measure_theory.group.action ⟷ Mathlib.MeasureTheory.Group.Action

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

@@ -32,7 +32,7 @@ namespace MeasureTheory
 variable {G M α : Type _} {s : Set α}
 
 #print MeasureTheory.VAddInvariantMeasure /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
 /-- A measure `μ : measure α` is invariant under an additive action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c +ᵥ x` is equal to
 the measure of `s`. -/
@@ -43,7 +43,7 @@ class VAddInvariantMeasure (M α : Type _) [VAdd M α] {_ : MeasurableSpace α}
 -/
 
 #print MeasureTheory.SMulInvariantMeasure /-
-/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:400:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
 /-- A measure `μ : measure α` is invariant under a multiplicative action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c • x` is equal to
 the measure of `s`. -/

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

@@ -32,7 +32,7 @@ namespace MeasureTheory
 variable {G M α : Type _} {s : Set α}
 
 #print MeasureTheory.VAddInvariantMeasure /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
 /-- A measure `μ : measure α` is invariant under an additive action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c +ᵥ x` is equal to
 the measure of `s`. -/
@@ -43,7 +43,7 @@ class VAddInvariantMeasure (M α : Type _) [VAdd M α] {_ : MeasurableSpace α}
 -/
 
 #print MeasureTheory.SMulInvariantMeasure /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:404:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
 /-- A measure `μ : measure α` is invariant under a multiplicative action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c • x` is equal to
 the measure of `s`. -/

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

@@ -3,10 +3,10 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Mathbin.MeasureTheory.Group.MeasurableEquiv
-import Mathbin.MeasureTheory.Measure.Regular
-import Mathbin.Dynamics.Ergodic.MeasurePreserving
-import Mathbin.Dynamics.Minimal
+import MeasureTheory.Group.MeasurableEquiv
+import MeasureTheory.Measure.Regular
+import Dynamics.Ergodic.MeasurePreserving
+import Dynamics.Minimal
 
 #align_import measure_theory.group.action from "leanprover-community/mathlib"@"61b5e2755ccb464b68d05a9acf891ae04992d09d"
 
@@ -32,7 +32,7 @@ namespace MeasureTheory
 variable {G M α : Type _} {s : Set α}
 
 #print MeasureTheory.VAddInvariantMeasure /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
 /-- A measure `μ : measure α` is invariant under an additive action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c +ᵥ x` is equal to
 the measure of `s`. -/
@@ -43,7 +43,7 @@ class VAddInvariantMeasure (M α : Type _) [VAdd M α] {_ : MeasurableSpace α}
 -/
 
 #print MeasureTheory.SMulInvariantMeasure /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
 /-- A measure `μ : measure α` is invariant under a multiplicative action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c • x` is equal to
 the measure of `s`. -/

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module measure_theory.group.action
-! leanprover-community/mathlib commit 61b5e2755ccb464b68d05a9acf891ae04992d09d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Group.MeasurableEquiv
 import Mathbin.MeasureTheory.Measure.Regular
 import Mathbin.Dynamics.Ergodic.MeasurePreserving
 import Mathbin.Dynamics.Minimal
 
+#align_import measure_theory.group.action from "leanprover-community/mathlib"@"61b5e2755ccb464b68d05a9acf891ae04992d09d"
+
 /-!
 # Measures invariant under group actions
 

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

@@ -35,7 +35,7 @@ namespace MeasureTheory
 variable {G M α : Type _} {s : Set α}
 
 #print MeasureTheory.VAddInvariantMeasure /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
 /-- A measure `μ : measure α` is invariant under an additive action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c +ᵥ x` is equal to
 the measure of `s`. -/
@@ -46,7 +46,7 @@ class VAddInvariantMeasure (M α : Type _) [VAdd M α] {_ : MeasurableSpace α}
 -/
 
 #print MeasureTheory.SMulInvariantMeasure /-
-/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
 /-- A measure `μ : measure α` is invariant under a multiplicative action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c • x` is equal to
 the measure of `s`. -/
@@ -81,17 +81,21 @@ instance add [SMulInvariantMeasure M α μ] [SMulInvariantMeasure M α ν] :
 #align measure_theory.vadd_invariant_measure.add MeasureTheory.VAddInvariantMeasure.add
 -/
 
+#print MeasureTheory.SMulInvariantMeasure.smul /-
 @[to_additive]
 instance smul [SMulInvariantMeasure M α μ] (c : ℝ≥0∞) : SMulInvariantMeasure M α (c • μ) :=
   ⟨fun a s hs => show c • _ = c • _ from congr_arg ((· • ·) c) (measure_preimage_smul μ a hs)⟩
 #align measure_theory.smul_invariant_measure.smul MeasureTheory.SMulInvariantMeasure.smul
 #align measure_theory.vadd_invariant_measure.vadd MeasureTheory.VAddInvariantMeasure.vadd
+-/
 
