measure_theory.group.prod ⟷ Mathlib.MeasureTheory.Group.Prod

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

@@ -325,7 +325,7 @@ theorem absolutelyContinuous_of_isMulLeftInvariant [IsMulLeftInvariant ν] (hν
   refine' absolutely_continuous.mk fun s sm hνs => _
   have h1 := measure_mul_lintegral_eq μ ν sm 1 measurable_one
   simp_rw [Pi.one_apply, lintegral_one, mul_one, (measure_mul_right_null ν _).mpr hνs,
-    lintegral_zero, mul_eq_zero, measure_univ_eq_zero.not.mpr hν, or_false_iff] at h1 
+    lintegral_zero, mul_eq_zero, measure_univ_eq_zero.not.mpr hν, or_false_iff] at h1
   exact h1
 #align measure_theory.absolutely_continuous_of_is_mul_left_invariant MeasureTheory.absolutelyContinuous_of_isMulLeftInvariant
 #align measure_theory.absolutely_continuous_of_is_add_left_invariant MeasureTheory.absolutelyContinuous_of_isAddLeftInvariant
@@ -338,13 +338,13 @@ theorem ae_measure_preimage_mul_right_lt_top [IsMulLeftInvariant ν] (sm : Measu
   by
   refine' ae_of_forall_measure_lt_top_ae_restrict' ν.inv _ _
   intro A hA h2A h3A
-  simp only [ν.inv_apply] at h3A 
+  simp only [ν.inv_apply] at h3A
   apply ae_lt_top (measurable_measure_mul_right ν sm)
   have h1 := measure_mul_lintegral_eq μ ν sm (A⁻¹.indicator 1) (measurable_one.indicator hA.inv)
-  rw [lintegral_indicator _ hA.inv] at h1 
+  rw [lintegral_indicator _ hA.inv] at h1
   simp_rw [Pi.one_apply, set_lintegral_one, ← image_inv, indicator_image inv_injective, image_inv, ←
     indicator_mul_right _ fun x => ν ((fun y => y * x) ⁻¹' s), Function.comp, Pi.one_apply,
-    mul_one] at h1 
+    mul_one] at h1
   rw [← lintegral_indicator _ hA, ← h1]
   exact ENNReal.mul_ne_top hμs h3A.ne
 #align measure_theory.ae_measure_preimage_mul_right_lt_top MeasureTheory.ae_measure_preimage_mul_right_lt_top
@@ -404,7 +404,7 @@ theorem measure_mul_measure_eq [IsMulLeftInvariant ν] {s t : Set G} (hs : Measu
   have h2 :=
     measure_lintegral_div_measure μ ν hs h2s h3s (t.indicator fun x => 1)
       (measurable_const.indicator ht)
-  rw [lintegral_indicator _ ht, set_lintegral_one] at h1 h2 
+  rw [lintegral_indicator _ ht, set_lintegral_one] at h1 h2
   rw [← h1, mul_left_comm, h2]
 #align measure_theory.measure_mul_measure_eq MeasureTheory.measure_mul_measure_eq
 #align measure_theory.measure_add_measure_eq MeasureTheory.measure_add_measure_eq
@@ -597,11 +597,11 @@ theorem quasiMeasurePreserving_mul_left [IsMulRightInvariant μ] (g : G) :
   have :=
     (quasi_measure_preserving_mul_right μ.inv g⁻¹).mono (inv_absolutely_continuous μ.inv)
       (absolutely_continuous_inv μ.inv)
-  rw [μ.inv_inv] at this 
+  rw [μ.inv_inv] at this
   have :=
     (quasi_measure_preserving_inv_of_right_invariant μ).comp
       (this.comp (quasi_measure_preserving_inv_of_right_invariant μ))
-  simp_rw [Function.comp, mul_inv_rev, inv_inv] at this 
+  simp_rw [Function.comp, mul_inv_rev, inv_inv] at this
   exact this
 #align measure_theory.quasi_measure_preserving_mul_left MeasureTheory.quasiMeasurePreserving_mul_left
 #align measure_theory.quasi_measure_preserving_add_left MeasureTheory.quasiMeasurePreserving_add_left

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
 -/
-import Mathbin.MeasureTheory.Constructions.Prod.Basic
-import Mathbin.MeasureTheory.Group.Measure
+import MeasureTheory.Constructions.Prod.Basic
+import MeasureTheory.Group.Measure
 
 #align_import measure_theory.group.prod from "leanprover-community/mathlib"@"599fffe78f0e11eb6a034e834ec51882167b9688"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
-
-! This file was ported from Lean 3 source module measure_theory.group.prod
-! leanprover-community/mathlib commit 599fffe78f0e11eb6a034e834ec51882167b9688
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Constructions.Prod.Basic
 import Mathbin.MeasureTheory.Group.Measure
 
+#align_import measure_theory.group.prod from "leanprover-community/mathlib"@"599fffe78f0e11eb6a034e834ec51882167b9688"
+
 /-!
 # Measure theory in the product of groups
 

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

@@ -57,6 +57,7 @@ variable [Group G] [MeasurableMul₂ G]
 
 variable (μ ν : Measure G) [SigmaFinite ν] [SigmaFinite μ] {s : Set G}
 
+#print MeasurableEquiv.shearMulRight /-
 /-- The map `(x, y) ↦ (x, xy)` as a `measurable_equiv`. -/
 @[to_additive "The map `(x, y) ↦ (x, x + y)` as a `measurable_equiv`."]
 protected def MeasurableEquiv.shearMulRight [MeasurableInv G] : G × G ≃ᵐ G × G :=
@@ -67,7 +68,9 @@ protected def MeasurableEquiv.shearMulRight [MeasurableInv G] : G × G ≃ᵐ G
     measurable_inv_fun := measurable_fst.prod_mk <| measurable_fst.inv.mul measurable_snd }
 #align measurable_equiv.shear_mul_right MeasurableEquiv.shearMulRight
 #align measurable_equiv.shear_add_right MeasurableEquiv.shearAddRight
+-/
 
+#print MeasurableEquiv.shearDivRight /-
 /-- The map `(x, y) ↦ (x, y / x)` as a `measurable_equiv` with as inverse `(x, y) ↦ (x, yx)` -/
 @[to_additive
       "The map `(x, y) ↦ (x, y - x)` as a `measurable_equiv` with as inverse `(x, y) ↦ (x, y + x)`."]
@@ -79,6 +82,7 @@ protected def MeasurableEquiv.shearDivRight [MeasurableInv G] : G × G ≃ᵐ G
     measurable_inv_fun := measurable_fst.prod_mk <| measurable_snd.mul measurable_fst }
 #align measurable_equiv.shear_div_right MeasurableEquiv.shearDivRight
 #align measurable_equiv.shear_sub_right MeasurableEquiv.shearSubRight
+-/
 
 variable {G}
 
@@ -88,6 +92,7 @@ open Measure
 
 section LeftInvariant
 
+#print MeasureTheory.measurePreserving_prod_mul /-
 /-- The multiplicative shear mapping `(x, y) ↦ (x, xy)` preserves the measure `μ × ν`.
 This condition is part of the definition of a measurable group in [Halmos, §59].
 There, the map in this lemma is called `S`. -/
@@ -99,7 +104,9 @@ theorem measurePreserving_prod_mul [IsMulLeftInvariant ν] :
     Filter.eventually_of_forall <| map_mul_left_eq_self ν
 #align measure_theory.measure_preserving_prod_mul MeasureTheory.measurePreserving_prod_mul
 #align measure_theory.measure_preserving_prod_add MeasureTheory.measurePreserving_prod_add
+-/
 
+#print MeasureTheory.measurePreserving_prod_mul_swap /-
 /-- The map `(x, y) ↦ (y, yx)` sends the measure `μ × ν` to `ν × μ`.
 This is the map `SR` in [Halmos, §59].
 `S` is the map `(x, y) ↦ (x, xy)` and `R` is `prod.swap`. -/
@@ -110,8 +117,10 @@ theorem measurePreserving_prod_mul_swap [IsMulLeftInvariant μ] :
   (measurePreserving_prod_mul ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_mul_swap MeasureTheory.measurePreserving_prod_mul_swap
 #align measure_theory.measure_preserving_prod_add_swap MeasureTheory.measurePreserving_prod_add_swap
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print MeasureTheory.measurable_measure_mul_right /-
 @[to_additive]
 theorem measurable_measure_mul_right (hs : MeasurableSet s) :
     Measurable fun x => μ ((fun y => y * x) ⁻¹' s) :=
@@ -124,9 +133,11 @@ theorem measurable_measure_mul_right (hs : MeasurableSet s) :
   exact measurable_const.prod_mk measurable_mul (measurable_set.univ.prod hs)
 #align measure_theory.measurable_measure_mul_right MeasureTheory.measurable_measure_mul_right
 #align measure_theory.measurable_measure_add_right MeasureTheory.measurable_measure_add_right
+-/
 
 variable [MeasurableInv G]
 
+#print MeasureTheory.measurePreserving_prod_inv_mul /-
 /-- The map `(x, y) ↦ (x, x⁻¹y)` is measure-preserving.
 This is the function `S⁻¹` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)`. -/
@@ -137,9 +148,11 @@ theorem measurePreserving_prod_inv_mul [IsMulLeftInvariant ν] :
   (measurePreserving_prod_mul μ ν).symm <| MeasurableEquiv.shearMulRight G
 #align measure_theory.measure_preserving_prod_inv_mul MeasureTheory.measurePreserving_prod_inv_mul
 #align measure_theory.measure_preserving_prod_neg_add MeasureTheory.measurePreserving_prod_neg_add
+-/
 
 variable [IsMulLeftInvariant μ]
 
+#print MeasureTheory.measurePreserving_prod_inv_mul_swap /-
 /-- The map `(x, y) ↦ (y, y⁻¹x)` sends `μ × ν` to `ν × μ`.
 This is the function `S⁻¹R` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)` and `R` is `prod.swap`. -/
@@ -150,7 +163,9 @@ theorem measurePreserving_prod_inv_mul_swap :
   (measurePreserving_prod_inv_mul ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_inv_mul_swap MeasureTheory.measurePreserving_prod_inv_mul_swap
 #align measure_theory.measure_preserving_prod_neg_add_swap MeasureTheory.measurePreserving_prod_neg_add_swap
+-/
 
+#print MeasureTheory.measurePreserving_mul_prod_inv /-
 /-- The map `(x, y) ↦ (yx, x⁻¹)` is measure-preserving.
 This is the function `S⁻¹RSR` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)` and `R` is `prod.swap`. -/
@@ -164,9 +179,11 @@ theorem measurePreserving_mul_prod_inv [IsMulLeftInvariant ν] :
   simp_rw [Function.comp_apply, mul_inv_rev, inv_mul_cancel_right]
 #align measure_theory.measure_preserving_mul_prod_inv MeasureTheory.measurePreserving_mul_prod_inv
 #align measure_theory.measure_preserving_add_prod_neg MeasureTheory.measurePreserving_add_prod_neg
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print MeasureTheory.quasiMeasurePreserving_inv /-
 @[to_additive]
 theorem quasiMeasurePreserving_inv : QuasiMeasurePreserving (Inv.inv : G → G) μ μ :=
   by
@@ -182,7 +199,9 @@ theorem quasiMeasurePreserving_inv : QuasiMeasurePreserving (Inv.inv : G → G)
     inv_preimage, inv_inv, measure_mono_null (inter_subset_right _ _) hμs, lintegral_zero]
 #align measure_theory.quasi_measure_preserving_inv MeasureTheory.quasiMeasurePreserving_inv
 #align measure_theory.quasi_measure_preserving_neg MeasureTheory.quasiMeasurePreserving_neg
+-/
 
+#print MeasureTheory.measure_inv_null /-
 @[to_additive]
 theorem measure_inv_null : μ s⁻¹ = 0 ↔ μ s = 0 :=
   by
@@ -191,13 +210,17 @@ theorem measure_inv_null : μ s⁻¹ = 0 ↔ μ s = 0 :=
   exact (quasi_measure_preserving_inv μ).preimage_null hs
 #align measure_theory.measure_inv_null MeasureTheory.measure_inv_null
 #align measure_theory.measure_neg_null MeasureTheory.measure_neg_null
+-/
 
+#print MeasureTheory.inv_absolutelyContinuous /-
 @[to_additive]
 theorem inv_absolutelyContinuous : μ.inv ≪ μ :=
   (quasiMeasurePreserving_inv μ).AbsolutelyContinuous
 #align measure_theory.inv_absolutely_continuous MeasureTheory.inv_absolutelyContinuous
 #align measure_theory.neg_absolutely_continuous MeasureTheory.neg_absolutelyContinuous
+-/
 
+#print MeasureTheory.absolutelyContinuous_inv /-
 @[to_additive]
 theorem absolutelyContinuous_inv : μ ≪ μ.inv :=
   by
@@ -205,7 +228,9 @@ theorem absolutelyContinuous_inv : μ ≪ μ.inv :=
   simp_rw [inv_apply μ s, measure_inv_null, imp_self]
 #align measure_theory.absolutely_continuous_inv MeasureTheory.absolutelyContinuous_inv
 #align measure_theory.absolutely_continuous_neg MeasureTheory.absolutelyContinuous_neg
+-/
 
+#print MeasureTheory.lintegral_lintegral_mul_inv /-
 @[to_additive]
 theorem lintegral_lintegral_mul_inv [IsMulLeftInvariant ν] (f : G → G → ℝ≥0∞)
     (hf : AEMeasurable (uncurry f) (μ.Prod ν)) :
@@ -223,7 +248,9 @@ theorem lintegral_lintegral_mul_inv [IsMulLeftInvariant ν] (f : G → G → ℝ
       h.ae_measurable
 #align measure_theory.lintegral_lintegral_mul_inv MeasureTheory.lintegral_lintegral_mul_inv
 #align measure_theory.lintegral_lintegral_add_neg MeasureTheory.lintegral_lintegral_add_neg
+-/
 
+#print MeasureTheory.measure_mul_right_null /-
 @[to_additive]
 theorem measure_mul_right_null (y : G) : μ ((fun x => x * y) ⁻¹' s) = 0 ↔ μ s = 0 :=
   calc
@@ -232,13 +259,17 @@ theorem measure_mul_right_null (y : G) : μ ((fun x => x * y) ⁻¹' s) = 0 ↔
     _ ↔ μ s = 0 := by simp only [measure_inv_null μ, measure_preimage_mul]
 #align measure_theory.measure_mul_right_null MeasureTheory.measure_mul_right_null
 #align measure_theory.measure_add_right_null MeasureTheory.measure_add_right_null
+-/
 
+#print MeasureTheory.measure_mul_right_ne_zero /-
 @[to_additive]
 theorem measure_mul_right_ne_zero (h2s : μ s ≠ 0) (y : G) : μ ((fun x => x * y) ⁻¹' s) ≠ 0 :=
   (not_congr (measure_mul_right_null μ y)).mpr h2s
 #align measure_theory.measure_mul_right_ne_zero MeasureTheory.measure_mul_right_ne_zero
 #align measure_theory.measure_add_right_ne_zero MeasureTheory.measure_add_right_ne_zero
+-/
 
+#print MeasureTheory.absolutelyContinuous_map_mul_right /-
 @[to_additive]
 theorem absolutelyContinuous_map_mul_right (g : G) : μ ≪ map (· * g) μ :=
   by
@@ -246,7 +277,9 @@ theorem absolutelyContinuous_map_mul_right (g : G) : μ ≪ map (· * g) μ :=
   rw [map_apply (measurable_mul_const g) hs, measure_mul_right_null]; exact id
 #align measure_theory.absolutely_continuous_map_mul_right MeasureTheory.absolutelyContinuous_map_mul_right
 #align measure_theory.absolutely_continuous_map_add_right MeasureTheory.absolutelyContinuous_map_add_right
+-/
 
+#print MeasureTheory.absolutelyContinuous_map_div_left /-
 @[to_additive]
 theorem absolutelyContinuous_map_div_left (g : G) : μ ≪ map (fun h => g / h) μ :=
   by
@@ -256,7 +289,9 @@ theorem absolutelyContinuous_map_div_left (g : G) : μ ≪ map (fun h => g / h)
   exact (absolutely_continuous_inv μ).map (measurable_const_mul g)
 #align measure_theory.absolutely_continuous_map_div_left MeasureTheory.absolutelyContinuous_map_div_left
 #align measure_theory.absolutely_continuous_map_sub_left MeasureTheory.absolutelyContinuous_map_sub_left
+-/
 
+#print MeasureTheory.measure_mul_lintegral_eq /-
 /-- This is the computation performed in the proof of [Halmos, §60 Th. A]. -/
 @[to_additive "This is the computation performed in the proof of [Halmos, §60 Th. A]."]
 theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s) (f : G → ℝ≥0∞)
@@ -282,7 +317,9 @@ theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s)
     set_lintegral_one]
 #align measure_theory.measure_mul_lintegral_eq MeasureTheory.measure_mul_lintegral_eq
 #align measure_theory.measure_add_lintegral_eq MeasureTheory.measure_add_lintegral_eq
+-/
 
+#print MeasureTheory.absolutelyContinuous_of_isMulLeftInvariant /-
 /-- Any two nonzero left-invariant measures are absolutely continuous w.r.t. each other. -/
 @[to_additive
       " Any two nonzero left-invariant measures are absolutely continuous w.r.t. each\nother. "]
@@ -295,7 +332,9 @@ theorem absolutelyContinuous_of_isMulLeftInvariant [IsMulLeftInvariant ν] (hν
   exact h1
 #align measure_theory.absolutely_continuous_of_is_mul_left_invariant MeasureTheory.absolutelyContinuous_of_isMulLeftInvariant
 #align measure_theory.absolutely_continuous_of_is_add_left_invariant MeasureTheory.absolutelyContinuous_of_isAddLeftInvariant
+-/
 
+#print MeasureTheory.ae_measure_preimage_mul_right_lt_top /-
 @[to_additive]
 theorem ae_measure_preimage_mul_right_lt_top [IsMulLeftInvariant ν] (sm : MeasurableSet s)
     (hμs : μ s ≠ ∞) : ∀ᵐ x ∂μ, ν ((fun y => y * x) ⁻¹' s) < ∞ :=
@@ -313,7 +352,9 @@ theorem ae_measure_preimage_mul_right_lt_top [IsMulLeftInvariant ν] (sm : Measu
   exact ENNReal.mul_ne_top hμs h3A.ne
 #align measure_theory.ae_measure_preimage_mul_right_lt_top MeasureTheory.ae_measure_preimage_mul_right_lt_top
 #align measure_theory.ae_measure_preimage_add_right_lt_top MeasureTheory.ae_measure_preimage_add_right_lt_top
+-/
 
