ^ (-r)‖₊ = ∫⁻ a : E, ENNReal.ofReal ((1 + ‖a‖) ^ (-r)) :=
     lintegral_nnnorm_eq_of_nonneg fun _ => rpow_nonneg_of_nonneg (by positivity) _
   rw [has_finite_integral, this]
   exact finite_integral_one_add_norm hnr

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

@@ -112,8 +112,9 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
   rwa [neg_lt_neg_iff, inv_mul_lt_iff' hr, one_mul]
 #align finite_integral_rpow_sub_one_pow_aux finite_integral_rpow_sub_one_pow_aux
 
-theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).AddHaarMeasure]
-    {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) : (∫⁻ x : E, ENNReal.ofReal ((1 + ‖x‖) ^ (-r))) < ∞ :=
+theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
+    [(@volume E _).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
+    (∫⁻ x : E, ENNReal.ofReal ((1 + ‖x‖) ^ (-r))) < ∞ :=
   by
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   -- We start by applying the layer cake formula
@@ -124,7 +125,7 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E
   -- 0 to 1 and from 1 to ∞
   have h_int :
     ∀ (t : ℝ) (ht : t ∈ Ioi (0 : ℝ)),
-      (volume { a : E | t ≤ (1 + ‖a‖) ^ (-r) } : ENNReal) =
+      (volume {a : E | t ≤ (1 + ‖a‖) ^ (-r)} : ENNReal) =
         volume (Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1)) :=
     by
     intro t ht
@@ -166,7 +167,7 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E
   exact WithTop.zero_lt_top
 #align finite_integral_one_add_norm finite_integral_one_add_norm
 
-theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).AddHaarMeasure]
+theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).IsAddHaarMeasure]
     {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) : Integrable fun x : E => (1 + ‖x‖) ^ (-r) :=
   by
   refine' ⟨by measurability, _⟩
@@ -178,7 +179,7 @@ theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).A
 #align integrable_one_add_norm integrable_one_add_norm
 
 theorem integrable_rpow_neg_one_add_norm_sq [MeasureSpace E] [BorelSpace E]
-    [(@volume E _).AddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
+    [(@volume E _).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
     Integrable fun x : E => (1 + ‖x‖ ^ 2) ^ (-r / 2) :=
   by
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr

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

@@ -112,9 +112,8 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
   rwa [neg_lt_neg_iff, inv_mul_lt_iff' hr, one_mul]
 #align finite_integral_rpow_sub_one_pow_aux finite_integral_rpow_sub_one_pow_aux
 
-theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
-    [(@volume E _).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
-    (∫⁻ x : E, ENNReal.ofReal ((1 + ‖x‖) ^ (-r))) < ∞ :=
+theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).AddHaarMeasure]
+    {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) : (∫⁻ x : E, ENNReal.ofReal ((1 + ‖x‖) ^ (-r))) < ∞ :=
   by
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   -- We start by applying the layer cake formula
@@ -167,7 +166,7 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
   exact WithTop.zero_lt_top
 #align finite_integral_one_add_norm finite_integral_one_add_norm
 
-theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).IsAddHaarMeasure]
+theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).AddHaarMeasure]
     {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) : Integrable fun x : E => (1 + ‖x‖) ^ (-r) :=
   by
   refine' ⟨by measurability, _⟩
@@ -179,7 +178,7 @@ theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).I
 #align integrable_one_add_norm integrable_one_add_norm
 
 theorem integrable_rpow_neg_one_add_norm_sq [MeasureSpace E] [BorelSpace E]
-    [(@volume E _).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
+    [(@volume E _).AddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
     Integrable fun x : E => (1 + ‖x‖ ^ 2) ^ (-r / 2) :=
   by
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr

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

@@ -29,7 +29,7 @@ than the dimension.
 
 noncomputable section
 
-open BigOperators NNReal Filter Topology ENNReal
+open scoped BigOperators NNReal Filter Topology ENNReal
 
 open Asymptotics Filter Set Real MeasureTheory FiniteDimensional
 

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

@@ -119,10 +119,7 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   -- We start by applying the layer cake formula
   have h_meas : Measurable fun ω : E => (1 + ‖ω‖) ^ (-r) := by measurability
-  have h_pos : ∀ x : E, 0 ≤ (1 + ‖x‖) ^ (-r) :=
-    by
-    intro x
-    positivity
+  have h_pos : ∀ x : E, 0 ≤ (1 + ‖x‖) ^ (-r) := by intro x; positivity
   rw [lintegral_eq_lintegral_meas_le volume h_pos h_meas]
   -- We use the first transformation of the integrant to show that we only have to integrate from
   -- 0 to 1 and from 1 to ∞

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

@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 
 ! This file was ported from Lean 3 source module analysis.special_functions.japanese_bracket
-! leanprover-community/mathlib commit 4fa54b337f7d52805480306db1b1439c741848c8
+! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.MeasureTheory.Measure.HaarLebesgue
+import Mathbin.MeasureTheory.Measure.Lebesgue.EqHaar
 import Mathbin.MeasureTheory.Integral.Layercake
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/f8c79b0a623404854a2902b836eac32156fd7712

@@ -4,13 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 
 ! This file was ported from Lean 3 source module analysis.special_functions.japanese_bracket
-! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
+! leanprover-community/mathlib commit 4fa54b337f7d52805480306db1b1439c741848c8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Measure.HaarLebesgue
 import Mathbin.MeasureTheory.Integral.Layercake
-import Mathbin.Analysis.SpecialFunctions.Pow.Tactic
 
 /-!
 # Japanese Bracket

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

@@ -4,12 +4,13 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 
 ! This file was ported from Lean 3 source module analysis.special_functions.japanese_bracket
-! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
+! leanprover-community/mathlib commit 0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Measure.HaarLebesgue
 import Mathbin.MeasureTheory.Integral.Layercake
+import Mathbin.Analysis.SpecialFunctions.Pow.Tactic
 
 /-!
 # Japanese Bracket

mathlib commit https://github.com/leanprover-community/mathlib/commit/738054fa93d43512da144ec45ce799d18fd44248

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 
 ! This file was ported from Lean 3 source module analysis.special_functions.japanese_bracket
-! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
+! leanprover-community/mathlib commit f0c8bf9245297a541f468be517f1bde6195105e9
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
+import Mathbin.MeasureTheory.Measure.HaarLebesgue
 import Mathbin.MeasureTheory.Integral.Layercake
 
 /-!