+#print MeasureTheory.SMulInvariantMeasure.smul_nnreal /-
 @[to_additive]
 instance smul_nnreal [SMulInvariantMeasure M α μ] (c : ℝ≥0) : SMulInvariantMeasure M α (c • μ) :=
   SMulInvariantMeasure.smul c
 #align measure_theory.smul_invariant_measure.smul_nnreal MeasureTheory.SMulInvariantMeasure.smul_nnreal
 #align measure_theory.vadd_invariant_measure.vadd_nnreal MeasureTheory.VAddInvariantMeasure.vadd_nnreal
+-/
 
 end SmulInvariantMeasure
 
@@ -125,6 +129,7 @@ end MeasurableSMul
 variable (G) {m : MeasurableSpace α} [Group G] [MulAction G α] [MeasurableSpace G]
   [MeasurableSMul G α] (c : G) (μ : Measure α)
 
+#print MeasureTheory.smulInvariantMeasure_tfae /-
 /-- Equivalent definitions of a measure invariant under a multiplicative action of a group.
 
 - 0: `smul_invariant_measure G α μ`;
@@ -158,6 +163,7 @@ theorem smulInvariantMeasure_tfae :
   tfae_finish
 #align measure_theory.smul_invariant_measure_tfae MeasureTheory.smulInvariantMeasure_tfae
 #align measure_theory.vadd_invariant_measure_tfae MeasureTheory.vaddInvariantMeasure_tfae
+-/
 
 /-- Equivalent definitions of a measure invariant under an additive action of a group.
 
@@ -206,13 +212,16 @@ theorem NullMeasurableSet.smul {s} (hs : NullMeasurableSet s μ) (c : G) :
 #align measure_theory.null_measurable_set.vadd MeasureTheory.NullMeasurableSet.vadd
 -/
 
+#print MeasureTheory.measure_smul_null /-
 theorem measure_smul_null {s} (h : μ s = 0) (c : G) : μ (c • s) = 0 := by rwa [measure_smul]
 #align measure_theory.measure_smul_null MeasureTheory.measure_smul_null
+-/
 
 section IsMinimal
 
 variable (G) [TopologicalSpace α] [ContinuousConstSMul G α] [MulAction.IsMinimal G α] {K U : Set α}
 
+#print MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_compact_ne_zero /-
 /-- If measure `μ` is invariant under a group action and is nonzero on a compact set `K`, then it is
 positive on any nonempty open set. In case of a regular measure, one can assume `μ ≠ 0` instead of
 `μ K ≠ 0`, see `measure_theory.measure_is_open_pos_of_smul_invariant_of_ne_zero`. -/
@@ -226,12 +235,14 @@ theorem measure_isOpen_pos_of_smulInvariant_of_compact_ne_zero (hK : IsCompact K
         (measure_biUnion_null_iff t.countable_toSet).2 fun _ _ => by rwa [measure_smul]
 #align measure_theory.measure_is_open_pos_of_smul_invariant_of_compact_ne_zero MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_compact_ne_zero
 #align measure_theory.measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero MeasureTheory.measure_isOpen_pos_of_vaddInvariant_of_compact_ne_zero
+-/
 
 /-- If measure `μ` is invariant under an additive group action and is nonzero on a compact set `K`,
 then it is positive on any nonempty open set. In case of a regular measure, one can assume `μ ≠ 0`
 instead of `μ K ≠ 0`, see `measure_theory.measure_is_open_pos_of_vadd_invariant_of_ne_zero`. -/
 add_decl_doc measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero
 
+#print MeasureTheory.isLocallyFiniteMeasure_of_smulInvariant /-
 @[to_additive]
 theorem isLocallyFiniteMeasure_of_smulInvariant (hU : IsOpen U) (hne : U.Nonempty) (hμU : μ U ≠ ∞) :
     IsLocallyFiniteMeasure μ :=
@@ -241,9 +252,11 @@ theorem isLocallyFiniteMeasure_of_smulInvariant (hU : IsOpen U) (hne : U.Nonempt
       Ne.lt_top <| by rwa [measure_preimage_smul]⟩⟩
 #align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.isLocallyFiniteMeasure_of_smulInvariant
 #align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.isLocallyFiniteMeasure_of_vaddInvariant
+-/
 
 variable [Measure.Regular μ]
 
+#print MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_ne_zero /-
 @[to_additive]
 theorem measure_isOpen_pos_of_smulInvariant_of_ne_zero (hμ : μ ≠ 0) (hU : IsOpen U)
     (hne : U.Nonempty) : 0 < μ U :=
@@ -251,7 +264,9 @@ theorem measure_isOpen_pos_of_smulInvariant_of_ne_zero (hμ : μ ≠ 0) (hU : Is
   measure_isOpen_pos_of_smulInvariant_of_compact_ne_zero G hK hμK hU hne
 #align measure_theory.measure_is_open_pos_of_smul_invariant_of_ne_zero MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_ne_zero
 #align measure_theory.measure_is_open_pos_of_vadd_invariant_of_ne_zero MeasureTheory.measure_isOpen_pos_of_vaddInvariant_of_ne_zero
+-/
 