+#print MeasureTheory.ae_measure_preimage_mul_right_lt_top_of_ne_zero /-
 @[to_additive]
 theorem ae_measure_preimage_mul_right_lt_top_of_ne_zero [IsMulLeftInvariant ν]
     (sm : MeasurableSet s) (h2s : ν s ≠ 0) (h3s : ν s ≠ ∞) :
@@ -326,7 +367,9 @@ theorem ae_measure_preimage_mul_right_lt_top_of_ne_zero [IsMulLeftInvariant ν]
   rw [hν, measure.coe_zero, Pi.zero_apply]
 #align measure_theory.ae_measure_preimage_mul_right_lt_top_of_ne_zero MeasureTheory.ae_measure_preimage_mul_right_lt_top_of_ne_zero
 #align measure_theory.ae_measure_preimage_add_right_lt_top_of_ne_zero MeasureTheory.ae_measure_preimage_add_right_lt_top_of_ne_zero
+-/
 
+#print MeasureTheory.measure_lintegral_div_measure /-
 /-- A technical lemma relating two different measures. This is basically [Halmos, §60 Th. A].
   Note that if `f` is the characteristic function of a measurable set `t` this states that
   `μ t = c * μ s` for a constant `c` that does not depend on `μ`.
@@ -351,7 +394,9 @@ theorem measure_lintegral_div_measure [IsMulLeftInvariant ν] (sm : MeasurableSe
   simp_rw [ENNReal.mul_div_cancel' (measure_mul_right_ne_zero ν h2s _) hx.ne]
 #align measure_theory.measure_lintegral_div_measure MeasureTheory.measure_lintegral_div_measure
 #align measure_theory.measure_lintegral_sub_measure MeasureTheory.measure_lintegral_sub_measure
+-/
 
+#print MeasureTheory.measure_mul_measure_eq /-
 @[to_additive]
 theorem measure_mul_measure_eq [IsMulLeftInvariant ν] {s t : Set G} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (h2s : ν s ≠ 0) (h3s : ν s ≠ ∞) : μ s * ν t = ν s * μ t :=
@@ -366,7 +411,9 @@ theorem measure_mul_measure_eq [IsMulLeftInvariant ν] {s t : Set G} (hs : Measu
   rw [← h1, mul_left_comm, h2]
 #align measure_theory.measure_mul_measure_eq MeasureTheory.measure_mul_measure_eq
 #align measure_theory.measure_add_measure_eq MeasureTheory.measure_add_measure_eq
+-/
 
+#print MeasureTheory.measure_eq_div_smul /-
 /-- Left invariant Borel measures on a measurable group are unique (up to a scalar). -/
 @[to_additive
       " Left invariant Borel measures on an additive measurable group are unique\n  (up to a scalar). "]
@@ -377,11 +424,13 @@ theorem measure_eq_div_smul [IsMulLeftInvariant ν] (hs : MeasurableSet s) (h2s
     measure_mul_measure_eq μ ν hs ht h2s h3s, mul_div_assoc, ENNReal.mul_div_cancel' h2s h3s]
 #align measure_theory.measure_eq_div_smul MeasureTheory.measure_eq_div_smul
 #align measure_theory.measure_eq_sub_vadd MeasureTheory.measure_eq_sub_vadd
+-/
 
 end LeftInvariant
 
 section RightInvariant
 
+#print MeasureTheory.measurePreserving_prod_mul_right /-
 @[to_additive measure_preserving_prod_add_right]
 theorem measurePreserving_prod_mul_right [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.2 * z.1)) (μ.Prod ν) (μ.Prod ν) :=
@@ -389,7 +438,9 @@ theorem measurePreserving_prod_mul_right [IsMulRightInvariant ν] :
     Filter.eventually_of_forall <| map_mul_right_eq_self ν
 #align measure_theory.measure_preserving_prod_mul_right MeasureTheory.measurePreserving_prod_mul_right
 #align measure_theory.measure_preserving_prod_add_right MeasureTheory.measurePreserving_prod_add_right
+-/
 
+#print MeasureTheory.measurePreserving_prod_mul_swap_right /-
 /-- The map `(x, y) ↦ (y, xy)` sends the measure `μ × ν` to `ν × μ`. -/
 @[to_additive measure_preserving_prod_add_swap_right
       " The map `(x, y) ↦ (y, x + y)` sends the measure `μ × ν` to `ν × μ`. "]
@@ -398,7 +449,9 @@ theorem measurePreserving_prod_mul_swap_right [IsMulRightInvariant μ] :
   (measurePreserving_prod_mul_right ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_mul_swap_right MeasureTheory.measurePreserving_prod_mul_swap_right
 #align measure_theory.measure_preserving_prod_add_swap_right MeasureTheory.measurePreserving_prod_add_swap_right
+-/
 
+#print MeasureTheory.measurePreserving_mul_prod /-
 /-- The map `(x, y) ↦ (xy, y)` preserves the measure `μ × ν`. -/
 @[to_additive measure_preserving_add_prod
       " The map `(x, y) ↦ (x + y, y)` preserves the measure `μ × ν`. "]
@@ -407,9 +460,11 @@ theorem measurePreserving_mul_prod [IsMulRightInvariant μ] :
   measurePreserving_swap.comp <| by apply measure_preserving_prod_mul_swap_right μ ν
 #align measure_theory.measure_preserving_mul_prod MeasureTheory.measurePreserving_mul_prod
 #align measure_theory.measure_preserving_add_prod MeasureTheory.measurePreserving_add_prod
+-/
 
 variable [MeasurableInv G]
 
+#print MeasureTheory.measurePreserving_prod_div /-
 /-- The map `(x, y) ↦ (x, y / x)` is measure-preserving. -/
 @[to_additive measure_preserving_prod_sub "The map `(x, y) ↦ (x, y - x)` is measure-preserving."]
 theorem measurePreserving_prod_div [IsMulRightInvariant ν] :
@@ -417,7 +472,9 @@ theorem measurePreserving_prod_div [IsMulRightInvariant ν] :
   (measurePreserving_prod_mul_right μ ν).symm (MeasurableEquiv.shearDivRight G).symm
 #align measure_theory.measure_preserving_prod_div MeasureTheory.measurePreserving_prod_div
 #align measure_theory.measure_preserving_prod_sub MeasureTheory.measurePreserving_prod_sub
+-/
 
+#print MeasureTheory.measurePreserving_prod_div_swap /-
 /-- The map `(x, y) ↦ (y, x / y)` sends `μ × ν` to `ν × μ`. -/
 @[to_additive measure_preserving_prod_sub_swap
       "The map `(x, y) ↦ (y, x - y)` sends `μ × ν` to `ν × μ`."]
@@ -426,7 +483,9 @@ theorem measurePreserving_prod_div_swap [IsMulRightInvariant μ] :
   (measurePreserving_prod_div ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_div_swap MeasureTheory.measurePreserving_prod_div_swap
 #align measure_theory.measure_preserving_prod_sub_swap MeasureTheory.measurePreserving_prod_sub_swap
+-/
 
+#print MeasureTheory.measurePreserving_div_prod /-
 /-- The map `(x, y) ↦ (x / y, y)` preserves the measure `μ × ν`. -/
 @[to_additive measure_preserving_sub_prod
       " The map `(x, y) ↦ (x - y, y)` preserves the measure `μ × ν`. "]
@@ -435,7 +494,9 @@ theorem measurePreserving_div_prod [IsMulRightInvariant μ] :
   measurePreserving_swap.comp <| by apply measure_preserving_prod_div_swap μ ν
 #align measure_theory.measure_preserving_div_prod MeasureTheory.measurePreserving_div_prod
 #align measure_theory.measure_preserving_sub_prod MeasureTheory.measurePreserving_sub_prod
+-/
 
+#print MeasureTheory.measurePreserving_mul_prod_inv_right /-
 /-- The map `(x, y) ↦ (xy, x⁻¹)` is measure-preserving. -/
 @[to_additive measure_preserving_add_prod_neg_right
       "The map `(x, y) ↦ (x + y, - x)` is measure-preserving."]
@@ -447,6 +508,7 @@ theorem measurePreserving_mul_prod_inv_right [IsMulRightInvariant μ] [IsMulRigh
   simp_rw [Function.comp_apply, div_mul_eq_div_div_swap, div_self', one_div]
 #align measure_theory.measure_preserving_mul_prod_inv_right MeasureTheory.measurePreserving_mul_prod_inv_right
 #align measure_theory.measure_preserving_add_prod_neg_right MeasureTheory.measurePreserving_add_prod_neg_right
+-/
 
 end RightInvariant
 
@@ -454,6 +516,7 @@ section QuasiMeasurePreserving
 
 variable [MeasurableInv G]
 
+#print MeasureTheory.quasiMeasurePreserving_inv_of_right_invariant /-
 @[to_additive]
 theorem quasiMeasurePreserving_inv_of_right_invariant [IsMulRightInvariant μ] :
     QuasiMeasurePreserving (Inv.inv : G → G) μ μ :=
@@ -464,7 +527,9 @@ theorem quasiMeasurePreserving_inv_of_right_invariant [IsMulRightInvariant μ] :
       (absolutely_continuous_inv μ.inv)
 #align measure_theory.quasi_measure_preserving_inv_of_right_invariant MeasureTheory.quasiMeasurePreserving_inv_of_right_invariant
 #align measure_theory.quasi_measure_preserving_neg_of_right_invariant MeasureTheory.quasiMeasurePreserving_neg_of_right_invariant
+-/
 
+#print MeasureTheory.quasiMeasurePreserving_div_left /-
 @[to_additive]
 theorem quasiMeasurePreserving_div_left [IsMulLeftInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g / h) μ μ :=
@@ -474,7 +539,9 @@ theorem quasiMeasurePreserving_div_left [IsMulLeftInvariant μ] (g : G) :
     (measure_preserving_mul_left μ g).QuasiMeasurePreserving.comp (quasi_measure_preserving_inv μ)
 #align measure_theory.quasi_measure_preserving_div_left MeasureTheory.quasiMeasurePreserving_div_left
 #align measure_theory.quasi_measure_preserving_sub_left MeasureTheory.quasiMeasurePreserving_sub_left
+-/
 
+#print MeasureTheory.quasiMeasurePreserving_div_left_of_right_invariant /-
 @[to_additive]
 theorem quasiMeasurePreserving_div_left_of_right_invariant [IsMulRightInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g / h) μ μ :=
@@ -485,7 +552,9 @@ theorem quasiMeasurePreserving_div_left_of_right_invariant [IsMulRightInvariant
       (absolutely_continuous_inv μ.inv)
 #align measure_theory.quasi_measure_preserving_div_left_of_right_invariant MeasureTheory.quasiMeasurePreserving_div_left_of_right_invariant
 #align measure_theory.quasi_measure_preserving_sub_left_of_right_invariant MeasureTheory.quasiMeasurePreserving_sub_left_of_right_invariant
+-/
 
+#print MeasureTheory.quasiMeasurePreserving_div_of_right_invariant /-
 @[to_additive]
 theorem quasiMeasurePreserving_div_of_right_invariant [IsMulRightInvariant μ] :
     QuasiMeasurePreserving (fun p : G × G => p.1 / p.2) (μ.Prod ν) μ :=
@@ -494,7 +563,9 @@ theorem quasiMeasurePreserving_div_of_right_invariant [IsMulRightInvariant μ] :
   exact (measure_preserving_div_right μ y).QuasiMeasurePreserving
 #align measure_theory.quasi_measure_preserving_div_of_right_invariant MeasureTheory.quasiMeasurePreserving_div_of_right_invariant
 #align measure_theory.quasi_measure_preserving_sub_of_right_invariant MeasureTheory.quasiMeasurePreserving_sub_of_right_invariant
+-/
 
+#print MeasureTheory.quasiMeasurePreserving_div /-
 @[to_additive]
 theorem quasiMeasurePreserving_div [IsMulLeftInvariant μ] :
     QuasiMeasurePreserving (fun p : G × G => p.1 / p.2) (μ.Prod ν) μ :=
@@ -502,7 +573,9 @@ theorem quasiMeasurePreserving_div [IsMulLeftInvariant μ] :
     ((absolutelyContinuous_inv μ).Prod AbsolutelyContinuous.rfl) (inv_absolutelyContinuous μ)
 #align measure_theory.quasi_measure_preserving_div MeasureTheory.quasiMeasurePreserving_div
 #align measure_theory.quasi_measure_preserving_sub MeasureTheory.quasiMeasurePreserving_sub
+-/
 
+#print MeasureTheory.quasiMeasurePreserving_mul_right /-
 /-- A *left*-invariant measure is quasi-preserved by *right*-multiplication.
 This should not be confused with `(measure_preserving_mul_right μ g).quasi_measure_preserving`. -/
 @[to_additive
@@ -514,7 +587,9 @@ theorem quasiMeasurePreserving_mul_right [IsMulLeftInvariant μ] (g : G) :
   rw [map_apply (measurable_mul_const g) hs, measure_mul_right_null]; exact id
 #align measure_theory.quasi_measure_preserving_mul_right MeasureTheory.quasiMeasurePreserving_mul_right
 #align measure_theory.quasi_measure_preserving_add_right MeasureTheory.quasiMeasurePreserving_add_right
+-/
 
+#print MeasureTheory.quasiMeasurePreserving_mul_left /-
 /-- A *right*-invariant measure is quasi-preserved by *left*-multiplication.
 This should not be confused with `(measure_preserving_mul_left μ g).quasi_measure_preserving`. -/
 @[to_additive
@@ -533,6 +608,7 @@ theorem quasiMeasurePreserving_mul_left [IsMulRightInvariant μ] (g : G) :
   exact this
 #align measure_theory.quasi_measure_preserving_mul_left MeasureTheory.quasiMeasurePreserving_mul_left
 #align measure_theory.quasi_measure_preserving_add_left MeasureTheory.quasiMeasurePreserving_add_left
+-/
 
 end QuasiMeasurePreserving
 

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

@@ -209,7 +209,7 @@ theorem absolutelyContinuous_inv : μ ≪ μ.inv :=
 @[to_additive]
 theorem lintegral_lintegral_mul_inv [IsMulLeftInvariant ν] (f : G → G → ℝ≥0∞)
     (hf : AEMeasurable (uncurry f) (μ.Prod ν)) :
-    (∫⁻ x, ∫⁻ y, f (y * x) x⁻¹ ∂ν ∂μ) = ∫⁻ x, ∫⁻ y, f x y ∂ν ∂μ :=
+    ∫⁻ x, ∫⁻ y, f (y * x) x⁻¹ ∂ν ∂μ = ∫⁻ x, ∫⁻ y, f x y ∂ν ∂μ :=
   by
   have h : Measurable fun z : G × G => (z.2 * z.1, z.1⁻¹) :=
     (measurable_snd.mul measurable_fst).prod_mk measurable_fst.inv
@@ -260,7 +260,7 @@ theorem absolutelyContinuous_map_div_left (g : G) : μ ≪ map (fun h => g / h)
 /-- This is the computation performed in the proof of [Halmos, §60 Th. A]. -/
 @[to_additive "This is the computation performed in the proof of [Halmos, §60 Th. A]."]
 theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s) (f : G → ℝ≥0∞)
-    (hf : Measurable f) : (μ s * ∫⁻ y, f y ∂ν) = ∫⁻ x, ν ((fun z => z * x) ⁻¹' s) * f x⁻¹ ∂μ :=
+    (hf : Measurable f) : μ s * ∫⁻ y, f y ∂ν = ∫⁻ x, ν ((fun z => z * x) ⁻¹' s) * f x⁻¹ ∂μ :=
   by
   rw [← set_lintegral_one, ← lintegral_indicator _ sm, ←
     lintegral_lintegral_mul (measurable_const.indicator sm).AEMeasurable hf.ae_measurable, ←
@@ -340,7 +340,7 @@ theorem ae_measure_preimage_mul_right_lt_top_of_ne_zero [IsMulLeftInvariant ν]
       "A technical lemma relating two different measures. This is basically\n[Halmos, §60 Th. A]. Note that if `f` is the characteristic function of a measurable set `t` this\nstates that `μ t = c * μ s` for a constant `c` that does not depend on `μ`.\n\nNote: There is a gap in the last step of the proof in [Halmos]. In the last line, the equality\n`g(-x) + ν(s - x) = f(x)` holds if we can prove that `0 < ν(s - x) < ∞`. The first inequality\nfollows from §59, Th. D, but the second inequality is not justified. We prove this inequality for\nalmost all `x` in `measure_theory.ae_measure_preimage_add_right_lt_top_of_ne_zero`."]
 theorem measure_lintegral_div_measure [IsMulLeftInvariant ν] (sm : MeasurableSet s) (h2s : ν s ≠ 0)
     (h3s : ν s ≠ ∞) (f : G → ℝ≥0∞) (hf : Measurable f) :
-    (μ s * ∫⁻ y, f y⁻¹ / ν ((fun x => x * y⁻¹) ⁻¹' s) ∂ν) = ∫⁻ x, f x ∂μ :=
+    μ s * ∫⁻ y, f y⁻¹ / ν ((fun x => x * y⁻¹) ⁻¹' s) ∂ν = ∫⁻ x, f x ∂μ :=
   by
   set g := fun y => f y⁻¹ / ν ((fun x => x * y⁻¹) ⁻¹' s)
   have hg : Measurable g :=

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

@@ -230,7 +230,6 @@ theorem measure_mul_right_null (y : G) : μ ((fun x => x * y) ⁻¹' s) = 0 ↔
     μ ((fun x => x * y) ⁻¹' s) = 0 ↔ μ ((fun x => y⁻¹ * x) ⁻¹' s⁻¹)⁻¹ = 0 := by
       simp_rw [← inv_preimage, preimage_preimage, mul_inv_rev, inv_inv]
     _ ↔ μ s = 0 := by simp only [measure_inv_null μ, measure_preimage_mul]
-    
 #align measure_theory.measure_mul_right_null MeasureTheory.measure_mul_right_null
 #align measure_theory.measure_add_right_null MeasureTheory.measure_add_right_null
 