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

@@ -107,7 +107,7 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
   refine' lt_of_le_of_lt (set_lintegral_mono (by measurability) (by measurability) h_int) _
   refine' integrable_on.set_lintegral_lt_top _
   rw [← intervalIntegrable_iff_integrable_Ioc_of_le zero_le_one]
-  apply intervalIntegral.intervalIntegrableRpow'
+  apply intervalIntegral.intervalIntegrable_rpow'
   rwa [neg_lt_neg_iff, inv_mul_lt_iff' hr, one_mul]
 #align finite_integral_rpow_sub_one_pow_aux finite_integral_rpow_sub_one_pow_aux
 
@@ -169,7 +169,7 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
   exact WithTop.zero_lt_top
 #align finite_integral_one_add_norm finite_integral_one_add_norm
 
-theorem integrableOneAddNorm [MeasureSpace E] [BorelSpace E] [(@volume E _).IsAddHaarMeasure]
+theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).IsAddHaarMeasure]
     {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) : Integrable fun x : E => (1 + ‖x‖) ^ (-r) :=
   by
   refine' ⟨by measurability, _⟩
@@ -178,20 +178,20 @@ theorem integrableOneAddNorm [MeasureSpace E] [BorelSpace E] [(@volume E _).IsAd
     lintegral_nnnorm_eq_of_nonneg fun _ => rpow_nonneg_of_nonneg (by positivity) _
   rw [has_finite_integral, this]
   exact finite_integral_one_add_norm hnr
-#align integrable_one_add_norm integrableOneAddNorm
+#align integrable_one_add_norm integrable_one_add_norm
 
-theorem integrableRpowNegOneAddNormSq [MeasureSpace E] [BorelSpace E]
+theorem integrable_rpow_neg_one_add_norm_sq [MeasureSpace E] [BorelSpace E]
     [(@volume E _).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
     Integrable fun x : E => (1 + ‖x‖ ^ 2) ^ (-r / 2) :=
   by
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   refine'
-    ((integrableOneAddNorm hnr).const_mul <| 2 ^ (r / 2)).mono (by measurability)
+    ((integrable_one_add_norm hnr).const_mul <| 2 ^ (r / 2)).mono (by measurability)
       (eventually_of_forall fun x => _)
   have h1 : 0 ≤ (1 + ‖x‖ ^ 2) ^ (-r / 2) := by positivity
   have h2 : 0 ≤ (1 + ‖x‖) ^ (-r) := by positivity
   have h3 : 0 ≤ (2 : ℝ) ^ (r / 2) := by positivity
   simp_rw [norm_mul, norm_eq_abs, abs_of_nonneg h1, abs_of_nonneg h2, abs_of_nonneg h3]
   exact rpow_neg_one_add_norm_sq_le _ hr
-#align integrable_rpow_neg_one_add_norm_sq integrableRpowNegOneAddNormSq
+#align integrable_rpow_neg_one_add_norm_sq integrable_rpow_neg_one_add_norm_sq
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -4,14 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
 
 ! This file was ported from Lean 3 source module analysis.special_functions.japanese_bracket
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 2c1d8ca2812b64f88992a5294ea3dba144755cd1
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.Analysis.SpecialFunctions.Integrals
-import Mathbin.Analysis.SpecialFunctions.Pow
 import Mathbin.MeasureTheory.Integral.Layercake
-import Mathbin.Tactic.Positivity
 
 /-!
 # Japanese Bracket

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -168,7 +168,7 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
     fun t ht => by rw [closedBall_rpow_sub_one_eq_empty_aux E hr ht, measure_empty]
   -- The integral over the constant zero function is finite:
   rw [set_lintegral_congr_fun measurableSet_Ioi (ae_of_all volume <| h_int''), lintegral_const 0,
-    zero_mul]
+    MulZeroClass.zero_mul]
   exact WithTop.zero_lt_top
 #align finite_integral_one_add_norm finite_integral_one_add_norm
 

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

@@ -31,7 +31,7 @@ than the dimension.
 
 noncomputable section
 
-open BigOperators NNReal Filter Topology Ennreal
+open BigOperators NNReal Filter Topology ENNReal
 
 open Asymptotics Filter Set Real MeasureTheory FiniteDimensional
 
@@ -91,16 +91,16 @@ variable [NormedSpace ℝ E] [FiniteDimensional ℝ E]
 variable {E}
 
 theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ) < r) :
-    (∫⁻ x : ℝ in Ioc 0 1, Ennreal.ofReal ((x ^ (-r⁻¹) - 1) ^ n)) < ∞ :=
+    (∫⁻ x : ℝ in Ioc 0 1, ENNReal.ofReal ((x ^ (-r⁻¹) - 1) ^ n)) < ∞ :=
   by
   have hr : 0 < r := lt_of_le_of_lt n.cast_nonneg hnr
   have h_int :
     ∀ (x : ℝ) (hx : x ∈ Ioc (0 : ℝ) 1),
-      Ennreal.ofReal ((x ^ (-r⁻¹) - 1) ^ n) ≤ Ennreal.ofReal (x ^ (-(r⁻¹ * n))) :=
+      ENNReal.ofReal ((x ^ (-r⁻¹) - 1) ^ n) ≤ ENNReal.ofReal (x ^ (-(r⁻¹ * n))) :=
     by
     intro x hx
     have hxr : 0 ≤ x ^ (-r⁻¹) := rpow_nonneg_of_nonneg hx.1.le _
-    apply Ennreal.ofReal_le_ofReal
+    apply ENNReal.ofReal_le_ofReal
     rw [← neg_mul, rpow_mul hx.1.le, rpow_nat_cast]
     refine' pow_le_pow_of_le_left _ (by simp only [sub_le_self_iff, zero_le_one]) n
     rw [le_sub_iff_add_le', add_zero]
@@ -116,7 +116,7 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
 
 theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
     [(@volume E _).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
-    (∫⁻ x : E, Ennreal.ofReal ((1 + ‖x‖) ^ (-r))) < ∞ :=
+    (∫⁻ x : E, ENNReal.ofReal ((1 + ‖x‖) ^ (-r))) < ∞ :=
   by
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   -- We start by applying the layer cake formula
@@ -130,7 +130,7 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
   -- 0 to 1 and from 1 to ∞
   have h_int :
     ∀ (t : ℝ) (ht : t ∈ Ioi (0 : ℝ)),
-      (volume { a : E | t ≤ (1 + ‖a‖) ^ (-r) } : Ennreal) =
+      (volume { a : E | t ≤ (1 + ‖a‖) ^ (-r) } : ENNReal) =
         volume (Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1)) :=
     by
     intro t ht
@@ -141,30 +141,30 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
   rw [set_lintegral_congr_fun measurableSet_Ioi (ae_of_all volume <| h_int)]
   have hIoi_eq : Ioi (0 : ℝ) = Ioc (0 : ℝ) 1 ∪ Ioi 1 := (Set.Ioc_union_Ioi_eq_Ioi zero_le_one).symm
   have hdisjoint : Disjoint (Ioc (0 : ℝ) 1) (Ioi 1) := by simp [disjoint_iff]
-  rw [hIoi_eq, lintegral_union measurableSet_Ioi hdisjoint, Ennreal.add_lt_top]
+  rw [hIoi_eq, lintegral_union measurableSet_Ioi hdisjoint, ENNReal.add_lt_top]
   have h_int' :
     ∀ (t : ℝ) (ht : t ∈ Ioc (0 : ℝ) 1),
-      (volume (Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1)) : Ennreal) =
-        Ennreal.ofReal ((t ^ (-r⁻¹) - 1) ^ FiniteDimensional.finrank ℝ E) *
+      (volume (Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1)) : ENNReal) =
+        ENNReal.ofReal ((t ^ (-r⁻¹) - 1) ^ FiniteDimensional.finrank ℝ E) *
           volume (Metric.ball (0 : E) 1) :=
     by
     intro t ht
     refine' volume.add_haar_closed_ball (0 : E) _
     rw [le_sub_iff_add_le', add_zero]
     exact Real.one_le_rpow_of_pos_of_le_one_of_nonpos ht.1 ht.2 (by simp [hr.le])
-  have h_meas' : Measurable fun a : ℝ => Ennreal.ofReal ((a ^ (-r⁻¹) - 1) ^ finrank ℝ E) := by
+  have h_meas' : Measurable fun a : ℝ => ENNReal.ofReal ((a ^ (-r⁻¹) - 1) ^ finrank ℝ E) := by
     measurability
   constructor
   -- The integral from 0 to 1:
   · rw [set_lintegral_congr_fun measurableSet_Ioc (ae_of_all volume <| h_int'),
-      lintegral_mul_const _ h_meas', Ennreal.mul_lt_top_iff]
+      lintegral_mul_const _ h_meas', ENNReal.mul_lt_top_iff]
     left
     -- We calculate the integral
     exact ⟨finite_integral_rpow_sub_one_pow_aux (finrank ℝ E) hnr, measure_ball_lt_top⟩
   -- The integral from 1 to ∞ is zero:
   have h_int'' :
     ∀ (t : ℝ) (ht : t ∈ Ioi (1 : ℝ)),
-      (volume (Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1)) : Ennreal) = 0 :=
+      (volume (Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1)) : ENNReal) = 0 :=
     fun t ht => by rw [closedBall_rpow_sub_one_eq_empty_aux E hr ht, measure_empty]
   -- The integral over the constant zero function is finite:
   rw [set_lintegral_congr_fun measurableSet_Ioi (ae_of_all volume <| h_int''), lintegral_const 0,
@@ -177,7 +177,7 @@ theorem integrableOneAddNorm [MeasureSpace E] [BorelSpace E] [(@volume E _).IsAd
   by
   refine' ⟨by measurability, _⟩
   -- Lower Lebesgue integral
-  have : (∫⁻ a : E, ‖(1 + ‖a‖) ^ (-r)‖₊) = ∫⁻ a : E, Ennreal.ofReal ((1 + ‖a‖) ^ (-r)) :=
+  have : (∫⁻ a : E, ‖(1 + ‖a‖) ^ (-r)‖₊) = ∫⁻ a : E, ENNReal.ofReal ((1 + ‖a‖) ^ (-r)) :=
     lintegral_nnnorm_eq_of_nonneg fun _ => rpow_nonneg_of_nonneg (by positivity) _
   rw [has_finite_integral, this]
   exact finite_integral_one_add_norm hnr

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

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.