+#print MeasureTheory.measure_pos_iff_nonempty_of_smulInvariant /-
 @[to_additive]
 theorem measure_pos_iff_nonempty_of_smulInvariant (hμ : μ ≠ 0) (hU : IsOpen U) :
     0 < μ U ↔ U.Nonempty :=
@@ -259,9 +274,9 @@ theorem measure_pos_iff_nonempty_of_smulInvariant (hμ : μ ≠ 0) (hU : IsOpen
     measure_isOpen_pos_of_smulInvariant_of_ne_zero G hμ hU⟩
 #align measure_theory.measure_pos_iff_nonempty_of_smul_invariant MeasureTheory.measure_pos_iff_nonempty_of_smulInvariant
 #align measure_theory.measure_pos_iff_nonempty_of_vadd_invariant MeasureTheory.measure_pos_iff_nonempty_of_vaddInvariant
+-/
 
-include G
-
+#print MeasureTheory.measure_eq_zero_iff_eq_empty_of_smulInvariant /-
 @[to_additive]
 theorem measure_eq_zero_iff_eq_empty_of_smulInvariant (hμ : μ ≠ 0) (hU : IsOpen U) :
     μ U = 0 ↔ U = ∅ := by
@@ -269,9 +284,11 @@ theorem measure_eq_zero_iff_eq_empty_of_smulInvariant (hμ : μ ≠ 0) (hU : IsO
     measure_pos_iff_nonempty_of_smul_invariant G hμ hU, nonempty_iff_ne_empty]
 #align measure_theory.measure_eq_zero_iff_eq_empty_of_smul_invariant MeasureTheory.measure_eq_zero_iff_eq_empty_of_smulInvariant
 #align measure_theory.measure_eq_zero_iff_eq_empty_of_vadd_invariant MeasureTheory.measure_eq_zero_iff_eq_empty_of_vaddInvariant
+-/
 
 end IsMinimal
 
+#print MeasureTheory.smul_ae_eq_self_of_mem_zpowers /-
 theorem smul_ae_eq_self_of_mem_zpowers {x y : G} (hs : (x • s : Set α) =ᵐ[μ] s)
     (hy : y ∈ Subgroup.zpowers x) : (y • s : Set α) =ᵐ[μ] s :=
   by
@@ -283,7 +300,9 @@ theorem smul_ae_eq_self_of_mem_zpowers {x y : G} (hs : (x • s : Set α) =ᵐ[
   simpa only [MulAction.toPermHom_apply, MulAction.toPerm_apply, image_smul, ←
     MonoidHom.map_zpow] using he.image_zpow_ae_eq he' k hs
 #align measure_theory.smul_ae_eq_self_of_mem_zpowers MeasureTheory.smul_ae_eq_self_of_mem_zpowers
+-/
 
+#print MeasureTheory.vadd_ae_eq_self_of_mem_zmultiples /-
 theorem vadd_ae_eq_self_of_mem_zmultiples {G : Type _} [MeasurableSpace G] [AddGroup G]
     [AddAction G α] [VAddInvariantMeasure G α μ] [MeasurableVAdd G α] {x y : G}
     (hs : (x +ᵥ s : Set α) =ᵐ[μ] s) (hy : y ∈ AddSubgroup.zmultiples x) :
@@ -299,6 +318,7 @@ theorem vadd_ae_eq_self_of_mem_zmultiples {G : Type _} [MeasurableSpace G] [AddG
           (by infer_instance : MeasurableVAdd G α) a }
   exact @smul_ae_eq_self_of_mem_zpowers (Multiplicative G) α _ _ _ _ _ _ _ _ _ _ hs hy
 #align measure_theory.vadd_ae_eq_self_of_mem_zmultiples MeasureTheory.vadd_ae_eq_self_of_mem_zmultiples
+-/
 
 attribute [to_additive vadd_ae_eq_self_of_mem_zmultiples] smul_ae_eq_self_of_mem_zpowers
 

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

@@ -35,7 +35,7 @@ namespace MeasureTheory
 variable {G M α : Type _} {s : Set α}
 
 #print MeasureTheory.VAddInvariantMeasure /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
 /-- A measure `μ : measure α` is invariant under an additive action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c +ᵥ x` is equal to
 the measure of `s`. -/
@@ -46,7 +46,7 @@ class VAddInvariantMeasure (M α : Type _) [VAdd M α] {_ : MeasurableSpace α}
 -/
 