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

@@ -93,7 +93,7 @@ This condition is part of the definition of a measurable group in [Halmos, §59]
 There, the map in this lemma is called `S`. -/
 @[to_additive measure_preserving_prod_add
       " The shear mapping `(x, y) ↦ (x, x + y)` preserves the measure `μ × ν`. "]
-theorem measurePreserving_prod_mul [MulLeftInvariant ν] :
+theorem measurePreserving_prod_mul [IsMulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.1 * z.2)) (μ.Prod ν) (μ.Prod ν) :=
   (MeasurePreserving.id μ).skew_product measurable_mul <|
     Filter.eventually_of_forall <| map_mul_left_eq_self ν
@@ -105,7 +105,7 @@ This is the map `SR` in [Halmos, §59].
 `S` is the map `(x, y) ↦ (x, xy)` and `R` is `prod.swap`. -/
 @[to_additive measure_preserving_prod_add_swap
       " The map `(x, y) ↦ (y, y + x)` sends the measure `μ × ν` to `ν × μ`. "]
-theorem measurePreserving_prod_mul_swap [MulLeftInvariant μ] :
+theorem measurePreserving_prod_mul_swap [IsMulLeftInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.2 * z.1)) (μ.Prod ν) (ν.Prod μ) :=
   (measurePreserving_prod_mul ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_mul_swap MeasureTheory.measurePreserving_prod_mul_swap
@@ -132,13 +132,13 @@ This is the function `S⁻¹` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)`. -/
 @[to_additive measure_preserving_prod_neg_add
       "The map `(x, y) ↦ (x, - x + y)` is measure-preserving."]
-theorem measurePreserving_prod_inv_mul [MulLeftInvariant ν] :
+theorem measurePreserving_prod_inv_mul [IsMulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.1⁻¹ * z.2)) (μ.Prod ν) (μ.Prod ν) :=
   (measurePreserving_prod_mul μ ν).symm <| MeasurableEquiv.shearMulRight G
 #align measure_theory.measure_preserving_prod_inv_mul MeasureTheory.measurePreserving_prod_inv_mul
 #align measure_theory.measure_preserving_prod_neg_add MeasureTheory.measurePreserving_prod_neg_add
 
-variable [MulLeftInvariant μ]
+variable [IsMulLeftInvariant μ]
 
 /-- The map `(x, y) ↦ (y, y⁻¹x)` sends `μ × ν` to `ν × μ`.
 This is the function `S⁻¹R` in [Halmos, §59],
@@ -156,10 +156,10 @@ This is the function `S⁻¹RSR` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)` and `R` is `prod.swap`. -/
 @[to_additive measure_preserving_add_prod_neg
       "The map `(x, y) ↦ (y + x, - x)` is measure-preserving."]
-theorem measurePreserving_mul_prod_inv [MulLeftInvariant ν] :
+theorem measurePreserving_mul_prod_inv [IsMulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.2 * z.1, z.1⁻¹)) (μ.Prod ν) (μ.Prod ν) :=
   by
-  convert(measure_preserving_prod_inv_mul_swap ν μ).comp (measure_preserving_prod_mul_swap μ ν)
+  convert (measure_preserving_prod_inv_mul_swap ν μ).comp (measure_preserving_prod_mul_swap μ ν)
   ext1 ⟨x, y⟩
   simp_rw [Function.comp_apply, mul_inv_rev, inv_mul_cancel_right]
 #align measure_theory.measure_preserving_mul_prod_inv MeasureTheory.measurePreserving_mul_prod_inv
@@ -207,7 +207,7 @@ theorem absolutelyContinuous_inv : μ ≪ μ.inv :=
 #align measure_theory.absolutely_continuous_neg MeasureTheory.absolutelyContinuous_neg
 
 @[to_additive]
-theorem lintegral_lintegral_mul_inv [MulLeftInvariant ν] (f : G → G → ℝ≥0∞)
+theorem lintegral_lintegral_mul_inv [IsMulLeftInvariant ν] (f : G → G → ℝ≥0∞)
     (hf : AEMeasurable (uncurry f) (μ.Prod ν)) :
     (∫⁻ x, ∫⁻ y, f (y * x) x⁻¹ ∂ν ∂μ) = ∫⁻ x, ∫⁻ y, f x y ∂ν ∂μ :=
   by
@@ -260,7 +260,7 @@ theorem absolutelyContinuous_map_div_left (g : G) : μ ≪ map (fun h => g / h)
 
 /-- This is the computation performed in the proof of [Halmos, §60 Th. A]. -/
 @[to_additive "This is the computation performed in the proof of [Halmos, §60 Th. A]."]
-theorem measure_mul_lintegral_eq [MulLeftInvariant ν] (sm : MeasurableSet s) (f : G → ℝ≥0∞)
+theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s) (f : G → ℝ≥0∞)
     (hf : Measurable f) : (μ s * ∫⁻ y, f y ∂ν) = ∫⁻ x, ν ((fun z => z * x) ⁻¹' s) * f x⁻¹ ∂μ :=
   by
   rw [← set_lintegral_one, ← lintegral_indicator _ sm, ←
@@ -287,18 +287,18 @@ theorem measure_mul_lintegral_eq [MulLeftInvariant ν] (sm : MeasurableSet s) (f
 /-- Any two nonzero left-invariant measures are absolutely continuous w.r.t. each other. -/
 @[to_additive
       " Any two nonzero left-invariant measures are absolutely continuous w.r.t. each\nother. "]
-theorem absolutelyContinuous_of_mulLeftInvariant [MulLeftInvariant ν] (hν : ν ≠ 0) : μ ≪ ν :=
+theorem absolutelyContinuous_of_isMulLeftInvariant [IsMulLeftInvariant ν] (hν : ν ≠ 0) : μ ≪ ν :=
   by
   refine' absolutely_continuous.mk fun s sm hνs => _
   have h1 := measure_mul_lintegral_eq μ ν sm 1 measurable_one
   simp_rw [Pi.one_apply, lintegral_one, mul_one, (measure_mul_right_null ν _).mpr hνs,
     lintegral_zero, mul_eq_zero, measure_univ_eq_zero.not.mpr hν, or_false_iff] at h1 
   exact h1
-#align measure_theory.absolutely_continuous_of_is_mul_left_invariant MeasureTheory.absolutelyContinuous_of_mulLeftInvariant
-#align measure_theory.absolutely_continuous_of_is_add_left_invariant MeasureTheory.absolutelyContinuous_of_addLeftInvariant
+#align measure_theory.absolutely_continuous_of_is_mul_left_invariant MeasureTheory.absolutelyContinuous_of_isMulLeftInvariant
+#align measure_theory.absolutely_continuous_of_is_add_left_invariant MeasureTheory.absolutelyContinuous_of_isAddLeftInvariant
 
 @[to_additive]
-theorem ae_measure_preimage_mul_right_lt_top [MulLeftInvariant ν] (sm : MeasurableSet s)
+theorem ae_measure_preimage_mul_right_lt_top [IsMulLeftInvariant ν] (sm : MeasurableSet s)
     (hμs : μ s ≠ ∞) : ∀ᵐ x ∂μ, ν ((fun y => y * x) ⁻¹' s) < ∞ :=
   by
   refine' ae_of_forall_measure_lt_top_ae_restrict' ν.inv _ _
@@ -316,8 +316,9 @@ theorem ae_measure_preimage_mul_right_lt_top [MulLeftInvariant ν] (sm : Measura
 #align measure_theory.ae_measure_preimage_add_right_lt_top MeasureTheory.ae_measure_preimage_add_right_lt_top
 
 @[to_additive]
-theorem ae_measure_preimage_mul_right_lt_top_of_ne_zero [MulLeftInvariant ν] (sm : MeasurableSet s)
-    (h2s : ν s ≠ 0) (h3s : ν s ≠ ∞) : ∀ᵐ x ∂μ, ν ((fun y => y * x) ⁻¹' s) < ∞ :=
+theorem ae_measure_preimage_mul_right_lt_top_of_ne_zero [IsMulLeftInvariant ν]
+    (sm : MeasurableSet s) (h2s : ν s ≠ 0) (h3s : ν s ≠ ∞) :
+    ∀ᵐ x ∂μ, ν ((fun y => y * x) ⁻¹' s) < ∞ :=
   by
   refine' (ae_measure_preimage_mul_right_lt_top ν ν sm h3s).filter_mono _
   refine' (absolutely_continuous_of_is_mul_left_invariant μ ν _).ae_le
@@ -338,7 +339,7 @@ theorem ae_measure_preimage_mul_right_lt_top_of_ne_zero [MulLeftInvariant ν] (s
   `measure_theory.ae_measure_preimage_mul_right_lt_top_of_ne_zero`. -/
 @[to_additive
       "A technical lemma relating two different measures. This is basically\n[Halmos, §60 Th. A]. Note that if `f` is the characteristic function of a measurable set `t` this\nstates that `μ t = c * μ s` for a constant `c` that does not depend on `μ`.\n\nNote: There is a gap in the last step of the proof in [Halmos]. In the last line, the equality\n`g(-x) + ν(s - x) = f(x)` holds if we can prove that `0 < ν(s - x) < ∞`. The first inequality\nfollows from §59, Th. D, but the second inequality is not justified. We prove this inequality for\nalmost all `x` in `measure_theory.ae_measure_preimage_add_right_lt_top_of_ne_zero`."]
-theorem measure_lintegral_div_measure [MulLeftInvariant ν] (sm : MeasurableSet s) (h2s : ν s ≠ 0)
+theorem measure_lintegral_div_measure [IsMulLeftInvariant ν] (sm : MeasurableSet s) (h2s : ν s ≠ 0)
     (h3s : ν s ≠ ∞) (f : G → ℝ≥0∞) (hf : Measurable f) :
     (μ s * ∫⁻ y, f y⁻¹ / ν ((fun x => x * y⁻¹) ⁻¹' s) ∂ν) = ∫⁻ x, f x ∂μ :=
   by
@@ -353,7 +354,7 @@ theorem measure_lintegral_div_measure [MulLeftInvariant ν] (sm : MeasurableSet
 #align measure_theory.measure_lintegral_sub_measure MeasureTheory.measure_lintegral_sub_measure
 
 @[to_additive]
-theorem measure_mul_measure_eq [MulLeftInvariant ν] {s t : Set G} (hs : MeasurableSet s)
+theorem measure_mul_measure_eq [IsMulLeftInvariant ν] {s t : Set G} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (h2s : ν s ≠ 0) (h3s : ν s ≠ ∞) : μ s * ν t = ν s * μ t :=
   by
   have h1 :=
@@ -370,7 +371,7 @@ theorem measure_mul_measure_eq [MulLeftInvariant ν] {s t : Set G} (hs : Measura
 /-- Left invariant Borel measures on a measurable group are unique (up to a scalar). -/
 @[to_additive
       " Left invariant Borel measures on an additive measurable group are unique\n  (up to a scalar). "]
-theorem measure_eq_div_smul [MulLeftInvariant ν] (hs : MeasurableSet s) (h2s : ν s ≠ 0)
+theorem measure_eq_div_smul [IsMulLeftInvariant ν] (hs : MeasurableSet s) (h2s : ν s ≠ 0)
     (h3s : ν s ≠ ∞) : μ = (μ s / ν s) • ν := by
   ext1 t ht
   rw [smul_apply, smul_eq_mul, mul_comm, ← mul_div_assoc, mul_comm,
@@ -383,7 +384,7 @@ end LeftInvariant
 section RightInvariant
 
 @[to_additive measure_preserving_prod_add_right]
-theorem measurePreserving_prod_mul_right [MulRightInvariant ν] :
+theorem measurePreserving_prod_mul_right [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.2 * z.1)) (μ.Prod ν) (μ.Prod ν) :=
   (MeasurePreserving.id μ).skew_product (measurable_snd.mul measurable_fst) <|
     Filter.eventually_of_forall <| map_mul_right_eq_self ν
@@ -393,7 +394,7 @@ theorem measurePreserving_prod_mul_right [MulRightInvariant ν] :
 /-- The map `(x, y) ↦ (y, xy)` sends the measure `μ × ν` to `ν × μ`. -/
 @[to_additive measure_preserving_prod_add_swap_right
       " The map `(x, y) ↦ (y, x + y)` sends the measure `μ × ν` to `ν × μ`. "]
-theorem measurePreserving_prod_mul_swap_right [MulRightInvariant μ] :
+theorem measurePreserving_prod_mul_swap_right [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.1 * z.2)) (μ.Prod ν) (ν.Prod μ) :=
   (measurePreserving_prod_mul_right ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_mul_swap_right MeasureTheory.measurePreserving_prod_mul_swap_right
@@ -402,7 +403,7 @@ theorem measurePreserving_prod_mul_swap_right [MulRightInvariant μ] :
 /-- The map `(x, y) ↦ (xy, y)` preserves the measure `μ × ν`. -/
 @[to_additive measure_preserving_add_prod
       " The map `(x, y) ↦ (x + y, y)` preserves the measure `μ × ν`. "]
-theorem measurePreserving_mul_prod [MulRightInvariant μ] :
+theorem measurePreserving_mul_prod [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.1 * z.2, z.2)) (μ.Prod ν) (μ.Prod ν) :=
   measurePreserving_swap.comp <| by apply measure_preserving_prod_mul_swap_right μ ν
 #align measure_theory.measure_preserving_mul_prod MeasureTheory.measurePreserving_mul_prod
@@ -412,7 +413,7 @@ variable [MeasurableInv G]
 
 /-- The map `(x, y) ↦ (x, y / x)` is measure-preserving. -/
 @[to_additive measure_preserving_prod_sub "The map `(x, y) ↦ (x, y - x)` is measure-preserving."]
-theorem measurePreserving_prod_div [MulRightInvariant ν] :
+theorem measurePreserving_prod_div [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.2 / z.1)) (μ.Prod ν) (μ.Prod ν) :=
   (measurePreserving_prod_mul_right μ ν).symm (MeasurableEquiv.shearDivRight G).symm
 #align measure_theory.measure_preserving_prod_div MeasureTheory.measurePreserving_prod_div
@@ -421,7 +422,7 @@ theorem measurePreserving_prod_div [MulRightInvariant ν] :
 /-- The map `(x, y) ↦ (y, x / y)` sends `μ × ν` to `ν × μ`. -/
 @[to_additive measure_preserving_prod_sub_swap
       "The map `(x, y) ↦ (y, x - y)` sends `μ × ν` to `ν × μ`."]
-theorem measurePreserving_prod_div_swap [MulRightInvariant μ] :
+theorem measurePreserving_prod_div_swap [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.1 / z.2)) (μ.Prod ν) (ν.Prod μ) :=
   (measurePreserving_prod_div ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_div_swap MeasureTheory.measurePreserving_prod_div_swap
@@ -430,7 +431,7 @@ theorem measurePreserving_prod_div_swap [MulRightInvariant μ] :
 /-- The map `(x, y) ↦ (x / y, y)` preserves the measure `μ × ν`. -/
 @[to_additive measure_preserving_sub_prod
       " The map `(x, y) ↦ (x - y, y)` preserves the measure `μ × ν`. "]
-theorem measurePreserving_div_prod [MulRightInvariant μ] :
+theorem measurePreserving_div_prod [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.1 / z.2, z.2)) (μ.Prod ν) (μ.Prod ν) :=
   measurePreserving_swap.comp <| by apply measure_preserving_prod_div_swap μ ν
 #align measure_theory.measure_preserving_div_prod MeasureTheory.measurePreserving_div_prod
@@ -439,10 +440,10 @@ theorem measurePreserving_div_prod [MulRightInvariant μ] :
 /-- The map `(x, y) ↦ (xy, x⁻¹)` is measure-preserving. -/
 @[to_additive measure_preserving_add_prod_neg_right
       "The map `(x, y) ↦ (x + y, - x)` is measure-preserving."]
-theorem measurePreserving_mul_prod_inv_right [MulRightInvariant μ] [MulRightInvariant ν] :
+theorem measurePreserving_mul_prod_inv_right [IsMulRightInvariant μ] [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1 * z.2, z.1⁻¹)) (μ.Prod ν) (μ.Prod ν) :=
   by
-  convert(measure_preserving_prod_div_swap ν μ).comp (measure_preserving_prod_mul_swap_right μ ν)
+  convert (measure_preserving_prod_div_swap ν μ).comp (measure_preserving_prod_mul_swap_right μ ν)
   ext1 ⟨x, y⟩
   simp_rw [Function.comp_apply, div_mul_eq_div_div_swap, div_self', one_div]
 #align measure_theory.measure_preserving_mul_prod_inv_right MeasureTheory.measurePreserving_mul_prod_inv_right
@@ -455,7 +456,7 @@ section QuasiMeasurePreserving
 variable [MeasurableInv G]
 
 @[to_additive]
-theorem quasiMeasurePreserving_inv_of_right_invariant [MulRightInvariant μ] :
+theorem quasiMeasurePreserving_inv_of_right_invariant [IsMulRightInvariant μ] :
     QuasiMeasurePreserving (Inv.inv : G → G) μ μ :=
   by
   rw [← μ.inv_inv]
@@ -466,7 +467,7 @@ theorem quasiMeasurePreserving_inv_of_right_invariant [MulRightInvariant μ] :
 #align measure_theory.quasi_measure_preserving_neg_of_right_invariant MeasureTheory.quasiMeasurePreserving_neg_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreserving_div_left [MulLeftInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_div_left [IsMulLeftInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g / h) μ μ :=
   by
   simp_rw [div_eq_mul_inv]
@@ -476,7 +477,7 @@ theorem quasiMeasurePreserving_div_left [MulLeftInvariant μ] (g : G) :
 #align measure_theory.quasi_measure_preserving_sub_left MeasureTheory.quasiMeasurePreserving_sub_left
 
 @[to_additive]
-theorem quasiMeasurePreserving_div_left_of_right_invariant [MulRightInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_div_left_of_right_invariant [IsMulRightInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g / h) μ μ :=
   by
   rw [← μ.inv_inv]
@@ -487,7 +488,7 @@ theorem quasiMeasurePreserving_div_left_of_right_invariant [MulRightInvariant μ
 #align measure_theory.quasi_measure_preserving_sub_left_of_right_invariant MeasureTheory.quasiMeasurePreserving_sub_left_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreserving_div_of_right_invariant [MulRightInvariant μ] :
+theorem quasiMeasurePreserving_div_of_right_invariant [IsMulRightInvariant μ] :
     QuasiMeasurePreserving (fun p : G × G => p.1 / p.2) (μ.Prod ν) μ :=
   by
   refine' quasi_measure_preserving.prod_of_left measurable_div (eventually_of_forall fun y => _)
@@ -496,7 +497,7 @@ theorem quasiMeasurePreserving_div_of_right_invariant [MulRightInvariant μ] :
 #align measure_theory.quasi_measure_preserving_sub_of_right_invariant MeasureTheory.quasiMeasurePreserving_sub_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreserving_div [MulLeftInvariant μ] :
+theorem quasiMeasurePreserving_div [IsMulLeftInvariant μ] :
     QuasiMeasurePreserving (fun p : G × G => p.1 / p.2) (μ.Prod ν) μ :=
   (quasiMeasurePreserving_div_of_right_invariant μ.inv ν).mono
     ((absolutelyContinuous_inv μ).Prod AbsolutelyContinuous.rfl) (inv_absolutelyContinuous μ)
@@ -507,7 +508,7 @@ theorem quasiMeasurePreserving_div [MulLeftInvariant μ] :
 This should not be confused with `(measure_preserving_mul_right μ g).quasi_measure_preserving`. -/
 @[to_additive
       "A *left*-invariant measure is quasi-preserved by *right*-addition.\nThis should not be confused with `(measure_preserving_add_right μ g).quasi_measure_preserving`. "]
-theorem quasiMeasurePreserving_mul_right [MulLeftInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_mul_right [IsMulLeftInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => h * g) μ μ :=
   by
   refine' ⟨measurable_mul_const g, absolutely_continuous.mk fun s hs => _⟩
@@ -519,7 +520,7 @@ theorem quasiMeasurePreserving_mul_right [MulLeftInvariant μ] (g : G) :
 This should not be confused with `(measure_preserving_mul_left μ g).quasi_measure_preserving`. -/
 @[to_additive
       "A *right*-invariant measure is quasi-preserved by *left*-addition.\nThis should not be confused with `(measure_preserving_add_left μ g).quasi_measure_preserving`. "]
-theorem quasiMeasurePreserving_mul_left [MulRightInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_mul_left [IsMulRightInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g * h) μ μ :=
   by
   have :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/34ebaffc1d1e8e783fc05438ec2e70af87275ac9

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
 
 ! This file was ported from Lean 3 source module measure_theory.group.prod
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
+! leanprover-community/mathlib commit 599fffe78f0e11eb6a034e834ec51882167b9688
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.MeasureTheory.Group.Measure
 
 /-!
 # Measure theory in the product of groups
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 In this file we show properties about measure theory in products of measurable groups
 and properties of iterated integrals in measurable groups.
 