@@ -81,7 +81,7 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
   have h_int : ∀ x : ℝ, x ∈ Ioc (0 : ℝ) 1 →
       ENNReal.ofReal ((x ^ (-r⁻¹) - 1) ^ n) ≤ ENNReal.ofReal (x ^ (-(r⁻¹ * n))) := fun x hx ↦ by
     apply ENNReal.ofReal_le_ofReal
-    rw [← neg_mul, rpow_mul hx.1.le, rpow_nat_cast]
+    rw [← neg_mul, rpow_mul hx.1.le, rpow_natCast]
     refine' pow_le_pow_left _ (by simp only [sub_le_self_iff, zero_le_one]) n
     rw [le_sub_iff_add_le', add_zero]
     refine' Real.one_le_rpow_of_pos_of_le_one_of_nonpos hx.1 hx.2 _

This adds the notation √r for Real.sqrt r. The precedence is such that √x⁻¹ is parsed as √(x⁻¹); not because this is particularly desirable, but because it's the default and the choice doesn't really matter.

This is extracted from #7907, which adds a more general nth root typeclass. The idea is to perform all the boring substitutions downstream quickly, so that we can play around with custom elaborators with a much slower rate of code-rot. This PR also won't rot as quickly, as it does not forbid writing x.sqrt as that PR does.

While perhaps claiming √ for Real.sqrt is greedy; it:

• Is far more common thatn NNReal.sqrt and Nat.sqrt
• Is far more interesting to mathlib than sqrt on Float
• Can be overloaded anyway, so this does not prevent downstream code using the notation on their own types.
• Will be replaced by a more general typeclass in a future PR.

Zulip

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -32,13 +32,13 @@ open Asymptotics Filter Set Real MeasureTheory FiniteDimensional
 
 variable {E : Type*} [NormedAddCommGroup E]
 
-theorem sqrt_one_add_norm_sq_le (x : E) : Real.sqrt ((1 : ℝ) + ‖x‖ ^ 2) ≤ 1 + ‖x‖ := by
+theorem sqrt_one_add_norm_sq_le (x : E) : √((1 : ℝ) + ‖x‖ ^ 2) ≤ 1 + ‖x‖ := by
   rw [sqrt_le_left (by positivity)]
   simp [add_sq]
 #align sqrt_one_add_norm_sq_le sqrt_one_add_norm_sq_le
 
 theorem one_add_norm_le_sqrt_two_mul_sqrt (x : E) :
-    (1 : ℝ) + ‖x‖ ≤ Real.sqrt 2 * sqrt ((1 : ℝ) + ‖x‖ ^ 2) := by
+    (1 : ℝ) + ‖x‖ ≤ √2 * √(1 + ‖x‖ ^ 2) := by
   rw [← sqrt_mul zero_le_two]
   have := sq_nonneg (‖x‖ - 1)
   apply le_sqrt_of_sq_le
@@ -49,7 +49,7 @@ theorem rpow_neg_one_add_norm_sq_le {r : ℝ} (x : E) (hr : 0 < r) :
     ((1 : ℝ) + ‖x‖ ^ 2) ^ (-r / 2) ≤ (2 : ℝ) ^ (r / 2) * (1 + ‖x‖) ^ (-r) :=
   calc
     ((1 : ℝ) + ‖x‖ ^ 2) ^ (-r / 2)
-      = (2 : ℝ) ^ (r / 2) * ((Real.sqrt 2 * Real.sqrt ((1 : ℝ) + ‖x‖ ^ 2)) ^ r)⁻¹ := by
+      = (2 : ℝ) ^ (r / 2) * ((√2 * √((1 : ℝ) + ‖x‖ ^ 2)) ^ r)⁻¹ := by
       rw [rpow_div_two_eq_sqrt, rpow_div_two_eq_sqrt, mul_rpow, mul_inv, rpow_neg,
         mul_inv_cancel_left₀] <;> positivity
     _ ≤ (2 : ℝ) ^ (r / 2) * ((1 + ‖x‖) ^ r)⁻¹ := by

@@ -94,8 +94,9 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
   rwa [neg_lt_neg_iff, inv_mul_lt_iff' hr, one_mul]
 #align finite_integral_rpow_sub_one_pow_aux finite_integral_rpow_sub_one_pow_aux
 
-theorem finite_integral_one_add_norm [MeasurableSpace E] [BorelSpace E] {μ : Measure E}
-    [μ.IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
+variable [MeasurableSpace E] [BorelSpace E] {μ : Measure E} [μ.IsAddHaarMeasure]
+
+theorem finite_integral_one_add_norm {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
     (∫⁻ x : E, ENNReal.ofReal ((1 + ‖x‖) ^ (-r)) ∂μ) < ∞ := by
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   -- We start by applying the layer cake formula
@@ -137,9 +138,8 @@ theorem finite_integral_one_add_norm [MeasurableSpace E] [BorelSpace E] {μ : Me
     exact WithTop.zero_lt_top
 #align finite_integral_one_add_norm finite_integral_one_add_norm
 
-theorem integrable_one_add_norm [MeasurableSpace E] [BorelSpace E] {μ : Measure E}
-    [μ.IsAddHaarMeasure]
-    {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) : Integrable (fun x : E => (1 + ‖x‖) ^ (-r)) μ := by
+theorem integrable_one_add_norm {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
+    Integrable (fun x ↦ (1 + ‖x‖) ^ (-r)) μ := by
   constructor
   · measurability
   -- Lower Lebesgue integral
@@ -149,9 +149,8 @@ theorem integrable_one_add_norm [MeasurableSpace E] [BorelSpace E] {μ : Measure
   exact finite_integral_one_add_norm hnr
 #align integrable_one_add_norm integrable_one_add_norm
 