 #print MeasureTheory.SMulInvariantMeasure /-
-/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:394:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
 /-- A measure `μ : measure α` is invariant under a multiplicative action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c • x` is equal to
 the measure of `s`. -/
@@ -233,14 +233,14 @@ instead of `μ K ≠ 0`, see `measure_theory.measure_is_open_pos_of_vadd_invaria
 add_decl_doc measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero
 
 @[to_additive]
-theorem locallyFiniteMeasure_of_smulInvariant (hU : IsOpen U) (hne : U.Nonempty) (hμU : μ U ≠ ∞) :
-    LocallyFiniteMeasure μ :=
+theorem isLocallyFiniteMeasure_of_smulInvariant (hU : IsOpen U) (hne : U.Nonempty) (hμU : μ U ≠ ∞) :
+    IsLocallyFiniteMeasure μ :=
   ⟨fun x =>
     let ⟨g, hg⟩ := hU.exists_smul_mem G x hne
     ⟨(· • ·) g ⁻¹' U, (hU.Preimage (continuous_id.const_smul _)).mem_nhds hg,
       Ne.lt_top <| by rwa [measure_preimage_smul]⟩⟩
-#align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.locallyFiniteMeasure_of_smulInvariant
-#align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.locallyFiniteMeasure_of_vaddInvariant
+#align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.isLocallyFiniteMeasure_of_smulInvariant
+#align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.isLocallyFiniteMeasure_of_vaddInvariant
 
 variable [Measure.Regular μ]
 

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

@@ -40,7 +40,7 @@ variable {G M α : Type _} {s : Set α}
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c +ᵥ x` is equal to
 the measure of `s`. -/
 class VAddInvariantMeasure (M α : Type _) [VAdd M α] {_ : MeasurableSpace α} (μ : Measure α) :
-  Prop where
+    Prop where
   measure_preimage_vadd : ∀ (c : M) ⦃s : Set α⦄, MeasurableSet s → μ ((fun x => c +ᵥ x) ⁻¹' s) = μ s
 #align measure_theory.vadd_invariant_measure MeasureTheory.VAddInvariantMeasure
 -/
@@ -52,7 +52,7 @@ measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x
 the measure of `s`. -/
 @[to_additive]
 class SMulInvariantMeasure (M α : Type _) [SMul M α] {_ : MeasurableSpace α} (μ : Measure α) :
-  Prop where
+    Prop where
   measure_preimage_smul : ∀ (c : M) ⦃s : Set α⦄, MeasurableSet s → μ ((fun x => c • x) ⁻¹' s) = μ s
 #align measure_theory.smul_invariant_measure MeasureTheory.SMulInvariantMeasure
 #align measure_theory.vadd_invariant_measure MeasureTheory.VAddInvariantMeasure

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 
 ! This file was ported from Lean 3 source module measure_theory.group.action
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 61b5e2755ccb464b68d05a9acf891ae04992d09d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Dynamics.Minimal
 /-!
 # Measures invariant under group actions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A measure `μ : measure α` is said to be *invariant* under an action of a group `G` if scalar
 multiplication by `c : G` is a measure preserving map for all `c`. In this file we define a
 typeclass for measures invariant under action of an (additive or multiplicative) group and prove
@@ -31,64 +34,73 @@ namespace MeasureTheory
 
 variable {G M α : Type _} {s : Set α}
 
+#print MeasureTheory.VAddInvariantMeasure /-
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
 /-- A measure `μ : measure α` is invariant under an additive action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c +ᵥ x` is equal to
 the measure of `s`. -/
-class VaddInvariantMeasure (M α : Type _) [VAdd M α] {_ : MeasurableSpace α} (μ : Measure α) :
+class VAddInvariantMeasure (M α : Type _) [VAdd M α] {_ : MeasurableSpace α} (μ : Measure α) :
   Prop where
   measure_preimage_vadd : ∀ (c : M) ⦃s : Set α⦄, MeasurableSet s → μ ((fun x => c +ᵥ x) ⁻¹' s) = μ s
-#align measure_theory.vadd_invariant_measure MeasureTheory.VaddInvariantMeasure
+#align measure_theory.vadd_invariant_measure MeasureTheory.VAddInvariantMeasure
+-/
 