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

@@ -289,7 +289,7 @@ theorem absolutelyContinuous_of_mulLeftInvariant [MulLeftInvariant ν] (hν : ν
   refine' absolutely_continuous.mk fun s sm hνs => _
   have h1 := measure_mul_lintegral_eq μ ν sm 1 measurable_one
   simp_rw [Pi.one_apply, lintegral_one, mul_one, (measure_mul_right_null ν _).mpr hνs,
-    lintegral_zero, mul_eq_zero, measure_univ_eq_zero.not.mpr hν, or_false_iff] at h1
+    lintegral_zero, mul_eq_zero, measure_univ_eq_zero.not.mpr hν, or_false_iff] at h1 
   exact h1
 #align measure_theory.absolutely_continuous_of_is_mul_left_invariant MeasureTheory.absolutelyContinuous_of_mulLeftInvariant
 #align measure_theory.absolutely_continuous_of_is_add_left_invariant MeasureTheory.absolutelyContinuous_of_addLeftInvariant
@@ -300,13 +300,13 @@ theorem ae_measure_preimage_mul_right_lt_top [MulLeftInvariant ν] (sm : Measura
   by
   refine' ae_of_forall_measure_lt_top_ae_restrict' ν.inv _ _
   intro A hA h2A h3A
-  simp only [ν.inv_apply] at h3A
+  simp only [ν.inv_apply] at h3A 
   apply ae_lt_top (measurable_measure_mul_right ν sm)
   have h1 := measure_mul_lintegral_eq μ ν sm (A⁻¹.indicator 1) (measurable_one.indicator hA.inv)
-  rw [lintegral_indicator _ hA.inv] at h1
+  rw [lintegral_indicator _ hA.inv] at h1 
   simp_rw [Pi.one_apply, set_lintegral_one, ← image_inv, indicator_image inv_injective, image_inv, ←
     indicator_mul_right _ fun x => ν ((fun y => y * x) ⁻¹' s), Function.comp, Pi.one_apply,
-    mul_one] at h1
+    mul_one] at h1 
   rw [← lintegral_indicator _ hA, ← h1]
   exact ENNReal.mul_ne_top hμs h3A.ne
 #align measure_theory.ae_measure_preimage_mul_right_lt_top MeasureTheory.ae_measure_preimage_mul_right_lt_top
@@ -359,7 +359,7 @@ theorem measure_mul_measure_eq [MulLeftInvariant ν] {s t : Set G} (hs : Measura
   have h2 :=
     measure_lintegral_div_measure μ ν hs h2s h3s (t.indicator fun x => 1)
       (measurable_const.indicator ht)
-  rw [lintegral_indicator _ ht, set_lintegral_one] at h1 h2
+  rw [lintegral_indicator _ ht, set_lintegral_one] at h1 h2 
   rw [← h1, mul_left_comm, h2]
 #align measure_theory.measure_mul_measure_eq MeasureTheory.measure_mul_measure_eq
 #align measure_theory.measure_add_measure_eq MeasureTheory.measure_add_measure_eq
@@ -522,11 +522,11 @@ theorem quasiMeasurePreserving_mul_left [MulRightInvariant μ] (g : G) :
   have :=
     (quasi_measure_preserving_mul_right μ.inv g⁻¹).mono (inv_absolutely_continuous μ.inv)
       (absolutely_continuous_inv μ.inv)
-  rw [μ.inv_inv] at this
+  rw [μ.inv_inv] at this 
   have :=
     (quasi_measure_preserving_inv_of_right_invariant μ).comp
       (this.comp (quasi_measure_preserving_inv_of_right_invariant μ))
-  simp_rw [Function.comp, mul_inv_rev, inv_inv] at this
+  simp_rw [Function.comp, mul_inv_rev, inv_inv] at this 
   exact this
 #align measure_theory.quasi_measure_preserving_mul_left MeasureTheory.quasiMeasurePreserving_mul_left
 #align measure_theory.quasi_measure_preserving_add_left MeasureTheory.quasiMeasurePreserving_add_left

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

@@ -90,7 +90,7 @@ This condition is part of the definition of a measurable group in [Halmos, §59]
 There, the map in this lemma is called `S`. -/
 @[to_additive measure_preserving_prod_add
       " The shear mapping `(x, y) ↦ (x, x + y)` preserves the measure `μ × ν`. "]
-theorem measurePreserving_prod_mul [IsMulLeftInvariant ν] :
+theorem measurePreserving_prod_mul [MulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.1 * z.2)) (μ.Prod ν) (μ.Prod ν) :=
   (MeasurePreserving.id μ).skew_product measurable_mul <|
     Filter.eventually_of_forall <| map_mul_left_eq_self ν
@@ -102,7 +102,7 @@ This is the map `SR` in [Halmos, §59].
 `S` is the map `(x, y) ↦ (x, xy)` and `R` is `prod.swap`. -/
 @[to_additive measure_preserving_prod_add_swap
       " The map `(x, y) ↦ (y, y + x)` sends the measure `μ × ν` to `ν × μ`. "]
-theorem measurePreserving_prod_mul_swap [IsMulLeftInvariant μ] :
+theorem measurePreserving_prod_mul_swap [MulLeftInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.2 * z.1)) (μ.Prod ν) (ν.Prod μ) :=
   (measurePreserving_prod_mul ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_mul_swap MeasureTheory.measurePreserving_prod_mul_swap
@@ -129,13 +129,13 @@ This is the function `S⁻¹` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)`. -/
 @[to_additive measure_preserving_prod_neg_add
       "The map `(x, y) ↦ (x, - x + y)` is measure-preserving."]
-theorem measurePreserving_prod_inv_mul [IsMulLeftInvariant ν] :
+theorem measurePreserving_prod_inv_mul [MulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.1⁻¹ * z.2)) (μ.Prod ν) (μ.Prod ν) :=
   (measurePreserving_prod_mul μ ν).symm <| MeasurableEquiv.shearMulRight G
 #align measure_theory.measure_preserving_prod_inv_mul MeasureTheory.measurePreserving_prod_inv_mul
 #align measure_theory.measure_preserving_prod_neg_add MeasureTheory.measurePreserving_prod_neg_add
 
-variable [IsMulLeftInvariant μ]
+variable [MulLeftInvariant μ]
 
 /-- The map `(x, y) ↦ (y, y⁻¹x)` sends `μ × ν` to `ν × μ`.
 This is the function `S⁻¹R` in [Halmos, §59],
@@ -153,7 +153,7 @@ This is the function `S⁻¹RSR` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)` and `R` is `prod.swap`. -/
 @[to_additive measure_preserving_add_prod_neg
       "The map `(x, y) ↦ (y + x, - x)` is measure-preserving."]
-theorem measurePreserving_mul_prod_inv [IsMulLeftInvariant ν] :
+theorem measurePreserving_mul_prod_inv [MulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.2 * z.1, z.1⁻¹)) (μ.Prod ν) (μ.Prod ν) :=
   by
   convert(measure_preserving_prod_inv_mul_swap ν μ).comp (measure_preserving_prod_mul_swap μ ν)
@@ -204,7 +204,7 @@ theorem absolutelyContinuous_inv : μ ≪ μ.inv :=
 #align measure_theory.absolutely_continuous_neg MeasureTheory.absolutelyContinuous_neg
 
 @[to_additive]
-theorem lintegral_lintegral_mul_inv [IsMulLeftInvariant ν] (f : G → G → ℝ≥0∞)
+theorem lintegral_lintegral_mul_inv [MulLeftInvariant ν] (f : G → G → ℝ≥0∞)
     (hf : AEMeasurable (uncurry f) (μ.Prod ν)) :
     (∫⁻ x, ∫⁻ y, f (y * x) x⁻¹ ∂ν ∂μ) = ∫⁻ x, ∫⁻ y, f x y ∂ν ∂μ :=
   by
@@ -257,7 +257,7 @@ theorem absolutelyContinuous_map_div_left (g : G) : μ ≪ map (fun h => g / h)
 
 /-- This is the computation performed in the proof of [Halmos, §60 Th. A]. -/
 @[to_additive "This is the computation performed in the proof of [Halmos, §60 Th. A]."]
-theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s) (f : G → ℝ≥0∞)
+theorem measure_mul_lintegral_eq [MulLeftInvariant ν] (sm : MeasurableSet s) (f : G → ℝ≥0∞)
     (hf : Measurable f) : (μ s * ∫⁻ y, f y ∂ν) = ∫⁻ x, ν ((fun z => z * x) ⁻¹' s) * f x⁻¹ ∂μ :=
   by
   rw [← set_lintegral_one, ← lintegral_indicator _ sm, ←
@@ -284,18 +284,18 @@ theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s)
 /-- Any two nonzero left-invariant measures are absolutely continuous w.r.t. each other. -/
 @[to_additive
       " Any two nonzero left-invariant measures are absolutely continuous w.r.t. each\nother. "]
-theorem absolutelyContinuous_of_isMulLeftInvariant [IsMulLeftInvariant ν] (hν : ν ≠ 0) : μ ≪ ν :=
+theorem absolutelyContinuous_of_mulLeftInvariant [MulLeftInvariant ν] (hν : ν ≠ 0) : μ ≪ ν :=
   by
   refine' absolutely_continuous.mk fun s sm hνs => _
   have h1 := measure_mul_lintegral_eq μ ν sm 1 measurable_one
   simp_rw [Pi.one_apply, lintegral_one, mul_one, (measure_mul_right_null ν _).mpr hνs,
     lintegral_zero, mul_eq_zero, measure_univ_eq_zero.not.mpr hν, or_false_iff] at h1
   exact h1
-#align measure_theory.absolutely_continuous_of_is_mul_left_invariant MeasureTheory.absolutelyContinuous_of_isMulLeftInvariant
-#align measure_theory.absolutely_continuous_of_is_add_left_invariant MeasureTheory.absolutelyContinuous_of_is_add_left_invariant
+#align measure_theory.absolutely_continuous_of_is_mul_left_invariant MeasureTheory.absolutelyContinuous_of_mulLeftInvariant
+#align measure_theory.absolutely_continuous_of_is_add_left_invariant MeasureTheory.absolutelyContinuous_of_addLeftInvariant
 
 @[to_additive]
-theorem ae_measure_preimage_mul_right_lt_top [IsMulLeftInvariant ν] (sm : MeasurableSet s)
+theorem ae_measure_preimage_mul_right_lt_top [MulLeftInvariant ν] (sm : MeasurableSet s)
     (hμs : μ s ≠ ∞) : ∀ᵐ x ∂μ, ν ((fun y => y * x) ⁻¹' s) < ∞ :=
   by
   refine' ae_of_forall_measure_lt_top_ae_restrict' ν.inv _ _
@@ -313,9 +313,8 @@ theorem ae_measure_preimage_mul_right_lt_top [IsMulLeftInvariant ν] (sm : Measu
 #align measure_theory.ae_measure_preimage_add_right_lt_top MeasureTheory.ae_measure_preimage_add_right_lt_top
 
 @[to_additive]
-theorem ae_measure_preimage_mul_right_lt_top_of_ne_zero [IsMulLeftInvariant ν]
-    (sm : MeasurableSet s) (h2s : ν s ≠ 0) (h3s : ν s ≠ ∞) :
-    ∀ᵐ x ∂μ, ν ((fun y => y * x) ⁻¹' s) < ∞ :=
+theorem ae_measure_preimage_mul_right_lt_top_of_ne_zero [MulLeftInvariant ν] (sm : MeasurableSet s)
+    (h2s : ν s ≠ 0) (h3s : ν s ≠ ∞) : ∀ᵐ x ∂μ, ν ((fun y => y * x) ⁻¹' s) < ∞ :=
   by
   refine' (ae_measure_preimage_mul_right_lt_top ν ν sm h3s).filter_mono _
   refine' (absolutely_continuous_of_is_mul_left_invariant μ ν _).ae_le
@@ -336,7 +335,7 @@ theorem ae_measure_preimage_mul_right_lt_top_of_ne_zero [IsMulLeftInvariant ν]
   `measure_theory.ae_measure_preimage_mul_right_lt_top_of_ne_zero`. -/
 @[to_additive
       "A technical lemma relating two different measures. This is basically\n[Halmos, §60 Th. A]. Note that if `f` is the characteristic function of a measurable set `t` this\nstates that `μ t = c * μ s` for a constant `c` that does not depend on `μ`.\n\nNote: There is a gap in the last step of the proof in [Halmos]. In the last line, the equality\n`g(-x) + ν(s - x) = f(x)` holds if we can prove that `0 < ν(s - x) < ∞`. The first inequality\nfollows from §59, Th. D, but the second inequality is not justified. We prove this inequality for\nalmost all `x` in `measure_theory.ae_measure_preimage_add_right_lt_top_of_ne_zero`."]
-theorem measure_lintegral_div_measure [IsMulLeftInvariant ν] (sm : MeasurableSet s) (h2s : ν s ≠ 0)
+theorem measure_lintegral_div_measure [MulLeftInvariant ν] (sm : MeasurableSet s) (h2s : ν s ≠ 0)
     (h3s : ν s ≠ ∞) (f : G → ℝ≥0∞) (hf : Measurable f) :
     (μ s * ∫⁻ y, f y⁻¹ / ν ((fun x => x * y⁻¹) ⁻¹' s) ∂ν) = ∫⁻ x, f x ∂μ :=
   by
@@ -351,7 +350,7 @@ theorem measure_lintegral_div_measure [IsMulLeftInvariant ν] (sm : MeasurableSe
 #align measure_theory.measure_lintegral_sub_measure MeasureTheory.measure_lintegral_sub_measure
 
 @[to_additive]
-theorem measure_mul_measure_eq [IsMulLeftInvariant ν] {s t : Set G} (hs : MeasurableSet s)
+theorem measure_mul_measure_eq [MulLeftInvariant ν] {s t : Set G} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (h2s : ν s ≠ 0) (h3s : ν s ≠ ∞) : μ s * ν t = ν s * μ t :=
   by
   have h1 :=
@@ -368,7 +367,7 @@ theorem measure_mul_measure_eq [IsMulLeftInvariant ν] {s t : Set G} (hs : Measu
 /-- Left invariant Borel measures on a measurable group are unique (up to a scalar). -/
 @[to_additive
       " Left invariant Borel measures on an additive measurable group are unique\n  (up to a scalar). "]
-theorem measure_eq_div_smul [IsMulLeftInvariant ν] (hs : MeasurableSet s) (h2s : ν s ≠ 0)
+theorem measure_eq_div_smul [MulLeftInvariant ν] (hs : MeasurableSet s) (h2s : ν s ≠ 0)
     (h3s : ν s ≠ ∞) : μ = (μ s / ν s) • ν := by
   ext1 t ht
   rw [smul_apply, smul_eq_mul, mul_comm, ← mul_div_assoc, mul_comm,
@@ -381,7 +380,7 @@ end LeftInvariant
 section RightInvariant
 