-theorem integrable_rpow_neg_one_add_norm_sq [MeasurableSpace E] [BorelSpace E] {μ : Measure E}
-    [μ.IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
-    Integrable (fun x : E => ((1 : ℝ) + ‖x‖ ^ 2) ^ (-r / 2)) μ := by
+theorem integrable_rpow_neg_one_add_norm_sq {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
+    Integrable (fun x ↦ ((1 : ℝ) + ‖x‖ ^ 2) ^ (-r / 2)) μ := by
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   refine ((integrable_one_add_norm hnr).const_mul <| (2 : ℝ) ^ (r / 2)).mono'
     ?_ (eventually_of_forall fun x => ?_)

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)

@@ -73,7 +73,6 @@ theorem closedBall_rpow_sub_one_eq_empty_aux {r t : ℝ} (hr : 0 < r) (ht : 1 <
 #align closed_ball_rpow_sub_one_eq_empty_aux closedBall_rpow_sub_one_eq_empty_aux
 
 variable [NormedSpace ℝ E] [FiniteDimensional ℝ E]
-
 variable {E}
 
 theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ) < r) :

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -101,7 +101,7 @@ theorem finite_integral_one_add_norm [MeasurableSpace E] [BorelSpace E] {μ : Me
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   -- We start by applying the layer cake formula
   have h_meas : Measurable fun ω : E => (1 + ‖ω‖) ^ (-r) :=
-    -- porting note: was `by measurability`
+    -- Porting note: was `by measurability`
     (measurable_norm.const_add _).pow_const _
   have h_pos : ∀ x : E, 0 ≤ (1 + ‖x‖) ^ (-r) := fun x ↦ by positivity
   rw [lintegral_eq_lintegral_meas_le μ (eventually_of_forall h_pos) h_meas.aemeasurable]

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -131,7 +131,7 @@ theorem finite_integral_one_add_norm [MeasurableSpace E] [BorelSpace E] {μ : Me
       (finite_integral_rpow_sub_one_pow_aux (finrank ℝ E) hnr).ne measure_ball_lt_top.ne
   · -- The integral from 1 to ∞ is zero:
     have h_int'' : ∀ t ∈ Ioi (1 : ℝ), f t = 0 := fun t ht => by
-      simp only [closedBall_rpow_sub_one_eq_empty_aux E hr ht, measure_empty]
+      simp only [f, closedBall_rpow_sub_one_eq_empty_aux E hr ht, measure_empty]
     -- The integral over the constant zero function is finite:
     rw [set_lintegral_congr_fun measurableSet_Ioi (ae_of_all volume <| h_int''), lintegral_const 0,
       zero_mul]

@@ -95,25 +95,25 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
   rwa [neg_lt_neg_iff, inv_mul_lt_iff' hr, one_mul]
 #align finite_integral_rpow_sub_one_pow_aux finite_integral_rpow_sub_one_pow_aux
 
-theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
-    [(volume : Measure E).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
-    (∫⁻ x : E, ENNReal.ofReal ((1 + ‖x‖) ^ (-r))) < ∞ := by
+theorem finite_integral_one_add_norm [MeasurableSpace E] [BorelSpace E] {μ : Measure E}
+    [μ.IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
+    (∫⁻ x : E, ENNReal.ofReal ((1 + ‖x‖) ^ (-r)) ∂μ) < ∞ := by
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   -- We start by applying the layer cake formula
   have h_meas : Measurable fun ω : E => (1 + ‖ω‖) ^ (-r) :=
     -- porting note: was `by measurability`
     (measurable_norm.const_add _).pow_const _
   have h_pos : ∀ x : E, 0 ≤ (1 + ‖x‖) ^ (-r) := fun x ↦ by positivity
-  rw [lintegral_eq_lintegral_meas_le volume (eventually_of_forall h_pos) h_meas.aemeasurable]
-  have h_int : ∀ t, 0 < t → volume {a : E | t ≤ (1 + ‖a‖) ^ (-r)} =
-      volume (Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1)) := fun t ht ↦ by
+  rw [lintegral_eq_lintegral_meas_le μ (eventually_of_forall h_pos) h_meas.aemeasurable]
+  have h_int : ∀ t, 0 < t → μ {a : E | t ≤ (1 + ‖a‖) ^ (-r)} =
+      μ (Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1)) := fun t ht ↦ by
     congr 1
     ext x
     simp only [mem_setOf_eq, mem_closedBall_zero_iff]
     exact le_rpow_one_add_norm_iff_norm_le hr (mem_Ioi.mp ht) x
   rw [set_lintegral_congr_fun measurableSet_Ioi (eventually_of_forall h_int)]
-  set f := fun t : ℝ ↦ volume (Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1))
-  set mB := volume (Metric.ball (0 : E) 1)
+  set f := fun t : ℝ ↦ μ (Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1))
+  set mB := μ (Metric.ball (0 : E) 1)
   -- the next two inequalities are in fact equalities but we don't need that
   calc
     ∫⁻ t in Ioi 0, f t ≤ ∫⁻ t in Ioc 0 1 ∪ Ioi 1, f t := lintegral_mono_set Ioi_subset_Ioc_union_Ioi
@@ -122,7 +122,7 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
   · -- We use estimates from auxiliary lemmas to deal with integral from `0` to `1`
     have h_int' : ∀ t ∈ Ioc (0 : ℝ) 1,
         f t = ENNReal.ofReal ((t ^ (-r⁻¹) - 1) ^ finrank ℝ E) * mB := fun t ht ↦ by
-      refine' volume.addHaar_closedBall (0 : E) _
+      refine' μ.addHaar_closedBall (0 : E) _
       rw [sub_nonneg]
       exact Real.one_le_rpow_of_pos_of_le_one_of_nonpos ht.1 ht.2 (by simp [hr.le])
     rw [set_lintegral_congr_fun measurableSet_Ioc (ae_of_all _ h_int'),
@@ -138,20 +138,21 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
     exact WithTop.zero_lt_top
 #align finite_integral_one_add_norm finite_integral_one_add_norm
 
-theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).IsAddHaarMeasure]
-    {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) : Integrable fun x : E => (1 + ‖x‖) ^ (-r) := by
+theorem integrable_one_add_norm [MeasurableSpace E] [BorelSpace E] {μ : Measure E}
+    [μ.IsAddHaarMeasure]
+    {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) : Integrable (fun x : E => (1 + ‖x‖) ^ (-r)) μ := by
   constructor
   · measurability
   -- Lower Lebesgue integral
-  have : (∫⁻ a : E, ‖(1 + ‖a‖) ^ (-r)‖₊) = ∫⁻ a : E, ENNReal.ofReal ((1 + ‖a‖) ^ (-r)) :=
+  have : (∫⁻ a : E, ‖(1 + ‖a‖) ^ (-r)‖₊ ∂μ) = ∫⁻ a : E, ENNReal.ofReal ((1 + ‖a‖) ^ (-r)) ∂μ :=
     lintegral_nnnorm_eq_of_nonneg fun _ => rpow_nonneg (by positivity) _
   rw [HasFiniteIntegral, this]
   exact finite_integral_one_add_norm hnr
 #align integrable_one_add_norm integrable_one_add_norm
 
-theorem integrable_rpow_neg_one_add_norm_sq [MeasureSpace E] [BorelSpace E]
-    [(@volume E _).IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
-    Integrable fun x : E => ((1 : ℝ) + ‖x‖ ^ 2) ^ (-r / 2) := by
+theorem integrable_rpow_neg_one_add_norm_sq [MeasurableSpace E] [BorelSpace E] {μ : Measure E}
+    [μ.IsAddHaarMeasure] {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) :
+    Integrable (fun x : E => ((1 : ℝ) + ‖x‖ ^ 2) ^ (-r / 2)) μ := by
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   refine ((integrable_one_add_norm hnr).const_mul <| (2 : ℝ) ^ (r / 2)).mono'
     ?_ (eventually_of_forall fun x => ?_)

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

@@ -141,8 +141,7 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
 theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).IsAddHaarMeasure]
     {r : ℝ} (hnr : (finrank ℝ E : ℝ) < r) : Integrable fun x : E => (1 + ‖x‖) ^ (-r) := by
   constructor
-  · -- porting note: was `measurability`
-    exact ((measurable_norm.const_add _).pow_const _).aestronglyMeasurable
+  · measurability
   -- Lower Lebesgue integral
   have : (∫⁻ a : E, ‖(1 + ‖a‖) ^ (-r)‖₊) = ∫⁻ a : E, ENNReal.ofReal ((1 + ‖a‖) ^ (-r)) :=
     lintegral_nnnorm_eq_of_nonneg fun _ => rpow_nonneg (by positivity) _
@@ -156,8 +155,7 @@ theorem integrable_rpow_neg_one_add_norm_sq [MeasureSpace E] [BorelSpace E]
   have hr : 0 < r := lt_of_le_of_lt (finrank ℝ E).cast_nonneg hnr
   refine ((integrable_one_add_norm hnr).const_mul <| (2 : ℝ) ^ (r / 2)).mono'
     ?_ (eventually_of_forall fun x => ?_)
-  · -- porting note: was `measurability`
-    exact (((measurable_id.norm.pow_const _).const_add _).pow_const _).aestronglyMeasurable
+  · measurability
   refine (abs_of_pos ?_).trans_le (rpow_neg_one_add_norm_sq_le x hr)
   positivity
 #align integrable_rpow_neg_one_add_norm_sq integrable_rpow_neg_one_add_norm_sq

This better matches other lemma names.

From LeanAPAP

@@ -145,7 +145,7 @@ theorem integrable_one_add_norm [MeasureSpace E] [BorelSpace E] [(@volume E _).I
     exact ((measurable_norm.const_add _).pow_const _).aestronglyMeasurable
   -- Lower Lebesgue integral
   have : (∫⁻ a : E, ‖(1 + ‖a‖) ^ (-r)‖₊) = ∫⁻ a : E, ENNReal.ofReal ((1 + ‖a‖) ^ (-r)) :=
-    lintegral_nnnorm_eq_of_nonneg fun _ => rpow_nonneg_of_nonneg (by positivity) _
+    lintegral_nnnorm_eq_of_nonneg fun _ => rpow_nonneg (by positivity) _
   rw [HasFiniteIntegral, this]
   exact finite_integral_one_add_norm hnr
 #align integrable_one_add_norm integrable_one_add_norm

We have in the library the lemma not_intervalIntegrable_of_tendsto_norm_atTop_of_deriv_isBigO_filter, saying that if a function tends to infinity at a point in an interval [a, b], then its derivative is not interval-integrable on [a, b]. We generalize this result to allow for any set instead of [a, b], and apply it to half-infinite intervals.

In particular, we characterize integrability of x^s on [a, +oo), and deduce that x^s is never integrable on [0, +oo). This makes it possible to remove one assumption in Lemma mellin_comp_rpow on the Mellin transform.