+#print MeasureTheory.SMulInvariantMeasure /-
 /- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
 /-- A measure `μ : measure α` is invariant under a multiplicative action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c • x` is equal to
 the measure of `s`. -/
 @[to_additive]
-class SmulInvariantMeasure (M α : Type _) [SMul M α] {_ : MeasurableSpace α} (μ : Measure α) :
+class SMulInvariantMeasure (M α : Type _) [SMul M α] {_ : MeasurableSpace α} (μ : Measure α) :
   Prop where
   measure_preimage_smul : ∀ (c : M) ⦃s : Set α⦄, MeasurableSet s → μ ((fun x => c • x) ⁻¹' s) = μ s
-#align measure_theory.smul_invariant_measure MeasureTheory.SmulInvariantMeasure
-#align measure_theory.vadd_invariant_measure MeasureTheory.VaddInvariantMeasure
+#align measure_theory.smul_invariant_measure MeasureTheory.SMulInvariantMeasure
+#align measure_theory.vadd_invariant_measure MeasureTheory.VAddInvariantMeasure
+-/
 
 namespace SmulInvariantMeasure
 
+#print MeasureTheory.SMulInvariantMeasure.zero /-
 @[to_additive]
-instance zero [MeasurableSpace α] [SMul M α] : SmulInvariantMeasure M α 0 :=
+instance zero [MeasurableSpace α] [SMul M α] : SMulInvariantMeasure M α 0 :=
   ⟨fun _ _ _ => rfl⟩
-#align measure_theory.smul_invariant_measure.zero MeasureTheory.SmulInvariantMeasure.zero
-#align measure_theory.vadd_invariant_measure.zero MeasureTheory.VaddInvariantMeasure.zero
+#align measure_theory.smul_invariant_measure.zero MeasureTheory.SMulInvariantMeasure.zero
+#align measure_theory.vadd_invariant_measure.zero MeasureTheory.VAddInvariantMeasure.zero
+-/
 
 variable [SMul M α] {m : MeasurableSpace α} {μ ν : Measure α}
 
+#print MeasureTheory.SMulInvariantMeasure.add /-
 @[to_additive]
-instance add [SmulInvariantMeasure M α μ] [SmulInvariantMeasure M α ν] :
-    SmulInvariantMeasure M α (μ + ν) :=
+instance add [SMulInvariantMeasure M α μ] [SMulInvariantMeasure M α ν] :
+    SMulInvariantMeasure M α (μ + ν) :=
   ⟨fun c s hs =>
     show _ + _ = _ + _ from
       congr_arg₂ (· + ·) (measure_preimage_smul μ c hs) (measure_preimage_smul ν c hs)⟩
-#align measure_theory.smul_invariant_measure.add MeasureTheory.SmulInvariantMeasure.add
-#align measure_theory.vadd_invariant_measure.add MeasureTheory.VaddInvariantMeasure.add
+#align measure_theory.smul_invariant_measure.add MeasureTheory.SMulInvariantMeasure.add
+#align measure_theory.vadd_invariant_measure.add MeasureTheory.VAddInvariantMeasure.add
+-/
 
 @[to_additive]
-instance smul [SmulInvariantMeasure M α μ] (c : ℝ≥0∞) : SmulInvariantMeasure M α (c • μ) :=
+instance smul [SMulInvariantMeasure M α μ] (c : ℝ≥0∞) : SMulInvariantMeasure M α (c • μ) :=
   ⟨fun a s hs => show c • _ = c • _ from congr_arg ((· • ·) c) (measure_preimage_smul μ a hs)⟩
-#align measure_theory.smul_invariant_measure.smul MeasureTheory.SmulInvariantMeasure.smul
-#align measure_theory.vadd_invariant_measure.vadd MeasureTheory.VaddInvariantMeasure.vadd
+#align measure_theory.smul_invariant_measure.smul MeasureTheory.SMulInvariantMeasure.smul
+#align measure_theory.vadd_invariant_measure.vadd MeasureTheory.VAddInvariantMeasure.vadd
 
 @[to_additive]
-instance smul_nNReal [SmulInvariantMeasure M α μ] (c : ℝ≥0) : SmulInvariantMeasure M α (c • μ) :=
-  SmulInvariantMeasure.smul c
-#align measure_theory.smul_invariant_measure.smul_nnreal MeasureTheory.SmulInvariantMeasure.smul_nNReal
-#align measure_theory.vadd_invariant_measure.vadd_nnreal MeasureTheory.VaddInvariantMeasure.vadd_nnreal
+instance smul_nnreal [SMulInvariantMeasure M α μ] (c : ℝ≥0) : SMulInvariantMeasure M α (c • μ) :=
+  SMulInvariantMeasure.smul c
+#align measure_theory.smul_invariant_measure.smul_nnreal MeasureTheory.SMulInvariantMeasure.smul_nnreal
+#align measure_theory.vadd_invariant_measure.vadd_nnreal MeasureTheory.VAddInvariantMeasure.vadd_nnreal
 
 end SmulInvariantMeasure
 
 section MeasurableSMul
 
 variable {m : MeasurableSpace α} [MeasurableSpace M] [SMul M α] [MeasurableSMul M α] (c : M)
-  (μ : Measure α) [SmulInvariantMeasure M α μ]
+  (μ : Measure α) [SMulInvariantMeasure M α μ]
 