 @[to_additive measure_preserving_prod_add_right]
-theorem measurePreserving_prod_mul_right [IsMulRightInvariant ν] :
+theorem measurePreserving_prod_mul_right [MulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.2 * z.1)) (μ.Prod ν) (μ.Prod ν) :=
   (MeasurePreserving.id μ).skew_product (measurable_snd.mul measurable_fst) <|
     Filter.eventually_of_forall <| map_mul_right_eq_self ν
@@ -391,7 +390,7 @@ theorem measurePreserving_prod_mul_right [IsMulRightInvariant ν] :
 /-- The map `(x, y) ↦ (y, xy)` sends the measure `μ × ν` to `ν × μ`. -/
 @[to_additive measure_preserving_prod_add_swap_right
       " The map `(x, y) ↦ (y, x + y)` sends the measure `μ × ν` to `ν × μ`. "]
-theorem measurePreserving_prod_mul_swap_right [IsMulRightInvariant μ] :
+theorem measurePreserving_prod_mul_swap_right [MulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.1 * z.2)) (μ.Prod ν) (ν.Prod μ) :=
   (measurePreserving_prod_mul_right ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_mul_swap_right MeasureTheory.measurePreserving_prod_mul_swap_right
@@ -400,7 +399,7 @@ theorem measurePreserving_prod_mul_swap_right [IsMulRightInvariant μ] :
 /-- The map `(x, y) ↦ (xy, y)` preserves the measure `μ × ν`. -/
 @[to_additive measure_preserving_add_prod
       " The map `(x, y) ↦ (x + y, y)` preserves the measure `μ × ν`. "]
-theorem measurePreserving_mul_prod [IsMulRightInvariant μ] :
+theorem measurePreserving_mul_prod [MulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.1 * z.2, z.2)) (μ.Prod ν) (μ.Prod ν) :=
   measurePreserving_swap.comp <| by apply measure_preserving_prod_mul_swap_right μ ν
 #align measure_theory.measure_preserving_mul_prod MeasureTheory.measurePreserving_mul_prod
@@ -410,7 +409,7 @@ variable [MeasurableInv G]
 
 /-- The map `(x, y) ↦ (x, y / x)` is measure-preserving. -/
 @[to_additive measure_preserving_prod_sub "The map `(x, y) ↦ (x, y - x)` is measure-preserving."]
-theorem measurePreserving_prod_div [IsMulRightInvariant ν] :
+theorem measurePreserving_prod_div [MulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.2 / z.1)) (μ.Prod ν) (μ.Prod ν) :=
   (measurePreserving_prod_mul_right μ ν).symm (MeasurableEquiv.shearDivRight G).symm
 #align measure_theory.measure_preserving_prod_div MeasureTheory.measurePreserving_prod_div
@@ -419,7 +418,7 @@ theorem measurePreserving_prod_div [IsMulRightInvariant ν] :
 /-- The map `(x, y) ↦ (y, x / y)` sends `μ × ν` to `ν × μ`. -/
 @[to_additive measure_preserving_prod_sub_swap
       "The map `(x, y) ↦ (y, x - y)` sends `μ × ν` to `ν × μ`."]
-theorem measurePreserving_prod_div_swap [IsMulRightInvariant μ] :
+theorem measurePreserving_prod_div_swap [MulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.1 / z.2)) (μ.Prod ν) (ν.Prod μ) :=
   (measurePreserving_prod_div ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_div_swap MeasureTheory.measurePreserving_prod_div_swap
@@ -428,7 +427,7 @@ theorem measurePreserving_prod_div_swap [IsMulRightInvariant μ] :
 /-- The map `(x, y) ↦ (x / y, y)` preserves the measure `μ × ν`. -/
 @[to_additive measure_preserving_sub_prod
       " The map `(x, y) ↦ (x - y, y)` preserves the measure `μ × ν`. "]
-theorem measurePreserving_div_prod [IsMulRightInvariant μ] :
+theorem measurePreserving_div_prod [MulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.1 / z.2, z.2)) (μ.Prod ν) (μ.Prod ν) :=
   measurePreserving_swap.comp <| by apply measure_preserving_prod_div_swap μ ν
 #align measure_theory.measure_preserving_div_prod MeasureTheory.measurePreserving_div_prod
@@ -437,7 +436,7 @@ theorem measurePreserving_div_prod [IsMulRightInvariant μ] :
 /-- The map `(x, y) ↦ (xy, x⁻¹)` is measure-preserving. -/
 @[to_additive measure_preserving_add_prod_neg_right
       "The map `(x, y) ↦ (x + y, - x)` is measure-preserving."]
-theorem measurePreserving_mul_prod_inv_right [IsMulRightInvariant μ] [IsMulRightInvariant ν] :
+theorem measurePreserving_mul_prod_inv_right [MulRightInvariant μ] [MulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1 * z.2, z.1⁻¹)) (μ.Prod ν) (μ.Prod ν) :=
   by
   convert(measure_preserving_prod_div_swap ν μ).comp (measure_preserving_prod_mul_swap_right μ ν)
@@ -453,7 +452,7 @@ section QuasiMeasurePreserving
 variable [MeasurableInv G]
 
 @[to_additive]
-theorem quasiMeasurePreserving_inv_of_right_invariant [IsMulRightInvariant μ] :
+theorem quasiMeasurePreserving_inv_of_right_invariant [MulRightInvariant μ] :
     QuasiMeasurePreserving (Inv.inv : G → G) μ μ :=
   by
   rw [← μ.inv_inv]
@@ -464,7 +463,7 @@ theorem quasiMeasurePreserving_inv_of_right_invariant [IsMulRightInvariant μ] :
 #align measure_theory.quasi_measure_preserving_neg_of_right_invariant MeasureTheory.quasiMeasurePreserving_neg_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreserving_div_left [IsMulLeftInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_div_left [MulLeftInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g / h) μ μ :=
   by
   simp_rw [div_eq_mul_inv]
@@ -474,7 +473,7 @@ theorem quasiMeasurePreserving_div_left [IsMulLeftInvariant μ] (g : G) :
 #align measure_theory.quasi_measure_preserving_sub_left MeasureTheory.quasiMeasurePreserving_sub_left
 
 @[to_additive]
-theorem quasiMeasurePreserving_div_left_of_right_invariant [IsMulRightInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_div_left_of_right_invariant [MulRightInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g / h) μ μ :=
   by
   rw [← μ.inv_inv]
@@ -485,7 +484,7 @@ theorem quasiMeasurePreserving_div_left_of_right_invariant [IsMulRightInvariant
 #align measure_theory.quasi_measure_preserving_sub_left_of_right_invariant MeasureTheory.quasiMeasurePreserving_sub_left_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreserving_div_of_right_invariant [IsMulRightInvariant μ] :
+theorem quasiMeasurePreserving_div_of_right_invariant [MulRightInvariant μ] :
     QuasiMeasurePreserving (fun p : G × G => p.1 / p.2) (μ.Prod ν) μ :=
   by
   refine' quasi_measure_preserving.prod_of_left measurable_div (eventually_of_forall fun y => _)
@@ -494,7 +493,7 @@ theorem quasiMeasurePreserving_div_of_right_invariant [IsMulRightInvariant μ] :
 #align measure_theory.quasi_measure_preserving_sub_of_right_invariant MeasureTheory.quasiMeasurePreserving_sub_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreserving_div [IsMulLeftInvariant μ] :
+theorem quasiMeasurePreserving_div [MulLeftInvariant μ] :
     QuasiMeasurePreserving (fun p : G × G => p.1 / p.2) (μ.Prod ν) μ :=
   (quasiMeasurePreserving_div_of_right_invariant μ.inv ν).mono
     ((absolutelyContinuous_inv μ).Prod AbsolutelyContinuous.rfl) (inv_absolutelyContinuous μ)
@@ -505,7 +504,7 @@ theorem quasiMeasurePreserving_div [IsMulLeftInvariant μ] :
 This should not be confused with `(measure_preserving_mul_right μ g).quasi_measure_preserving`. -/
 @[to_additive
       "A *left*-invariant measure is quasi-preserved by *right*-addition.\nThis should not be confused with `(measure_preserving_add_right μ g).quasi_measure_preserving`. "]
-theorem quasiMeasurePreserving_mul_right [IsMulLeftInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_mul_right [MulLeftInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => h * g) μ μ :=
   by
   refine' ⟨measurable_mul_const g, absolutely_continuous.mk fun s hs => _⟩
@@ -517,7 +516,7 @@ theorem quasiMeasurePreserving_mul_right [IsMulLeftInvariant μ] (g : G) :
 This should not be confused with `(measure_preserving_mul_left μ g).quasi_measure_preserving`. -/
 @[to_additive
       "A *right*-invariant measure is quasi-preserved by *left*-addition.\nThis should not be confused with `(measure_preserving_add_left μ g).quasi_measure_preserving`. "]
-theorem quasiMeasurePreserving_mul_left [IsMulRightInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_mul_left [MulRightInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g * h) μ μ :=
   by
   have :=

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

@@ -46,7 +46,7 @@ open Function MeasureTheory
 
 open Filter hiding map
 
-open Classical ENNReal Pointwise MeasureTheory
+open scoped Classical ENNReal Pointwise MeasureTheory
 
 variable (G : Type _) [MeasurableSpace G]
 

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

@@ -116,11 +116,7 @@ theorem measurable_measure_mul_right (hs : MeasurableSet s) :
   suffices
     Measurable fun y =>
       μ ((fun x => (x, y)) ⁻¹' ((fun z : G × G => ((1 : G), z.1 * z.2)) ⁻¹' univ ×ˢ s))
-    by
-    convert this
-    ext1 x
-    congr 1 with y : 1
-    simp
+    by convert this; ext1 x; congr 1 with y : 1; simp
   apply measurable_measure_prod_mk_right
   exact measurable_const.prod_mk measurable_mul (measurable_set.univ.prod hs)
 #align measure_theory.measurable_measure_mul_right MeasureTheory.measurable_measure_mul_right
@@ -267,7 +263,7 @@ theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s)
   rw [← set_lintegral_one, ← lintegral_indicator _ sm, ←
     lintegral_lintegral_mul (measurable_const.indicator sm).AEMeasurable hf.ae_measurable, ←
     lintegral_lintegral_mul_inv μ ν]
-  swap
+  swap;
   ·
     exact
       (((measurable_const.indicator sm).comp measurable_fst).mul
@@ -279,12 +275,7 @@ theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s)
     ∀ x y,
       s.indicator (fun z : G => (1 : ℝ≥0∞)) (y * x) =
         ((fun z => z * x) ⁻¹' s).indicator (fun b : G => 1) y :=
-    by
-    intro x y
-    symm
-    convert indicator_comp_right fun y => y * x
-    ext1 z
-    rfl
+    by intro x y; symm; convert indicator_comp_right fun y => y * x; ext1 z; rfl
   simp_rw [this, lintegral_mul_const _ (ms _), lintegral_indicator _ (measurable_mul_const _ sm),
     set_lintegral_one]
 #align measure_theory.measure_mul_lintegral_eq MeasureTheory.measure_mul_lintegral_eq

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: Floris van Doorn
 
 ! This file was ported from Lean 3 source module measure_theory.group.prod
-! leanprover-community/mathlib commit ec247d43814751ffceb33b758e8820df2372bf6f
+! 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.Constructions.Prod
+import Mathbin.MeasureTheory.Constructions.Prod.Basic
 import Mathbin.MeasureTheory.Group.Measure
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/cc5dd6244981976cc9da7afc4eee5682b037a013

@@ -50,13 +50,13 @@ open Classical ENNReal Pointwise MeasureTheory
 
 variable (G : Type _) [MeasurableSpace G]
 
-variable [Group G] [HasMeasurableMul₂ G]
+variable [Group G] [MeasurableMul₂ G]
 
 variable (μ ν : Measure G) [SigmaFinite ν] [SigmaFinite μ] {s : Set G}
 
 /-- The map `(x, y) ↦ (x, xy)` as a `measurable_equiv`. -/
 @[to_additive "The map `(x, y) ↦ (x, x + y)` as a `measurable_equiv`."]
-protected def MeasurableEquiv.shearMulRight [HasMeasurableInv G] : G × G ≃ᵐ G × G :=
+protected def MeasurableEquiv.shearMulRight [MeasurableInv G] : G × G ≃ᵐ G × G :=
   {
     Equiv.prodShear (Equiv.refl _)
       Equiv.mulLeft with
@@ -68,7 +68,7 @@ protected def MeasurableEquiv.shearMulRight [HasMeasurableInv G] : G × G ≃ᵐ
 /-- The map `(x, y) ↦ (x, y / x)` as a `measurable_equiv` with as inverse `(x, y) ↦ (x, yx)` -/
 @[to_additive
       "The map `(x, y) ↦ (x, y - x)` as a `measurable_equiv` with as inverse `(x, y) ↦ (x, y + x)`."]
-protected def MeasurableEquiv.shearDivRight [HasMeasurableInv G] : G × G ≃ᵐ G × G :=
+protected def MeasurableEquiv.shearDivRight [MeasurableInv G] : G × G ≃ᵐ G × G :=
   {
     Equiv.prodShear (Equiv.refl _)
       Equiv.divRight with
@@ -126,7 +126,7 @@ theorem measurable_measure_mul_right (hs : MeasurableSet s) :
 #align measure_theory.measurable_measure_mul_right MeasureTheory.measurable_measure_mul_right
 #align measure_theory.measurable_measure_add_right MeasureTheory.measurable_measure_add_right
 
-variable [HasMeasurableInv G]
+variable [MeasurableInv G]
 
 /-- The map `(x, y) ↦ (x, x⁻¹y)` is measure-preserving.
 This is the function `S⁻¹` in [Halmos, §59],
@@ -415,7 +415,7 @@ theorem measurePreserving_mul_prod [IsMulRightInvariant μ] :
 #align measure_theory.measure_preserving_mul_prod MeasureTheory.measurePreserving_mul_prod
 #align measure_theory.measure_preserving_add_prod MeasureTheory.measurePreserving_add_prod
 
-variable [HasMeasurableInv G]
+variable [MeasurableInv G]
 
 /-- The map `(x, y) ↦ (x, y / x)` is measure-preserving. -/
 @[to_additive measure_preserving_prod_sub "The map `(x, y) ↦ (x, y - x)` is measure-preserving."]
@@ -459,7 +459,7 @@ end RightInvariant
 
 section QuasiMeasurePreserving
 
-variable [HasMeasurableInv G]
+variable [MeasurableInv G]
 
 @[to_additive]
 theorem quasiMeasurePreserving_inv_of_right_invariant [IsMulRightInvariant μ] :

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

@@ -90,23 +90,23 @@ This condition is part of the definition of a measurable group in [Halmos, §59]
 There, the map in this lemma is called `S`. -/
 @[to_additive measure_preserving_prod_add
       " The shear mapping `(x, y) ↦ (x, x + y)` preserves the measure `μ × ν`. "]
-theorem measurePreservingProdMul [IsMulLeftInvariant ν] :
+theorem measurePreserving_prod_mul [IsMulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.1 * z.2)) (μ.Prod ν) (μ.Prod ν) :=
-  (MeasurePreserving.id μ).skewProduct measurable_mul <|
+  (MeasurePreserving.id μ).skew_product measurable_mul <|
     Filter.eventually_of_forall <| map_mul_left_eq_self ν
-#align measure_theory.measure_preserving_prod_mul MeasureTheory.measurePreservingProdMul
-#align measure_theory.measure_preserving_prod_add MeasureTheory.measure_preserving_prod_add
+#align measure_theory.measure_preserving_prod_mul MeasureTheory.measurePreserving_prod_mul
+#align measure_theory.measure_preserving_prod_add MeasureTheory.measurePreserving_prod_add
 
 /-- The map `(x, y) ↦ (y, yx)` sends the measure `μ × ν` to `ν × μ`.
 This is the map `SR` in [Halmos, §59].
 `S` is the map `(x, y) ↦ (x, xy)` and `R` is `prod.swap`. -/
 @[to_additive measure_preserving_prod_add_swap
       " The map `(x, y) ↦ (y, y + x)` sends the measure `μ × ν` to `ν × μ`. "]
-theorem measurePreservingProdMulSwap [IsMulLeftInvariant μ] :
+theorem measurePreserving_prod_mul_swap [IsMulLeftInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.2 * z.1)) (μ.Prod ν) (ν.Prod μ) :=
-  (measurePreservingProdMul ν μ).comp measurePreservingSwap
-#align measure_theory.measure_preserving_prod_mul_swap MeasureTheory.measurePreservingProdMulSwap
-#align measure_theory.measure_preserving_prod_add_swap MeasureTheory.measure_preserving_prod_add_swap
+  (measurePreserving_prod_mul ν μ).comp measurePreserving_swap
+#align measure_theory.measure_preserving_prod_mul_swap MeasureTheory.measurePreserving_prod_mul_swap
+#align measure_theory.measure_preserving_prod_add_swap MeasureTheory.measurePreserving_prod_add_swap
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[to_additive]
@@ -133,11 +133,11 @@ This is the function `S⁻¹` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)`. -/
 @[to_additive measure_preserving_prod_neg_add
       "The map `(x, y) ↦ (x, - x + y)` is measure-preserving."]
-theorem measurePreservingProdInvMul [IsMulLeftInvariant ν] :
+theorem measurePreserving_prod_inv_mul [IsMulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.1⁻¹ * z.2)) (μ.Prod ν) (μ.Prod ν) :=
-  (measurePreservingProdMul μ ν).symm <| MeasurableEquiv.shearMulRight G
-#align measure_theory.measure_preserving_prod_inv_mul MeasureTheory.measurePreservingProdInvMul
-#align measure_theory.measure_preserving_prod_neg_add MeasureTheory.measure_preserving_prod_neg_add
+  (measurePreserving_prod_mul μ ν).symm <| MeasurableEquiv.shearMulRight G
+#align measure_theory.measure_preserving_prod_inv_mul MeasureTheory.measurePreserving_prod_inv_mul
+#align measure_theory.measure_preserving_prod_neg_add MeasureTheory.measurePreserving_prod_neg_add
 
 variable [IsMulLeftInvariant μ]
 
@@ -146,30 +146,30 @@ This is the function `S⁻¹R` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)` and `R` is `prod.swap`. -/
 @[to_additive measure_preserving_prod_neg_add_swap
       "The map `(x, y) ↦ (y, - y + x)` sends `μ × ν` to `ν × μ`."]
-theorem measurePreservingProdInvMulSwap :
+theorem measurePreserving_prod_inv_mul_swap :
     MeasurePreserving (fun z : G × G => (z.2, z.2⁻¹ * z.1)) (μ.Prod ν) (ν.Prod μ) :=
-  (measurePreservingProdInvMul ν μ).comp measurePreservingSwap
-#align measure_theory.measure_preserving_prod_inv_mul_swap MeasureTheory.measurePreservingProdInvMulSwap
-#align measure_theory.measure_preserving_prod_neg_add_swap MeasureTheory.measure_preserving_prod_neg_add_swap
+  (measurePreserving_prod_inv_mul ν μ).comp measurePreserving_swap
+#align measure_theory.measure_preserving_prod_inv_mul_swap MeasureTheory.measurePreserving_prod_inv_mul_swap
+#align measure_theory.measure_preserving_prod_neg_add_swap MeasureTheory.measurePreserving_prod_neg_add_swap
 