@@ -90,7 +90,7 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
     exact hr.le
   refine' lt_of_le_of_lt (set_lintegral_mono' measurableSet_Ioc h_int) _
   refine' IntegrableOn.set_lintegral_lt_top _
-  rw [← intervalIntegrable_iff_integrable_Ioc_of_le zero_le_one]
+  rw [← intervalIntegrable_iff_integrableOn_Ioc_of_le zero_le_one]
   apply intervalIntegral.intervalIntegrable_rpow'
   rwa [neg_lt_neg_iff, inv_mul_lt_iff' hr, one_mul]
 #align finite_integral_rpow_sub_one_pow_aux finite_integral_rpow_sub_one_pow_aux

The names for lemmas about monotonicity of (a ^ ·) and (· ^ n) were a mess. This PR tidies up everything related by following the naming convention for (a * ·) and (· * b). Namely, (a ^ ·) is pow_right and (· ^ n) is pow_left in lemma names. All lemma renames follow the corresponding multiplication lemma names closely.

Renames

Algebra.GroupPower.Order

• pow_mono → pow_right_mono
• pow_le_pow → pow_le_pow_right
• pow_le_pow_of_le_left → pow_le_pow_left
• pow_lt_pow_of_lt_left → pow_lt_pow_left
• strictMonoOn_pow → pow_left_strictMonoOn
• pow_strictMono_right → pow_right_strictMono
• pow_lt_pow → pow_lt_pow_right
• pow_lt_pow_iff → pow_lt_pow_iff_right
• pow_le_pow_iff → pow_le_pow_iff_right
• self_lt_pow → lt_self_pow
• strictAnti_pow → pow_right_strictAnti
• pow_lt_pow_iff_of_lt_one → pow_lt_pow_iff_right_of_lt_one
• pow_lt_pow_of_lt_one → pow_lt_pow_right_of_lt_one
• lt_of_pow_lt_pow → lt_of_pow_lt_pow_left
• le_of_pow_le_pow → le_of_pow_le_pow_left
• pow_lt_pow₀ → pow_lt_pow_right₀

Algebra.GroupPower.CovariantClass

• pow_le_pow_of_le_left' → pow_le_pow_left'
• nsmul_le_nsmul_of_le_right → nsmul_le_nsmul_right
• pow_lt_pow' → pow_lt_pow_right'
• nsmul_lt_nsmul → nsmul_lt_nsmul_left
• pow_strictMono_left → pow_right_strictMono'
• nsmul_strictMono_right → nsmul_left_strictMono
• StrictMono.pow_right' → StrictMono.pow_const
• StrictMono.nsmul_left → StrictMono.const_nsmul
• pow_strictMono_right' → pow_left_strictMono
• nsmul_strictMono_left → nsmul_right_strictMono
• Monotone.pow_right → Monotone.pow_const
• Monotone.nsmul_left → Monotone.const_nsmul
• lt_of_pow_lt_pow' → lt_of_pow_lt_pow_left'
• lt_of_nsmul_lt_nsmul → lt_of_nsmul_lt_nsmul_right
• pow_le_pow' → pow_le_pow_right'
• nsmul_le_nsmul → nsmul_le_nsmul_left
• pow_le_pow_of_le_one' → pow_le_pow_right_of_le_one'
• nsmul_le_nsmul_of_nonpos → nsmul_le_nsmul_left_of_nonpos
• le_of_pow_le_pow' → le_of_pow_le_pow_left'
• le_of_nsmul_le_nsmul' → le_of_nsmul_le_nsmul_right'
• pow_le_pow_iff' → pow_le_pow_iff_right'
• nsmul_le_nsmul_iff → nsmul_le_nsmul_iff_left
• pow_lt_pow_iff' → pow_lt_pow_iff_right'
• nsmul_lt_nsmul_iff → nsmul_lt_nsmul_iff_left

Data.Nat.Pow

• Nat.pow_lt_pow_of_lt_left → Nat.pow_lt_pow_left
• Nat.pow_le_iff_le_left → Nat.pow_le_pow_iff_left
• Nat.pow_lt_iff_lt_left → Nat.pow_lt_pow_iff_left

Lemmas added

• pow_le_pow_iff_left
• pow_lt_pow_iff_left
• pow_right_injective
• pow_right_inj
• Nat.pow_le_pow_left to have the correct name since Nat.pow_le_pow_of_le_left is in Std.
• Nat.pow_le_pow_right to have the correct name since Nat.pow_le_pow_of_le_right is in Std.

Lemmas removed

• self_le_pow was a duplicate of le_self_pow.
• Nat.pow_lt_pow_of_lt_right is defeq to pow_lt_pow_right.
• Nat.pow_right_strictMono is defeq to pow_right_strictMono.
• Nat.pow_le_iff_le_right is defeq to pow_le_pow_iff_right.
• Nat.pow_lt_iff_lt_right is defeq to pow_lt_pow_iff_right.

Other changes

• A bunch of proofs have been golfed.
• Some lemma assumptions have been turned from 0 < n or 1 ≤ n to n ≠ 0.
• A few Nat lemmas have been protected.
• One docstring has been fixed.