+#print MeasureTheory.measurePreserving_smul /-
 @[simp, to_additive]
 theorem measurePreserving_smul : MeasurePreserving ((· • ·) c) μ μ :=
   { Measurable := measurable_const_smul c
@@ -98,12 +110,15 @@ theorem measurePreserving_smul : MeasurePreserving ((· • ·) c) μ μ :=
       exact smul_invariant_measure.measure_preimage_smul μ c hs }
 #align measure_theory.measure_preserving_smul MeasureTheory.measurePreserving_smul
 #align measure_theory.measure_preserving_vadd MeasureTheory.measurePreserving_vadd
+-/
 
+#print MeasureTheory.map_smul /-
 @[simp, to_additive]
 theorem map_smul : map ((· • ·) c) μ = μ :=
   (measurePreserving_smul c μ).map_eq
 #align measure_theory.map_smul MeasureTheory.map_smul
 #align measure_theory.map_vadd MeasureTheory.map_vadd
+-/
 
 end MeasurableSMul
 
@@ -126,9 +141,9 @@ variable (G) {m : MeasurableSpace α} [Group G] [MulAction G α] [MeasurableSpac
 
 - 6: for any `c : G`, scalar multiplication by `c` is a measure preserving map. -/
 @[to_additive]
-theorem smulInvariantMeasure_tFAE :
+theorem smulInvariantMeasure_tfae :
     TFAE
-      [SmulInvariantMeasure G α μ, ∀ (c : G) (s), MeasurableSet s → μ ((· • ·) c ⁻¹' s) = μ s,
+      [SMulInvariantMeasure G α μ, ∀ (c : G) (s), MeasurableSet s → μ ((· • ·) c ⁻¹' s) = μ s,
         ∀ (c : G) (s), MeasurableSet s → μ (c • s) = μ s, ∀ (c : G) (s), μ ((· • ·) c ⁻¹' s) = μ s,
         ∀ (c : G) (s), μ (c • s) = μ s, ∀ c : G, Measure.map ((· • ·) c) μ = μ,
         ∀ c : G, MeasurePreserving ((· • ·) c) μ μ] :=
@@ -141,8 +156,8 @@ theorem smulInvariantMeasure_tFAE :
   tfae_have 5 → 3; exact fun H c s hs => H c s
   tfae_have 3 → 2; · intro H c s hs; rw [preimage_smul]; exact H c⁻¹ s hs
   tfae_finish
-#align measure_theory.smul_invariant_measure_tfae MeasureTheory.smulInvariantMeasure_tFAE
-#align measure_theory.vadd_invariant_measure_tfae MeasureTheory.vadd_invariant_measure_tFAE
+#align measure_theory.smul_invariant_measure_tfae MeasureTheory.smulInvariantMeasure_tfae
+#align measure_theory.vadd_invariant_measure_tfae MeasureTheory.vaddInvariantMeasure_tfae
 
 /-- Equivalent definitions of a measure invariant under an additive action of a group.
 
@@ -161,22 +176,27 @@ theorem smulInvariantMeasure_tFAE :
 - 6: for any `c : G`, vector addition of `c` is a measure preserving map. -/
 add_decl_doc vadd_invariant_measure_tfae
 
-variable {G} [SmulInvariantMeasure G α μ]
+variable {G} [SMulInvariantMeasure G α μ]
 
+#print MeasureTheory.measure_preimage_smul /-
 @[simp, to_additive]
 theorem measure_preimage_smul (s : Set α) : μ ((· • ·) c ⁻¹' s) = μ s :=
-  ((smulInvariantMeasure_tFAE G μ).out 0 3).mp ‹_› c s
+  ((smulInvariantMeasure_tfae G μ).out 0 3).mp ‹_› c s
 #align measure_theory.measure_preimage_smul MeasureTheory.measure_preimage_smul
 #align measure_theory.measure_preimage_vadd MeasureTheory.measure_preimage_vadd
+-/
 
+#print MeasureTheory.measure_smul /-
 @[simp, to_additive]
 theorem measure_smul (s : Set α) : μ (c • s) = μ s :=
-  ((smulInvariantMeasure_tFAE G μ).out 0 4).mp ‹_› c s
+  ((smulInvariantMeasure_tfae G μ).out 0 4).mp ‹_› c s
 #align measure_theory.measure_smul MeasureTheory.measure_smul
 #align measure_theory.measure_vadd MeasureTheory.measure_vadd
+-/
 
 variable {μ}
 
+#print MeasureTheory.NullMeasurableSet.smul /-
 @[to_additive]
 theorem NullMeasurableSet.smul {s} (hs : NullMeasurableSet s μ) (c : G) :
     NullMeasurableSet (c • s) μ := by
@@ -184,6 +204,7 @@ theorem NullMeasurableSet.smul {s} (hs : NullMeasurableSet s μ) (c : G) :
     hs.preimage (measure_preserving_smul _ _).QuasiMeasurePreserving
 #align measure_theory.null_measurable_set.smul MeasureTheory.NullMeasurableSet.smul
 #align measure_theory.null_measurable_set.vadd MeasureTheory.NullMeasurableSet.vadd
+-/
 