 /-- The map `(x, y) ↦ (yx, x⁻¹)` is measure-preserving.
 This is the function `S⁻¹RSR` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)` and `R` is `prod.swap`. -/
 @[to_additive measure_preserving_add_prod_neg
       "The map `(x, y) ↦ (y + x, - x)` is measure-preserving."]
-theorem measurePreservingMulProdInv [IsMulLeftInvariant ν] :
+theorem measurePreserving_mul_prod_inv [IsMulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.2 * z.1, z.1⁻¹)) (μ.Prod ν) (μ.Prod ν) :=
   by
   convert(measure_preserving_prod_inv_mul_swap ν μ).comp (measure_preserving_prod_mul_swap μ ν)
   ext1 ⟨x, y⟩
   simp_rw [Function.comp_apply, mul_inv_rev, inv_mul_cancel_right]
-#align measure_theory.measure_preserving_mul_prod_inv MeasureTheory.measurePreservingMulProdInv
-#align measure_theory.measure_preserving_add_prod_neg MeasureTheory.measure_preserving_add_prod_neg
+#align measure_theory.measure_preserving_mul_prod_inv MeasureTheory.measurePreserving_mul_prod_inv
+#align measure_theory.measure_preserving_add_prod_neg MeasureTheory.measurePreserving_add_prod_neg
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 @[to_additive]
-theorem quasiMeasurePreservingInv : QuasiMeasurePreserving (Inv.inv : G → G) μ μ :=
+theorem quasiMeasurePreserving_inv : QuasiMeasurePreserving (Inv.inv : G → G) μ μ :=
   by
   refine' ⟨measurable_inv, absolutely_continuous.mk fun s hsm hμs => _⟩
   rw [map_apply measurable_inv hsm, inv_preimage]
@@ -181,8 +181,8 @@ theorem quasiMeasurePreservingInv : QuasiMeasurePreserving (Inv.inv : G → G) 
   have hsm' : MeasurableSet (s⁻¹ ×ˢ s⁻¹) := hsm.inv.prod hsm.inv
   simp_rw [map_apply hf hsm', prod_apply_symm (hf hsm'), preimage_preimage, mk_preimage_prod,
     inv_preimage, inv_inv, measure_mono_null (inter_subset_right _ _) hμs, lintegral_zero]
-#align measure_theory.quasi_measure_preserving_inv MeasureTheory.quasiMeasurePreservingInv
-#align measure_theory.quasi_measure_preserving_neg MeasureTheory.quasi_measure_preserving_neg
+#align measure_theory.quasi_measure_preserving_inv MeasureTheory.quasiMeasurePreserving_inv
+#align measure_theory.quasi_measure_preserving_neg MeasureTheory.quasiMeasurePreserving_neg
 
 @[to_additive]
 theorem measure_inv_null : μ s⁻¹ = 0 ↔ μ s = 0 :=
@@ -194,27 +194,27 @@ theorem measure_inv_null : μ s⁻¹ = 0 ↔ μ s = 0 :=
 #align measure_theory.measure_neg_null MeasureTheory.measure_neg_null
 
 @[to_additive]
-theorem invAbsolutelyContinuous : μ.inv ≪ μ :=
-  (quasiMeasurePreservingInv μ).AbsolutelyContinuous
-#align measure_theory.inv_absolutely_continuous MeasureTheory.invAbsolutelyContinuous
-#align measure_theory.neg_absolutely_continuous MeasureTheory.neg_absolutely_continuous
+theorem inv_absolutelyContinuous : μ.inv ≪ μ :=
+  (quasiMeasurePreserving_inv μ).AbsolutelyContinuous
+#align measure_theory.inv_absolutely_continuous MeasureTheory.inv_absolutelyContinuous
+#align measure_theory.neg_absolutely_continuous MeasureTheory.neg_absolutelyContinuous
 
 @[to_additive]
-theorem absolutelyContinuousInv : μ ≪ μ.inv :=
+theorem absolutelyContinuous_inv : μ ≪ μ.inv :=
   by
   refine' absolutely_continuous.mk fun s hs => _
   simp_rw [inv_apply μ s, measure_inv_null, imp_self]
-#align measure_theory.absolutely_continuous_inv MeasureTheory.absolutelyContinuousInv
-#align measure_theory.absolutely_continuous_neg MeasureTheory.absolutely_continuous_neg
+#align measure_theory.absolutely_continuous_inv MeasureTheory.absolutelyContinuous_inv
+#align measure_theory.absolutely_continuous_neg MeasureTheory.absolutelyContinuous_neg
 
 @[to_additive]
 theorem lintegral_lintegral_mul_inv [IsMulLeftInvariant ν] (f : G → G → ℝ≥0∞)
-    (hf : AeMeasurable (uncurry f) (μ.Prod ν)) :
+    (hf : AEMeasurable (uncurry f) (μ.Prod ν)) :
     (∫⁻ x, ∫⁻ y, f (y * x) x⁻¹ ∂ν ∂μ) = ∫⁻ x, ∫⁻ y, f x y ∂ν ∂μ :=
   by
   have h : Measurable fun z : G × G => (z.2 * z.1, z.1⁻¹) :=
     (measurable_snd.mul measurable_fst).prod_mk measurable_fst.inv
-  have h2f : AeMeasurable (uncurry fun x y => f (y * x) x⁻¹) (μ.prod ν) :=
+  have h2f : AEMeasurable (uncurry fun x y => f (y * x) x⁻¹) (μ.prod ν) :=
     hf.comp_quasi_measure_preserving (measure_preserving_mul_prod_inv μ ν).QuasiMeasurePreserving
   simp_rw [lintegral_lintegral h2f, lintegral_lintegral hf]
   conv_rhs => rw [← (measure_preserving_mul_prod_inv μ ν).map_eq]
@@ -242,22 +242,22 @@ theorem measure_mul_right_ne_zero (h2s : μ s ≠ 0) (y : G) : μ ((fun x => x *
 #align measure_theory.measure_add_right_ne_zero MeasureTheory.measure_add_right_ne_zero
 
 @[to_additive]
-theorem absolutelyContinuousMapMulRight (g : G) : μ ≪ map (· * g) μ :=
+theorem absolutelyContinuous_map_mul_right (g : G) : μ ≪ map (· * g) μ :=
   by
   refine' absolutely_continuous.mk fun s hs => _
   rw [map_apply (measurable_mul_const g) hs, measure_mul_right_null]; exact id
-#align measure_theory.absolutely_continuous_map_mul_right MeasureTheory.absolutelyContinuousMapMulRight
-#align measure_theory.absolutely_continuous_map_add_right MeasureTheory.absolutely_continuous_map_add_right
+#align measure_theory.absolutely_continuous_map_mul_right MeasureTheory.absolutelyContinuous_map_mul_right
+#align measure_theory.absolutely_continuous_map_add_right MeasureTheory.absolutelyContinuous_map_add_right
 
 @[to_additive]
-theorem absolutelyContinuousMapDivLeft (g : G) : μ ≪ map (fun h => g / h) μ :=
+theorem absolutelyContinuous_map_div_left (g : G) : μ ≪ map (fun h => g / h) μ :=
   by
   simp_rw [div_eq_mul_inv]
   rw [← map_map (measurable_const_mul g) measurable_inv]
   conv_lhs => rw [← map_mul_left_eq_self μ g]
   exact (absolutely_continuous_inv μ).map (measurable_const_mul g)
-#align measure_theory.absolutely_continuous_map_div_left MeasureTheory.absolutelyContinuousMapDivLeft
-#align measure_theory.absolutely_continuous_map_sub_left MeasureTheory.absolutely_continuous_map_sub_left
+#align measure_theory.absolutely_continuous_map_div_left MeasureTheory.absolutelyContinuous_map_div_left
+#align measure_theory.absolutely_continuous_map_sub_left MeasureTheory.absolutelyContinuous_map_sub_left
 
 /-- This is the computation performed in the proof of [Halmos, §60 Th. A]. -/
 @[to_additive "This is the computation performed in the proof of [Halmos, §60 Th. A]."]
@@ -265,13 +265,13 @@ theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s)
     (hf : Measurable f) : (μ s * ∫⁻ y, f y ∂ν) = ∫⁻ x, ν ((fun z => z * x) ⁻¹' s) * f x⁻¹ ∂μ :=
   by
   rw [← set_lintegral_one, ← lintegral_indicator _ sm, ←
-    lintegral_lintegral_mul (measurable_const.indicator sm).AeMeasurable hf.ae_measurable, ←
+    lintegral_lintegral_mul (measurable_const.indicator sm).AEMeasurable hf.ae_measurable, ←
     lintegral_lintegral_mul_inv μ ν]
   swap
   ·
     exact
       (((measurable_const.indicator sm).comp measurable_fst).mul
-          (hf.comp measurable_snd)).AeMeasurable
+          (hf.comp measurable_snd)).AEMeasurable
   have ms :
     ∀ x : G, Measurable fun y => ((fun z => z * x) ⁻¹' s).indicator (fun z => (1 : ℝ≥0∞)) y :=
     fun x => measurable_const.indicator (measurable_mul_const _ sm)
@@ -293,15 +293,15 @@ theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s)
 /-- Any two nonzero left-invariant measures are absolutely continuous w.r.t. each other. -/
 @[to_additive
       " Any two nonzero left-invariant measures are absolutely continuous w.r.t. each\nother. "]
-theorem absolutelyContinuousOfIsMulLeftInvariant [IsMulLeftInvariant ν] (hν : ν ≠ 0) : μ ≪ ν :=
+theorem absolutelyContinuous_of_isMulLeftInvariant [IsMulLeftInvariant ν] (hν : ν ≠ 0) : μ ≪ ν :=
   by
   refine' absolutely_continuous.mk fun s sm hνs => _
   have h1 := measure_mul_lintegral_eq μ ν sm 1 measurable_one
   simp_rw [Pi.one_apply, lintegral_one, mul_one, (measure_mul_right_null ν _).mpr hνs,
     lintegral_zero, mul_eq_zero, measure_univ_eq_zero.not.mpr hν, or_false_iff] at h1
   exact h1
-#align measure_theory.absolutely_continuous_of_is_mul_left_invariant MeasureTheory.absolutelyContinuousOfIsMulLeftInvariant
-#align measure_theory.absolutely_continuous_of_is_add_left_invariant MeasureTheory.absolutely_continuous_of_is_add_left_invariant
+#align measure_theory.absolutely_continuous_of_is_mul_left_invariant MeasureTheory.absolutelyContinuous_of_isMulLeftInvariant
+#align measure_theory.absolutely_continuous_of_is_add_left_invariant MeasureTheory.absolutelyContinuous_of_is_add_left_invariant
 
 @[to_additive]
 theorem ae_measure_preimage_mul_right_lt_top [IsMulLeftInvariant ν] (sm : MeasurableSet s)
@@ -390,70 +390,70 @@ end LeftInvariant
 section RightInvariant
 
 @[to_additive measure_preserving_prod_add_right]
-theorem measurePreservingProdMulRight [IsMulRightInvariant ν] :
+theorem measurePreserving_prod_mul_right [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.2 * z.1)) (μ.Prod ν) (μ.Prod ν) :=
-  (MeasurePreserving.id μ).skewProduct (measurable_snd.mul measurable_fst) <|
+  (MeasurePreserving.id μ).skew_product (measurable_snd.mul measurable_fst) <|
     Filter.eventually_of_forall <| map_mul_right_eq_self ν
-#align measure_theory.measure_preserving_prod_mul_right MeasureTheory.measurePreservingProdMulRight
-#align measure_theory.measure_preserving_prod_add_right MeasureTheory.measure_preserving_prod_add_right
+#align measure_theory.measure_preserving_prod_mul_right MeasureTheory.measurePreserving_prod_mul_right
+#align measure_theory.measure_preserving_prod_add_right MeasureTheory.measurePreserving_prod_add_right
 
 /-- The map `(x, y) ↦ (y, xy)` sends the measure `μ × ν` to `ν × μ`. -/
 @[to_additive measure_preserving_prod_add_swap_right
       " The map `(x, y) ↦ (y, x + y)` sends the measure `μ × ν` to `ν × μ`. "]
-theorem measurePreservingProdMulSwapRight [IsMulRightInvariant μ] :
+theorem measurePreserving_prod_mul_swap_right [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.1 * z.2)) (μ.Prod ν) (ν.Prod μ) :=
-  (measurePreservingProdMulRight ν μ).comp measurePreservingSwap
-#align measure_theory.measure_preserving_prod_mul_swap_right MeasureTheory.measurePreservingProdMulSwapRight
-#align measure_theory.measure_preserving_prod_add_swap_right MeasureTheory.measure_preserving_prod_add_swap_right
+  (measurePreserving_prod_mul_right ν μ).comp measurePreserving_swap
+#align measure_theory.measure_preserving_prod_mul_swap_right MeasureTheory.measurePreserving_prod_mul_swap_right
+#align measure_theory.measure_preserving_prod_add_swap_right MeasureTheory.measurePreserving_prod_add_swap_right
 
 /-- The map `(x, y) ↦ (xy, y)` preserves the measure `μ × ν`. -/
 @[to_additive measure_preserving_add_prod
       " The map `(x, y) ↦ (x + y, y)` preserves the measure `μ × ν`. "]
-theorem measurePreservingMulProd [IsMulRightInvariant μ] :
+theorem measurePreserving_mul_prod [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.1 * z.2, z.2)) (μ.Prod ν) (μ.Prod ν) :=
-  measurePreservingSwap.comp <| by apply measure_preserving_prod_mul_swap_right μ ν
-#align measure_theory.measure_preserving_mul_prod MeasureTheory.measurePreservingMulProd
-#align measure_theory.measure_preserving_add_prod MeasureTheory.measure_preserving_add_prod
+  measurePreserving_swap.comp <| by apply measure_preserving_prod_mul_swap_right μ ν
+#align measure_theory.measure_preserving_mul_prod MeasureTheory.measurePreserving_mul_prod
+#align measure_theory.measure_preserving_add_prod MeasureTheory.measurePreserving_add_prod
 
 variable [HasMeasurableInv G]
 
 /-- The map `(x, y) ↦ (x, y / x)` is measure-preserving. -/
 @[to_additive measure_preserving_prod_sub "The map `(x, y) ↦ (x, y - x)` is measure-preserving."]
-theorem measurePreservingProdDiv [IsMulRightInvariant ν] :
+theorem measurePreserving_prod_div [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.2 / z.1)) (μ.Prod ν) (μ.Prod ν) :=
-  (measurePreservingProdMulRight μ ν).symm (MeasurableEquiv.shearDivRight G).symm
-#align measure_theory.measure_preserving_prod_div MeasureTheory.measurePreservingProdDiv
-#align measure_theory.measure_preserving_prod_sub MeasureTheory.measure_preserving_prod_sub
+  (measurePreserving_prod_mul_right μ ν).symm (MeasurableEquiv.shearDivRight G).symm
+#align measure_theory.measure_preserving_prod_div MeasureTheory.measurePreserving_prod_div
+#align measure_theory.measure_preserving_prod_sub MeasureTheory.measurePreserving_prod_sub
 
 /-- The map `(x, y) ↦ (y, x / y)` sends `μ × ν` to `ν × μ`. -/
 @[to_additive measure_preserving_prod_sub_swap
       "The map `(x, y) ↦ (y, x - y)` sends `μ × ν` to `ν × μ`."]
-theorem measurePreservingProdDivSwap [IsMulRightInvariant μ] :
+theorem measurePreserving_prod_div_swap [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.1 / z.2)) (μ.Prod ν) (ν.Prod μ) :=
-  (measurePreservingProdDiv ν μ).comp measurePreservingSwap
-#align measure_theory.measure_preserving_prod_div_swap MeasureTheory.measurePreservingProdDivSwap
-#align measure_theory.measure_preserving_prod_sub_swap MeasureTheory.measure_preserving_prod_sub_swap
+  (measurePreserving_prod_div ν μ).comp measurePreserving_swap
+#align measure_theory.measure_preserving_prod_div_swap MeasureTheory.measurePreserving_prod_div_swap
+#align measure_theory.measure_preserving_prod_sub_swap MeasureTheory.measurePreserving_prod_sub_swap
 
 /-- The map `(x, y) ↦ (x / y, y)` preserves the measure `μ × ν`. -/
 @[to_additive measure_preserving_sub_prod
       " The map `(x, y) ↦ (x - y, y)` preserves the measure `μ × ν`. "]
-theorem measurePreservingDivProd [IsMulRightInvariant μ] :
+theorem measurePreserving_div_prod [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.1 / z.2, z.2)) (μ.Prod ν) (μ.Prod ν) :=
-  measurePreservingSwap.comp <| by apply measure_preserving_prod_div_swap μ ν
-#align measure_theory.measure_preserving_div_prod MeasureTheory.measurePreservingDivProd
-#align measure_theory.measure_preserving_sub_prod MeasureTheory.measure_preserving_sub_prod
+  measurePreserving_swap.comp <| by apply measure_preserving_prod_div_swap μ ν
+#align measure_theory.measure_preserving_div_prod MeasureTheory.measurePreserving_div_prod
+#align measure_theory.measure_preserving_sub_prod MeasureTheory.measurePreserving_sub_prod
 
 /-- The map `(x, y) ↦ (xy, x⁻¹)` is measure-preserving. -/
 @[to_additive measure_preserving_add_prod_neg_right
       "The map `(x, y) ↦ (x + y, - x)` is measure-preserving."]
-theorem measurePreservingMulProdInvRight [IsMulRightInvariant μ] [IsMulRightInvariant ν] :
+theorem measurePreserving_mul_prod_inv_right [IsMulRightInvariant μ] [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1 * z.2, z.1⁻¹)) (μ.Prod ν) (μ.Prod ν) :=
   by
   convert(measure_preserving_prod_div_swap ν μ).comp (measure_preserving_prod_mul_swap_right μ ν)
   ext1 ⟨x, y⟩
   simp_rw [Function.comp_apply, div_mul_eq_div_div_swap, div_self', one_div]
-#align measure_theory.measure_preserving_mul_prod_inv_right MeasureTheory.measurePreservingMulProdInvRight
-#align measure_theory.measure_preserving_add_prod_neg_right MeasureTheory.measure_preserving_add_prod_neg_right
+#align measure_theory.measure_preserving_mul_prod_inv_right MeasureTheory.measurePreserving_mul_prod_inv_right
+#align measure_theory.measure_preserving_add_prod_neg_right MeasureTheory.measurePreserving_add_prod_neg_right
 
 end RightInvariant
 
@@ -462,71 +462,71 @@ section QuasiMeasurePreserving
 variable [HasMeasurableInv G]
 