@@ -83,7 +83,7 @@ theorem finite_integral_rpow_sub_one_pow_aux {r : ℝ} (n : ℕ) (hnr : (n : ℝ
       ENNReal.ofReal ((x ^ (-r⁻¹) - 1) ^ n) ≤ ENNReal.ofReal (x ^ (-(r⁻¹ * n))) := fun x hx ↦ by
     apply ENNReal.ofReal_le_ofReal
     rw [← neg_mul, rpow_mul hx.1.le, rpow_nat_cast]
-    refine' pow_le_pow_of_le_left _ (by simp only [sub_le_self_iff, zero_le_one]) n
+    refine' pow_le_pow_left _ (by simp only [sub_le_self_iff, zero_le_one]) n
     rw [le_sub_iff_add_le', add_zero]
     refine' Real.one_le_rpow_of_pos_of_le_one_of_nonpos hx.1 hx.2 _
     rw [Right.neg_nonpos_iff, inv_nonneg]

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>

@@ -26,7 +26,6 @@ than the dimension.
 
 noncomputable section
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 open scoped BigOperators NNReal Filter Topology ENNReal
 
 open Asymptotics Filter Set Real MeasureTheory FiniteDimensional

The layercake formulas (a typical example of which is ∫⁻ f^p ∂μ = p * ∫⁻ t in 0..∞, t^(p-1) * μ {ω | f(ω) > t}) had been originally proven assuming measurability and nonnegativity of f. This PR generalizes them to null-measurable and a.e.-nonnegative f.

Co-authored-by: kkytola <“kalle.kytola@aalto.fi”> Co-authored-by: kkytola <39528102+kkytola@users.noreply.github.com>

@@ -105,7 +105,7 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
     -- porting note: was `by measurability`
     (measurable_norm.const_add _).pow_const _
   have h_pos : ∀ x : E, 0 ≤ (1 + ‖x‖) ^ (-r) := fun x ↦ by positivity
-  rw [lintegral_eq_lintegral_meas_le volume h_pos h_meas]
+  rw [lintegral_eq_lintegral_meas_le volume (eventually_of_forall h_pos) h_meas.aemeasurable]
   have h_int : ∀ t, 0 < t → volume {a : E | t ≤ (1 + ‖a‖) ^ (-r)} =
       volume (Metric.closedBall (0 : E) (t ^ (-r⁻¹) - 1)) := fun t ht ↦ by
     congr 1

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

This has nice performance benefits.

@@ -31,7 +31,7 @@ open scoped BigOperators NNReal Filter Topology ENNReal
 
 open Asymptotics Filter Set Real MeasureTheory FiniteDimensional
 
-variable {E : Type _} [NormedAddCommGroup E]
+variable {E : Type*} [NormedAddCommGroup E]
 
 theorem sqrt_one_add_norm_sq_le (x : E) : Real.sqrt ((1 : ℝ) + ‖x‖ ^ 2) ≤ 1 + ‖x‖ := by
   rw [sqrt_le_left (by positivity)]

@@ -26,7 +26,7 @@ than the dimension.
 
 noncomputable section
 
-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
 open scoped BigOperators NNReal Filter Topology ENNReal
 
 open Asymptotics Filter Set Real MeasureTheory FiniteDimensional

• 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) 2022 Moritz Doll. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Moritz Doll
-
-! This file was ported from Lean 3 source module analysis.special_functions.japanese_bracket
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Measure.Lebesgue.EqHaar
 import Mathlib.MeasureTheory.Integral.Layercake
 
+#align_import analysis.special_functions.japanese_bracket from "leanprover-community/mathlib"@"fd5edc43dc4f10b85abfe544b88f82cf13c5f844"
+
 /-!
 # Japanese Bracket
 

Grepping for [^ .:{-] [^ :] and reviewing the results. Once I started I couldn't stop. :-)

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -162,6 +162,6 @@ theorem integrable_rpow_neg_one_add_norm_sq [MeasureSpace E] [BorelSpace E]
     ?_ (eventually_of_forall fun x => ?_)
   · -- porting note: was `measurability`
     exact (((measurable_id.norm.pow_const _).const_add _).pow_const _).aestronglyMeasurable
-  refine (abs_of_pos ?_).trans_le  (rpow_neg_one_add_norm_sq_le x hr)
+  refine (abs_of_pos ?_).trans_le (rpow_neg_one_add_norm_sq_le x hr)
   positivity
 #align integrable_rpow_neg_one_add_norm_sq integrable_rpow_neg_one_add_norm_sq

This is supposed to mean "an additive Haar measure", not adding something to Haar, so it should be one word and not two.

@@ -126,12 +126,12 @@ theorem finite_integral_one_add_norm [MeasureSpace E] [BorelSpace E]
   · -- We use estimates from auxiliary lemmas to deal with integral from `0` to `1`
     have h_int' : ∀ t ∈ Ioc (0 : ℝ) 1,
         f t = ENNReal.ofReal ((t ^ (-r⁻¹) - 1) ^ finrank ℝ E) * mB := fun t ht ↦ by
-      refine' volume.add_haar_closedBall (0 : E) _
+      refine' volume.addHaar_closedBall (0 : E) _
       rw [sub_nonneg]
       exact Real.one_le_rpow_of_pos_of_le_one_of_nonpos ht.1 ht.2 (by simp [hr.le])
     rw [set_lintegral_congr_fun measurableSet_Ioc (ae_of_all _ h_int'),
       lintegral_mul_const' _ _ measure_ball_lt_top.ne]
-    exact ENNReal.mul_lt_top 
+    exact ENNReal.mul_lt_top
       (finite_integral_rpow_sub_one_pow_aux (finrank ℝ E) hnr).ne measure_ball_lt_top.ne
   · -- The integral from 1 to ∞ is zero:
     have h_int'' : ∀ t ∈ Ioi (1 : ℝ), f t = 0 := fun t ht => by
@@ -165,4 +165,3 @@ theorem integrable_rpow_neg_one_add_norm_sq [MeasureSpace E] [BorelSpace E]
   refine (abs_of_pos ?_).trans_le  (rpow_neg_one_add_norm_sq_le x hr)
   positivity
 #align integrable_rpow_neg_one_add_norm_sq integrable_rpow_neg_one_add_norm_sq
-