 theorem measure_smul_null {s} (h : μ s = 0) (c : G) : μ (c • s) = 0 := by rwa [measure_smul]
 #align measure_theory.measure_smul_null MeasureTheory.measure_smul_null
@@ -196,15 +217,15 @@ variable (G) [TopologicalSpace α] [ContinuousConstSMul G α] [MulAction.IsMinim
 positive on any nonempty open set. In case of a regular measure, one can assume `μ ≠ 0` instead of
 `μ K ≠ 0`, see `measure_theory.measure_is_open_pos_of_smul_invariant_of_ne_zero`. -/
 @[to_additive]
-theorem measure_isOpen_pos_of_smul_invariant_of_compact_ne_zero (hK : IsCompact K) (hμK : μ K ≠ 0)
+theorem measure_isOpen_pos_of_smulInvariant_of_compact_ne_zero (hK : IsCompact K) (hμK : μ K ≠ 0)
     (hU : IsOpen U) (hne : U.Nonempty) : 0 < μ U :=
   let ⟨t, ht⟩ := hK.exists_finite_cover_smul G hU hne
   pos_iff_ne_zero.2 fun hμU =>
     hμK <|
       measure_mono_null ht <|
         (measure_biUnion_null_iff t.countable_toSet).2 fun _ _ => by rwa [measure_smul]
-#align measure_theory.measure_is_open_pos_of_smul_invariant_of_compact_ne_zero MeasureTheory.measure_isOpen_pos_of_smul_invariant_of_compact_ne_zero
-#align measure_theory.measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero MeasureTheory.measure_isOpen_pos_of_vadd_invariant_of_compact_ne_zero
+#align measure_theory.measure_is_open_pos_of_smul_invariant_of_compact_ne_zero MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_compact_ne_zero
+#align measure_theory.measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero MeasureTheory.measure_isOpen_pos_of_vaddInvariant_of_compact_ne_zero
 
 /-- If measure `μ` is invariant under an additive group action and is nonzero on a compact set `K`,
 then it is positive on any nonempty open set. In case of a regular measure, one can assume `μ ≠ 0`
@@ -212,42 +233,42 @@ instead of `μ K ≠ 0`, see `measure_theory.measure_is_open_pos_of_vadd_invaria
 add_decl_doc measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero
 
 @[to_additive]
-theorem locallyFiniteMeasure_of_smul_invariant (hU : IsOpen U) (hne : U.Nonempty) (hμU : μ U ≠ ∞) :
+theorem locallyFiniteMeasure_of_smulInvariant (hU : IsOpen U) (hne : U.Nonempty) (hμU : μ U ≠ ∞) :
     LocallyFiniteMeasure μ :=
   ⟨fun x =>
     let ⟨g, hg⟩ := hU.exists_smul_mem G x hne
     ⟨(· • ·) g ⁻¹' U, (hU.Preimage (continuous_id.const_smul _)).mem_nhds hg,
       Ne.lt_top <| by rwa [measure_preimage_smul]⟩⟩
-#align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.locallyFiniteMeasure_of_smul_invariant
-#align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.locallyFiniteMeasure_of_vadd_invariant
+#align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.locallyFiniteMeasure_of_smulInvariant
+#align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.locallyFiniteMeasure_of_vaddInvariant
 
 variable [Measure.Regular μ]
 
 @[to_additive]
-theorem measure_isOpen_pos_of_smul_invariant_of_ne_zero (hμ : μ ≠ 0) (hU : IsOpen U)
+theorem measure_isOpen_pos_of_smulInvariant_of_ne_zero (hμ : μ ≠ 0) (hU : IsOpen U)
     (hne : U.Nonempty) : 0 < μ U :=
   let ⟨K, hK, hμK⟩ := Regular.exists_compact_not_null.mpr hμ
-  measure_isOpen_pos_of_smul_invariant_of_compact_ne_zero G hK hμK hU hne
-#align measure_theory.measure_is_open_pos_of_smul_invariant_of_ne_zero MeasureTheory.measure_isOpen_pos_of_smul_invariant_of_ne_zero
-#align measure_theory.measure_is_open_pos_of_vadd_invariant_of_ne_zero MeasureTheory.measure_isOpen_pos_of_vadd_invariant_of_ne_zero
+  measure_isOpen_pos_of_smulInvariant_of_compact_ne_zero G hK hμK hU hne
+#align measure_theory.measure_is_open_pos_of_smul_invariant_of_ne_zero MeasureTheory.measure_isOpen_pos_of_smulInvariant_of_ne_zero
+#align measure_theory.measure_is_open_pos_of_vadd_invariant_of_ne_zero MeasureTheory.measure_isOpen_pos_of_vaddInvariant_of_ne_zero
 