 @[to_additive]
-theorem quasiMeasurePreservingInvOfRightInvariant [IsMulRightInvariant μ] :
+theorem quasiMeasurePreserving_inv_of_right_invariant [IsMulRightInvariant μ] :
     QuasiMeasurePreserving (Inv.inv : G → G) μ μ :=
   by
   rw [← μ.inv_inv]
   exact
     (quasi_measure_preserving_inv μ.inv).mono (inv_absolutely_continuous μ.inv)
       (absolutely_continuous_inv μ.inv)
-#align measure_theory.quasi_measure_preserving_inv_of_right_invariant MeasureTheory.quasiMeasurePreservingInvOfRightInvariant
-#align measure_theory.quasi_measure_preserving_neg_of_right_invariant MeasureTheory.quasi_measure_preserving_neg_of_right_invariant
+#align measure_theory.quasi_measure_preserving_inv_of_right_invariant MeasureTheory.quasiMeasurePreserving_inv_of_right_invariant
+#align measure_theory.quasi_measure_preserving_neg_of_right_invariant MeasureTheory.quasiMeasurePreserving_neg_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreservingDivLeft [IsMulLeftInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_div_left [IsMulLeftInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g / h) μ μ :=
   by
   simp_rw [div_eq_mul_inv]
   exact
     (measure_preserving_mul_left μ g).QuasiMeasurePreserving.comp (quasi_measure_preserving_inv μ)
-#align measure_theory.quasi_measure_preserving_div_left MeasureTheory.quasiMeasurePreservingDivLeft
-#align measure_theory.quasi_measure_preserving_sub_left MeasureTheory.quasi_measure_preserving_sub_left
+#align measure_theory.quasi_measure_preserving_div_left MeasureTheory.quasiMeasurePreserving_div_left
+#align measure_theory.quasi_measure_preserving_sub_left MeasureTheory.quasiMeasurePreserving_sub_left
 
 @[to_additive]
-theorem quasiMeasurePreservingDivLeftOfRightInvariant [IsMulRightInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_div_left_of_right_invariant [IsMulRightInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g / h) μ μ :=
   by
   rw [← μ.inv_inv]
   exact
     (quasi_measure_preserving_div_left μ.inv g).mono (inv_absolutely_continuous μ.inv)
       (absolutely_continuous_inv μ.inv)
-#align measure_theory.quasi_measure_preserving_div_left_of_right_invariant MeasureTheory.quasiMeasurePreservingDivLeftOfRightInvariant
-#align measure_theory.quasi_measure_preserving_sub_left_of_right_invariant MeasureTheory.quasi_measure_preserving_sub_left_of_right_invariant
+#align measure_theory.quasi_measure_preserving_div_left_of_right_invariant MeasureTheory.quasiMeasurePreserving_div_left_of_right_invariant
+#align measure_theory.quasi_measure_preserving_sub_left_of_right_invariant MeasureTheory.quasiMeasurePreserving_sub_left_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreservingDivOfRightInvariant [IsMulRightInvariant μ] :
+theorem quasiMeasurePreserving_div_of_right_invariant [IsMulRightInvariant μ] :
     QuasiMeasurePreserving (fun p : G × G => p.1 / p.2) (μ.Prod ν) μ :=
   by
   refine' quasi_measure_preserving.prod_of_left measurable_div (eventually_of_forall fun y => _)
   exact (measure_preserving_div_right μ y).QuasiMeasurePreserving
-#align measure_theory.quasi_measure_preserving_div_of_right_invariant MeasureTheory.quasiMeasurePreservingDivOfRightInvariant
-#align measure_theory.quasi_measure_preserving_sub_of_right_invariant MeasureTheory.quasi_measure_preserving_sub_of_right_invariant
+#align measure_theory.quasi_measure_preserving_div_of_right_invariant MeasureTheory.quasiMeasurePreserving_div_of_right_invariant
+#align measure_theory.quasi_measure_preserving_sub_of_right_invariant MeasureTheory.quasiMeasurePreserving_sub_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreservingDiv [IsMulLeftInvariant μ] :
+theorem quasiMeasurePreserving_div [IsMulLeftInvariant μ] :
     QuasiMeasurePreserving (fun p : G × G => p.1 / p.2) (μ.Prod ν) μ :=
-  (quasiMeasurePreservingDivOfRightInvariant μ.inv ν).mono
-    ((absolutelyContinuousInv μ).Prod AbsolutelyContinuous.rfl) (invAbsolutelyContinuous μ)
-#align measure_theory.quasi_measure_preserving_div MeasureTheory.quasiMeasurePreservingDiv
-#align measure_theory.quasi_measure_preserving_sub MeasureTheory.quasi_measure_preserving_sub
+  (quasiMeasurePreserving_div_of_right_invariant μ.inv ν).mono
+    ((absolutelyContinuous_inv μ).Prod AbsolutelyContinuous.rfl) (inv_absolutelyContinuous μ)
+#align measure_theory.quasi_measure_preserving_div MeasureTheory.quasiMeasurePreserving_div
+#align measure_theory.quasi_measure_preserving_sub MeasureTheory.quasiMeasurePreserving_sub
 
 /-- A *left*-invariant measure is quasi-preserved by *right*-multiplication.
 This should not be confused with `(measure_preserving_mul_right μ g).quasi_measure_preserving`. -/
 @[to_additive
       "A *left*-invariant measure is quasi-preserved by *right*-addition.\nThis should not be confused with `(measure_preserving_add_right μ g).quasi_measure_preserving`. "]
-theorem quasiMeasurePreservingMulRight [IsMulLeftInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_mul_right [IsMulLeftInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => h * g) μ μ :=
   by
   refine' ⟨measurable_mul_const g, absolutely_continuous.mk fun s hs => _⟩
   rw [map_apply (measurable_mul_const g) hs, measure_mul_right_null]; exact id
-#align measure_theory.quasi_measure_preserving_mul_right MeasureTheory.quasiMeasurePreservingMulRight
-#align measure_theory.quasi_measure_preserving_add_right MeasureTheory.quasi_measure_preserving_add_right
+#align measure_theory.quasi_measure_preserving_mul_right MeasureTheory.quasiMeasurePreserving_mul_right
+#align measure_theory.quasi_measure_preserving_add_right MeasureTheory.quasiMeasurePreserving_add_right
 
 /-- A *right*-invariant measure is quasi-preserved by *left*-multiplication.
 This should not be confused with `(measure_preserving_mul_left μ g).quasi_measure_preserving`. -/
 @[to_additive
       "A *right*-invariant measure is quasi-preserved by *left*-addition.\nThis should not be confused with `(measure_preserving_add_left μ g).quasi_measure_preserving`. "]
-theorem quasiMeasurePreservingMulLeft [IsMulRightInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_mul_left [IsMulRightInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g * h) μ μ :=
   by
   have :=
@@ -538,8 +538,8 @@ theorem quasiMeasurePreservingMulLeft [IsMulRightInvariant μ] (g : G) :
       (this.comp (quasi_measure_preserving_inv_of_right_invariant μ))
   simp_rw [Function.comp, mul_inv_rev, inv_inv] at this
   exact this
-#align measure_theory.quasi_measure_preserving_mul_left MeasureTheory.quasiMeasurePreservingMulLeft
-#align measure_theory.quasi_measure_preserving_add_left MeasureTheory.quasi_measure_preserving_add_left
+#align measure_theory.quasi_measure_preserving_mul_left MeasureTheory.quasiMeasurePreserving_mul_left
+#align measure_theory.quasi_measure_preserving_add_left MeasureTheory.quasiMeasurePreserving_add_left
 
 end QuasiMeasurePreserving
 

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

@@ -160,7 +160,7 @@ where `S` is the map `(x, y) ↦ (x, xy)` and `R` is `prod.swap`. -/
 theorem measurePreservingMulProdInv [IsMulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.2 * z.1, z.1⁻¹)) (μ.Prod ν) (μ.Prod ν) :=
   by
-  convert (measure_preserving_prod_inv_mul_swap ν μ).comp (measure_preserving_prod_mul_swap μ ν)
+  convert(measure_preserving_prod_inv_mul_swap ν μ).comp (measure_preserving_prod_mul_swap μ ν)
   ext1 ⟨x, y⟩
   simp_rw [Function.comp_apply, mul_inv_rev, inv_mul_cancel_right]
 #align measure_theory.measure_preserving_mul_prod_inv MeasureTheory.measurePreservingMulProdInv
@@ -449,7 +449,7 @@ theorem measurePreservingDivProd [IsMulRightInvariant μ] :
 theorem measurePreservingMulProdInvRight [IsMulRightInvariant μ] [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1 * z.2, z.1⁻¹)) (μ.Prod ν) (μ.Prod ν) :=
   by
-  convert (measure_preserving_prod_div_swap ν μ).comp (measure_preserving_prod_mul_swap_right μ ν)
+  convert(measure_preserving_prod_div_swap ν μ).comp (measure_preserving_prod_mul_swap_right μ ν)
   ext1 ⟨x, y⟩
   simp_rw [Function.comp_apply, div_mul_eq_div_div_swap, div_self', one_div]
 #align measure_theory.measure_preserving_mul_prod_inv_right MeasureTheory.measurePreservingMulProdInvRight

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

@@ -46,7 +46,7 @@ open Function MeasureTheory
 
 open Filter hiding map
 
-open Classical Ennreal Pointwise MeasureTheory
+open Classical ENNReal Pointwise MeasureTheory
 
 variable (G : Type _) [MeasurableSpace G]
 
@@ -317,7 +317,7 @@ theorem ae_measure_preimage_mul_right_lt_top [IsMulLeftInvariant ν] (sm : Measu
     indicator_mul_right _ fun x => ν ((fun y => y * x) ⁻¹' s), Function.comp, Pi.one_apply,
     mul_one] at h1
   rw [← lintegral_indicator _ hA, ← h1]
-  exact Ennreal.mul_ne_top hμs h3A.ne
+  exact ENNReal.mul_ne_top hμs h3A.ne
 #align measure_theory.ae_measure_preimage_mul_right_lt_top MeasureTheory.ae_measure_preimage_mul_right_lt_top
 #align measure_theory.ae_measure_preimage_add_right_lt_top MeasureTheory.ae_measure_preimage_add_right_lt_top
 
@@ -355,7 +355,7 @@ theorem measure_lintegral_div_measure [IsMulLeftInvariant ν] (sm : MeasurableSe
   simp_rw [measure_mul_lintegral_eq μ ν sm g hg, g, inv_inv]
   refine' lintegral_congr_ae _
   refine' (ae_measure_preimage_mul_right_lt_top_of_ne_zero μ ν sm h2s h3s).mono fun x hx => _
-  simp_rw [Ennreal.mul_div_cancel' (measure_mul_right_ne_zero ν h2s _) hx.ne]
+  simp_rw [ENNReal.mul_div_cancel' (measure_mul_right_ne_zero ν h2s _) hx.ne]
 #align measure_theory.measure_lintegral_div_measure MeasureTheory.measure_lintegral_div_measure
 #align measure_theory.measure_lintegral_sub_measure MeasureTheory.measure_lintegral_sub_measure
 
@@ -381,7 +381,7 @@ theorem measure_eq_div_smul [IsMulLeftInvariant ν] (hs : MeasurableSet s) (h2s
     (h3s : ν s ≠ ∞) : μ = (μ s / ν s) • ν := by
   ext1 t ht
   rw [smul_apply, smul_eq_mul, mul_comm, ← mul_div_assoc, mul_comm,
-    measure_mul_measure_eq μ ν hs ht h2s h3s, mul_div_assoc, Ennreal.mul_div_cancel' h2s h3s]
+    measure_mul_measure_eq μ ν hs ht h2s h3s, mul_div_assoc, ENNReal.mul_div_cancel' h2s h3s]
 #align measure_theory.measure_eq_div_smul MeasureTheory.measure_eq_div_smul
 #align measure_theory.measure_eq_sub_vadd MeasureTheory.measure_eq_sub_vadd
 

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

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)

@@ -51,9 +51,7 @@ open Filter hiding map
 open scoped Classical ENNReal Pointwise MeasureTheory
 
 variable (G : Type*) [MeasurableSpace G]
-
 variable [Group G] [MeasurableMul₂ G]
-
 variable (μ ν : Measure G) [SigmaFinite ν] [SigmaFinite μ] {s : Set G}
 
 /-- The map `(x, y) ↦ (x, xy)` as a `MeasurableEquiv`. -/

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

@@ -330,7 +330,7 @@ theorem measure_lintegral_div_measure [IsMulLeftInvariant ν] (sm : MeasurableSe
   set g := fun y => f y⁻¹ / ν ((fun x => x * y⁻¹) ⁻¹' s)
   have hg : Measurable g :=
     (hf.comp measurable_inv).div ((measurable_measure_mul_right ν sm).comp measurable_inv)
-  simp_rw [measure_mul_lintegral_eq μ ν sm g hg, inv_inv]
+  simp_rw [measure_mul_lintegral_eq μ ν sm g hg, g, inv_inv]
   refine' lintegral_congr_ae _
   refine' (ae_measure_preimage_mul_right_lt_top_of_ne_zero μ ν sm h2s h3s).mono fun x hx => _
   simp_rw [ENNReal.mul_div_cancel' (measure_mul_right_ne_zero ν h2s _) hx.ne]

We prove that two regular Haar measures in a locally compact group coincide up to scalar multiplication, and the same thing for inner regular Haar measures. This is implemented in a new file MeasureTheory.Measure.Haar.Unique. A few results that used to be in the MeasureTheory.Measure.Haar.Basic are moved to this file (and extended) so several imports have to be changed.

@@ -32,6 +32,11 @@ scalar multiplication.
 The proof in [Halmos] seems to contain an omission in §60 Th. A, see
 `MeasureTheory.measure_lintegral_div_measure`.
 
+Note that this theory only applies in measurable groups, i.e., when multiplication and inversion
+are measurable. This is not the case in general in locally compact groups, or even in compact
+groups, when the topology is not second-countable. For arguments along the same line, but using
+continuous functions instead of measurable sets and working in the general locally compact
+setting, see the file `MeasureTheory.Measure.Haar.Unique.lean`.
 -/
 
 

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

This has nice performance benefits.

@@ -45,7 +45,7 @@ open Filter hiding map
 
 open scoped Classical ENNReal Pointwise MeasureTheory
 
-variable (G : Type _) [MeasurableSpace G]
+variable (G : Type*) [MeasurableSpace G]
 
 variable [Group G] [MeasurableMul₂ G]
 

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Floris van Doorn. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Floris van Doorn
-
-! This file was ported from Lean 3 source module measure_theory.group.prod
-! 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.Constructions.Prod.Basic
 import Mathlib.MeasureTheory.Group.Measure
 
+#align_import measure_theory.group.prod from "leanprover-community/mathlib"@"fd5edc43dc4f10b85abfe544b88f82cf13c5f844"
+
 /-!
 # Measure theory in the product of groups
 In this file we show properties about measure theory in products of measurable groups

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

@@ -27,7 +27,7 @@ preserves the measure `μ × ν`, which means that
 ```
   ∫ x, ∫ y, h x y ∂ν ∂μ = ∫ x, ∫ y, h (y * x) x⁻¹ ∂ν ∂μ
 ```
-If we apply this to `h x y := e x * f y⁻¹ / ν ((λ h, h * y⁻¹) ⁻¹' s)`, we can rewrite the RHS to
+If we apply this to `h x y := e x * f y⁻¹ / ν ((fun h ↦ h * y⁻¹) ⁻¹' s)`, we can rewrite the RHS to
 `μ(t)`, and the LHS to `c * μ(s)`, where `c = c(ν)` does not depend on `μ`.
 Applying this to `μ` and to `ν` gives `μ (t) / μ (s) = ν (t) / ν (s)`, which is the uniqueness up to
 scalar multiplication.

I have misported is_foo to Foo because I misunderstood the rule for IsLawfulFoo. This PR recover Is of Foo which is ported from is_foo. This PR also renames some misported theorems.

@@ -86,7 +86,7 @@ This condition is part of the definition of a measurable group in [Halmos, §59]
 There, the map in this lemma is called `S`. -/
 @[to_additive measurePreserving_prod_add
 " The shear mapping `(x, y) ↦ (x, x + y)` preserves the measure `μ × ν`. "]
-theorem measurePreserving_prod_mul [MulLeftInvariant ν] :
+theorem measurePreserving_prod_mul [IsMulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.1 * z.2)) (μ.prod ν) (μ.prod ν) :=
   (MeasurePreserving.id μ).skew_product measurable_mul <|
     Filter.eventually_of_forall <| map_mul_left_eq_self ν
@@ -98,7 +98,7 @@ This is the map `SR` in [Halmos, §59].
 `S` is the map `(x, y) ↦ (x, xy)` and `R` is `Prod.swap`. -/
 @[to_additive measurePreserving_prod_add_swap
 " The map `(x, y) ↦ (y, y + x)` sends the measure `μ × ν` to `ν × μ`. "]
-theorem measurePreserving_prod_mul_swap [MulLeftInvariant μ] :
+theorem measurePreserving_prod_mul_swap [IsMulLeftInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.2 * z.1)) (μ.prod ν) (ν.prod μ) :=
   (measurePreserving_prod_mul ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_mul_swap MeasureTheory.measurePreserving_prod_mul_swap
@@ -124,13 +124,13 @@ This is the function `S⁻¹` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)`. -/
 @[to_additive measurePreserving_prod_neg_add
 "The map `(x, y) ↦ (x, - x + y)` is measure-preserving."]
-theorem measurePreserving_prod_inv_mul [MulLeftInvariant ν] :
+theorem measurePreserving_prod_inv_mul [IsMulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.1⁻¹ * z.2)) (μ.prod ν) (μ.prod ν) :=
   (measurePreserving_prod_mul μ ν).symm <| MeasurableEquiv.shearMulRight G
 #align measure_theory.measure_preserving_prod_inv_mul MeasureTheory.measurePreserving_prod_inv_mul
 #align measure_theory.measure_preserving_prod_neg_add MeasureTheory.measurePreserving_prod_neg_add
 
-variable [MulLeftInvariant μ]
+variable [IsMulLeftInvariant μ]
 
 /-- The map `(x, y) ↦ (y, y⁻¹x)` sends `μ × ν` to `ν × μ`.
 This is the function `S⁻¹R` in [Halmos, §59],
@@ -148,7 +148,7 @@ This is the function `S⁻¹RSR` in [Halmos, §59],
 where `S` is the map `(x, y) ↦ (x, xy)` and `R` is `Prod.swap`. -/
 @[to_additive measurePreserving_add_prod_neg
 "The map `(x, y) ↦ (y + x, - x)` is measure-preserving."]
-theorem measurePreserving_mul_prod_inv [MulLeftInvariant ν] :
+theorem measurePreserving_mul_prod_inv [IsMulLeftInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.2 * z.1, z.1⁻¹)) (μ.prod ν) (μ.prod ν) := by
   convert (measurePreserving_prod_inv_mul_swap ν μ).comp (measurePreserving_prod_mul_swap μ ν)
     using 1
@@ -195,7 +195,7 @@ theorem absolutelyContinuous_inv : μ ≪ μ.inv := by
 #align measure_theory.absolutely_continuous_neg MeasureTheory.absolutelyContinuous_neg
 
 @[to_additive]
-theorem lintegral_lintegral_mul_inv [MulLeftInvariant ν] (f : G → G → ℝ≥0∞)
+theorem lintegral_lintegral_mul_inv [IsMulLeftInvariant ν] (f : G → G → ℝ≥0∞)
     (hf : AEMeasurable (uncurry f) (μ.prod ν)) :
     (∫⁻ x, ∫⁻ y, f (y * x) x⁻¹ ∂ν ∂μ) = ∫⁻ x, ∫⁻ y, f x y ∂ν ∂μ := by
   have h : Measurable fun z : G × G => (z.2 * z.1, z.1⁻¹) :=
@@ -244,7 +244,7 @@ theorem absolutelyContinuous_map_div_left (g : G) : μ ≪ map (fun h => g / h)
 
 /-- This is the computation performed in the proof of [Halmos, §60 Th. A]. -/
 @[to_additive "This is the computation performed in the proof of [Halmos, §60 Th. A]."]
-theorem measure_mul_lintegral_eq [MulLeftInvariant ν] (sm : MeasurableSet s) (f : G → ℝ≥0∞)
+theorem measure_mul_lintegral_eq [IsMulLeftInvariant ν] (sm : MeasurableSet s) (f : G → ℝ≥0∞)
     (hf : Measurable f) : (μ s * ∫⁻ y, f y ∂ν) = ∫⁻ x, ν ((fun z => z * x) ⁻¹' s) * f x⁻¹ ∂μ := by
   rw [← set_lintegral_one, ← lintegral_indicator _ sm,
     ← lintegral_lintegral_mul (measurable_const.indicator sm).aemeasurable hf.aemeasurable,
@@ -266,17 +266,17 @@ theorem measure_mul_lintegral_eq [MulLeftInvariant ν] (sm : MeasurableSet s) (f
 /-- Any two nonzero left-invariant measures are absolutely continuous w.r.t. each other. -/
 @[to_additive
 " Any two nonzero left-invariant measures are absolutely continuous w.r.t. each other. "]
-theorem absolutelyContinuous_of_mulLeftInvariant [MulLeftInvariant ν] (hν : ν ≠ 0) : μ ≪ ν := by
+theorem absolutelyContinuous_of_isMulLeftInvariant [IsMulLeftInvariant ν] (hν : ν ≠ 0) : μ ≪ ν := by
   refine' AbsolutelyContinuous.mk fun s sm hνs => _
   have h1 := measure_mul_lintegral_eq μ ν sm 1 measurable_one
   simp_rw [Pi.one_apply, lintegral_one, mul_one, (measure_mul_right_null ν _).mpr hνs,
     lintegral_zero, mul_eq_zero (M₀ := ℝ≥0∞), measure_univ_eq_zero.not.mpr hν, or_false_iff] at h1
   exact h1
-#align measure_theory.absolutely_continuous_of_is_mul_left_invariant MeasureTheory.absolutelyContinuous_of_mulLeftInvariant
-#align measure_theory.absolutely_continuous_of_is_add_left_invariant MeasureTheory.absolutelyContinuous_of_addLeftInvariant
+#align measure_theory.absolutely_continuous_of_is_mul_left_invariant MeasureTheory.absolutelyContinuous_of_isMulLeftInvariant
+#align measure_theory.absolutely_continuous_of_is_add_left_invariant MeasureTheory.absolutelyContinuous_of_isAddLeftInvariant
 
 @[to_additive]
-theorem ae_measure_preimage_mul_right_lt_top [MulLeftInvariant ν] (sm : MeasurableSet s)
+theorem ae_measure_preimage_mul_right_lt_top [IsMulLeftInvariant ν] (sm : MeasurableSet s)
     (hμs : μ s ≠ ∞) : ∀ᵐ x ∂μ, ν ((fun y => y * x) ⁻¹' s) < ∞ := by
   refine' ae_of_forall_measure_lt_top_ae_restrict' ν.inv _ _
   intro A hA _ h3A
@@ -293,11 +293,11 @@ theorem ae_measure_preimage_mul_right_lt_top [MulLeftInvariant ν] (sm : Measura
 #align measure_theory.ae_measure_preimage_add_right_lt_top MeasureTheory.ae_measure_preimage_add_right_lt_top
 
 @[to_additive]
-theorem ae_measure_preimage_mul_right_lt_top_of_ne_zero [MulLeftInvariant ν]
+theorem ae_measure_preimage_mul_right_lt_top_of_ne_zero [IsMulLeftInvariant ν]
     (sm : MeasurableSet s) (h2s : ν s ≠ 0) (h3s : ν s ≠ ∞) :
     ∀ᵐ x ∂μ, ν ((fun y => y * x) ⁻¹' s) < ∞ := by
   refine' (ae_measure_preimage_mul_right_lt_top ν ν sm h3s).filter_mono _
-  refine' (absolutelyContinuous_of_mulLeftInvariant μ ν _).ae_le
+  refine' (absolutelyContinuous_of_isMulLeftInvariant μ ν _).ae_le
   refine' mt _ h2s
   intro hν
   rw [hν, Measure.coe_zero, Pi.zero_apply]
@@ -322,7 +322,7 @@ Note: There is a gap in the last step of the proof in [Halmos]. In the last line
 `g(-x) + ν(s - x) = f(x)` holds if we can prove that `0 < ν(s - x) < ∞`. The first inequality
 follows from §59, Th. D, but the second inequality is not justified. We prove this inequality for
 almost all `x` in `MeasureTheory.ae_measure_preimage_add_right_lt_top_of_ne_zero`."]
-theorem measure_lintegral_div_measure [MulLeftInvariant ν] (sm : MeasurableSet s) (h2s : ν s ≠ 0)
+theorem measure_lintegral_div_measure [IsMulLeftInvariant ν] (sm : MeasurableSet s) (h2s : ν s ≠ 0)
     (h3s : ν s ≠ ∞) (f : G → ℝ≥0∞) (hf : Measurable f) :
     (μ s * ∫⁻ y, f y⁻¹ / ν ((fun x => x * y⁻¹) ⁻¹' s) ∂ν) = ∫⁻ x, f x ∂μ := by
   set g := fun y => f y⁻¹ / ν ((fun x => x * y⁻¹) ⁻¹' s)
@@ -336,7 +336,7 @@ theorem measure_lintegral_div_measure [MulLeftInvariant ν] (sm : MeasurableSet
 #align measure_theory.measure_lintegral_sub_measure MeasureTheory.measure_lintegral_sub_measure
 
 @[to_additive]
-theorem measure_mul_measure_eq [MulLeftInvariant ν] {s t : Set G} (hs : MeasurableSet s)
+theorem measure_mul_measure_eq [IsMulLeftInvariant ν] {s t : Set G} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (h2s : ν s ≠ 0) (h3s : ν s ≠ ∞) : μ s * ν t = ν s * μ t := by
   have h1 :=
     measure_lintegral_div_measure ν ν hs h2s h3s (t.indicator fun _ => 1)
@@ -352,7 +352,7 @@ theorem measure_mul_measure_eq [MulLeftInvariant ν] {s t : Set G} (hs : Measura
 /-- Left invariant Borel measures on a measurable group are unique (up to a scalar). -/
 @[to_additive
 " Left invariant Borel measures on an additive measurable group are unique (up to a scalar). "]
-theorem measure_eq_div_smul [MulLeftInvariant ν] (hs : MeasurableSet s) (h2s : ν s ≠ 0)
+theorem measure_eq_div_smul [IsMulLeftInvariant ν] (hs : MeasurableSet s) (h2s : ν s ≠ 0)
     (h3s : ν s ≠ ∞) : μ = (μ s / ν s) • ν := by
   ext1 t ht
   rw [smul_apply, smul_eq_mul, mul_comm, ← mul_div_assoc, mul_comm,
@@ -365,7 +365,7 @@ end LeftInvariant
 section RightInvariant
 
 @[to_additive measurePreserving_prod_add_right]
-theorem measurePreserving_prod_mul_right [MulRightInvariant ν] :
+theorem measurePreserving_prod_mul_right [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.2 * z.1)) (μ.prod ν) (μ.prod ν) :=
   MeasurePreserving.skew_product (g := fun x y => y * x) (MeasurePreserving.id μ)
     (measurable_snd.mul measurable_fst) <| Filter.eventually_of_forall <| map_mul_right_eq_self ν
@@ -375,7 +375,7 @@ theorem measurePreserving_prod_mul_right [MulRightInvariant ν] :
 /-- The map `(x, y) ↦ (y, xy)` sends the measure `μ × ν` to `ν × μ`. -/
 @[to_additive measurePreserving_prod_add_swap_right
 " The map `(x, y) ↦ (y, x + y)` sends the measure `μ × ν` to `ν × μ`. "]
-theorem measurePreserving_prod_mul_swap_right [MulRightInvariant μ] :
+theorem measurePreserving_prod_mul_swap_right [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.1 * z.2)) (μ.prod ν) (ν.prod μ) :=
   (measurePreserving_prod_mul_right ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_mul_swap_right MeasureTheory.measurePreserving_prod_mul_swap_right
@@ -384,7 +384,7 @@ theorem measurePreserving_prod_mul_swap_right [MulRightInvariant μ] :
 /-- The map `(x, y) ↦ (xy, y)` preserves the measure `μ × ν`. -/
 @[to_additive measurePreserving_add_prod
 " The map `(x, y) ↦ (x + y, y)` preserves the measure `μ × ν`. "]
-theorem measurePreserving_mul_prod [MulRightInvariant μ] :
+theorem measurePreserving_mul_prod [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.1 * z.2, z.2)) (μ.prod ν) (μ.prod ν) :=
   measurePreserving_swap.comp <| by apply measurePreserving_prod_mul_swap_right μ ν
 #align measure_theory.measure_preserving_mul_prod MeasureTheory.measurePreserving_mul_prod
@@ -394,7 +394,7 @@ variable [MeasurableInv G]
 
 /-- The map `(x, y) ↦ (x, y / x)` is measure-preserving. -/
 @[to_additive measurePreserving_prod_sub "The map `(x, y) ↦ (x, y - x)` is measure-preserving."]
-theorem measurePreserving_prod_div [MulRightInvariant ν] :
+theorem measurePreserving_prod_div [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1, z.2 / z.1)) (μ.prod ν) (μ.prod ν) :=
   (measurePreserving_prod_mul_right μ ν).symm (MeasurableEquiv.shearDivRight G).symm
 #align measure_theory.measure_preserving_prod_div MeasureTheory.measurePreserving_prod_div
@@ -403,7 +403,7 @@ theorem measurePreserving_prod_div [MulRightInvariant ν] :
 /-- The map `(x, y) ↦ (y, x / y)` sends `μ × ν` to `ν × μ`. -/
 @[to_additive measurePreserving_prod_sub_swap
       "The map `(x, y) ↦ (y, x - y)` sends `μ × ν` to `ν × μ`."]
-theorem measurePreserving_prod_div_swap [MulRightInvariant μ] :
+theorem measurePreserving_prod_div_swap [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.2, z.1 / z.2)) (μ.prod ν) (ν.prod μ) :=
   (measurePreserving_prod_div ν μ).comp measurePreserving_swap
 #align measure_theory.measure_preserving_prod_div_swap MeasureTheory.measurePreserving_prod_div_swap
@@ -412,7 +412,7 @@ theorem measurePreserving_prod_div_swap [MulRightInvariant μ] :
 /-- The map `(x, y) ↦ (x / y, y)` preserves the measure `μ × ν`. -/
 @[to_additive measurePreserving_sub_prod
 " The map `(x, y) ↦ (x - y, y)` preserves the measure `μ × ν`. "]
-theorem measurePreserving_div_prod [MulRightInvariant μ] :
+theorem measurePreserving_div_prod [IsMulRightInvariant μ] :
     MeasurePreserving (fun z : G × G => (z.1 / z.2, z.2)) (μ.prod ν) (μ.prod ν) :=
   measurePreserving_swap.comp <| by apply measurePreserving_prod_div_swap μ ν
 #align measure_theory.measure_preserving_div_prod MeasureTheory.measurePreserving_div_prod
@@ -421,7 +421,7 @@ theorem measurePreserving_div_prod [MulRightInvariant μ] :
 /-- The map `(x, y) ↦ (xy, x⁻¹)` is measure-preserving. -/
 @[to_additive measurePreserving_add_prod_neg_right
 "The map `(x, y) ↦ (x + y, - x)` is measure-preserving."]
-theorem measurePreserving_mul_prod_inv_right [MulRightInvariant μ] [MulRightInvariant ν] :
+theorem measurePreserving_mul_prod_inv_right [IsMulRightInvariant μ] [IsMulRightInvariant ν] :
     MeasurePreserving (fun z : G × G => (z.1 * z.2, z.1⁻¹)) (μ.prod ν) (μ.prod ν) := by
   convert (measurePreserving_prod_div_swap ν μ).comp (measurePreserving_prod_mul_swap_right μ ν)
     using 1
@@ -437,7 +437,7 @@ section QuasiMeasurePreserving
 variable [MeasurableInv G]
 
 @[to_additive]
-theorem quasiMeasurePreserving_inv_of_right_invariant [MulRightInvariant μ] :
+theorem quasiMeasurePreserving_inv_of_right_invariant [IsMulRightInvariant μ] :
     QuasiMeasurePreserving (Inv.inv : G → G) μ μ := by
   rw [← μ.inv_inv]
   exact
@@ -447,7 +447,7 @@ theorem quasiMeasurePreserving_inv_of_right_invariant [MulRightInvariant μ] :
 #align measure_theory.quasi_measure_preserving_neg_of_right_invariant MeasureTheory.quasiMeasurePreserving_neg_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreserving_div_left [MulLeftInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_div_left [IsMulLeftInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g / h) μ μ := by
   simp_rw [div_eq_mul_inv]
   exact
@@ -456,7 +456,7 @@ theorem quasiMeasurePreserving_div_left [MulLeftInvariant μ] (g : G) :
 #align measure_theory.quasi_measure_preserving_sub_left MeasureTheory.quasiMeasurePreserving_sub_left
 
 @[to_additive]
-theorem quasiMeasurePreserving_div_left_of_right_invariant [MulRightInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_div_left_of_right_invariant [IsMulRightInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g / h) μ μ := by
   rw [← μ.inv_inv]
   exact
@@ -466,7 +466,7 @@ theorem quasiMeasurePreserving_div_left_of_right_invariant [MulRightInvariant μ
 #align measure_theory.quasi_measure_preserving_sub_left_of_right_invariant MeasureTheory.quasiMeasurePreserving_sub_left_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreserving_div_of_right_invariant [MulRightInvariant μ] :
+theorem quasiMeasurePreserving_div_of_right_invariant [IsMulRightInvariant μ] :
     QuasiMeasurePreserving (fun p : G × G => p.1 / p.2) (μ.prod ν) μ := by
   refine' QuasiMeasurePreserving.prod_of_left measurable_div (eventually_of_forall fun y => _)
   exact (measurePreserving_div_right μ y).quasiMeasurePreserving
@@ -474,7 +474,7 @@ theorem quasiMeasurePreserving_div_of_right_invariant [MulRightInvariant μ] :
 #align measure_theory.quasi_measure_preserving_sub_of_right_invariant MeasureTheory.quasiMeasurePreserving_sub_of_right_invariant
 
 @[to_additive]
-theorem quasiMeasurePreserving_div [MulLeftInvariant μ] :
+theorem quasiMeasurePreserving_div [IsMulLeftInvariant μ] :
     QuasiMeasurePreserving (fun p : G × G => p.1 / p.2) (μ.prod ν) μ :=
   (quasiMeasurePreserving_div_of_right_invariant μ.inv ν).mono
     ((absolutelyContinuous_inv μ).prod AbsolutelyContinuous.rfl) (inv_absolutelyContinuous μ)
@@ -486,7 +486,7 @@ This should not be confused with `(measurePreserving_mul_right μ g).quasiMeasur
 @[to_additive
 "A *left*-invariant measure is quasi-preserved by *right*-addition.
 This should not be confused with `(measurePreserving_add_right μ g).quasiMeasurePreserving`. "]
-theorem quasiMeasurePreserving_mul_right [MulLeftInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_mul_right [IsMulLeftInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => h * g) μ μ := by
   refine' ⟨measurable_mul_const g, AbsolutelyContinuous.mk fun s hs => _⟩
   rw [map_apply (measurable_mul_const g) hs, measure_mul_right_null]; exact id
@@ -498,7 +498,7 @@ This should not be confused with `(measurePreserving_mul_left μ g).quasiMeasure
 @[to_additive
 "A *right*-invariant measure is quasi-preserved by *left*-addition.
 This should not be confused with `(measurePreserving_add_left μ g).quasiMeasurePreserving`. "]
-theorem quasiMeasurePreserving_mul_left [MulRightInvariant μ] (g : G) :
+theorem quasiMeasurePreserving_mul_left [IsMulRightInvariant μ] (g : G) :
     QuasiMeasurePreserving (fun h : G => g * h) μ μ := by
   have :=
     (quasiMeasurePreserving_mul_right μ.inv g⁻¹).mono (inv_absolutelyContinuous μ.inv)