 @[to_additive]
-theorem measure_pos_iff_nonempty_of_smul_invariant (hμ : μ ≠ 0) (hU : IsOpen U) :
+theorem measure_pos_iff_nonempty_of_smulInvariant (hμ : μ ≠ 0) (hU : IsOpen U) :
     0 < μ U ↔ U.Nonempty :=
   ⟨fun h => nonempty_of_measure_ne_zero h.ne',
-    measure_isOpen_pos_of_smul_invariant_of_ne_zero G hμ hU⟩
-#align measure_theory.measure_pos_iff_nonempty_of_smul_invariant MeasureTheory.measure_pos_iff_nonempty_of_smul_invariant
-#align measure_theory.measure_pos_iff_nonempty_of_vadd_invariant MeasureTheory.measure_pos_iff_nonempty_of_vadd_invariant
+    measure_isOpen_pos_of_smulInvariant_of_ne_zero G hμ hU⟩
+#align measure_theory.measure_pos_iff_nonempty_of_smul_invariant MeasureTheory.measure_pos_iff_nonempty_of_smulInvariant
+#align measure_theory.measure_pos_iff_nonempty_of_vadd_invariant MeasureTheory.measure_pos_iff_nonempty_of_vaddInvariant
 
 include G
 
 @[to_additive]
-theorem measure_eq_zero_iff_eq_empty_of_smul_invariant (hμ : μ ≠ 0) (hU : IsOpen U) :
+theorem measure_eq_zero_iff_eq_empty_of_smulInvariant (hμ : μ ≠ 0) (hU : IsOpen U) :
     μ U = 0 ↔ U = ∅ := by
   rw [← not_iff_not, ← Ne.def, ← pos_iff_ne_zero,
     measure_pos_iff_nonempty_of_smul_invariant G hμ hU, nonempty_iff_ne_empty]
-#align measure_theory.measure_eq_zero_iff_eq_empty_of_smul_invariant MeasureTheory.measure_eq_zero_iff_eq_empty_of_smul_invariant
-#align measure_theory.measure_eq_zero_iff_eq_empty_of_vadd_invariant MeasureTheory.measure_eq_zero_iff_eq_empty_of_vadd_invariant
+#align measure_theory.measure_eq_zero_iff_eq_empty_of_smul_invariant MeasureTheory.measure_eq_zero_iff_eq_empty_of_smulInvariant
+#align measure_theory.measure_eq_zero_iff_eq_empty_of_vadd_invariant MeasureTheory.measure_eq_zero_iff_eq_empty_of_vaddInvariant
 
 end IsMinimal
 
@@ -264,7 +285,7 @@ theorem smul_ae_eq_self_of_mem_zpowers {x y : G} (hs : (x • s : Set α) =ᵐ[
 #align measure_theory.smul_ae_eq_self_of_mem_zpowers MeasureTheory.smul_ae_eq_self_of_mem_zpowers
 
 theorem vadd_ae_eq_self_of_mem_zmultiples {G : Type _} [MeasurableSpace G] [AddGroup G]
-    [AddAction G α] [VaddInvariantMeasure G α μ] [MeasurableVAdd G α] {x y : G}
+    [AddAction G α] [VAddInvariantMeasure G α μ] [MeasurableVAdd G α] {x y : G}
     (hs : (x +ᵥ s : Set α) =ᵐ[μ] s) (hy : y ∈ AddSubgroup.zmultiples x) :
     (y +ᵥ s : Set α) =ᵐ[μ] s :=
   by

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

@@ -23,7 +23,7 @@ some basic properties of such measures.
 -/
 
 
-open ENNReal NNReal Pointwise Topology
+open scoped ENNReal NNReal Pointwise Topology
 
 open MeasureTheory MeasureTheory.Measure Set Function
 

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

@@ -134,20 +134,12 @@ theorem smulInvariantMeasure_tFAE :
         ∀ c : G, MeasurePreserving ((· • ·) c) μ μ] :=
   by
   tfae_have 1 ↔ 2; exact ⟨fun h => h.1, fun h => ⟨h⟩⟩
-  tfae_have 1 → 6;
-  · intro h c
-    exact (measure_preserving_smul c μ).map_eq
+  tfae_have 1 → 6; · intro h c; exact (measure_preserving_smul c μ).map_eq
   tfae_have 6 → 7; exact fun H c => ⟨measurable_const_smul c, H c⟩
   tfae_have 7 → 4; exact fun H c => (H c).measure_preimage_emb (measurableEmbedding_const_smul c)
-  tfae_have 4 → 5;
-  exact fun H c s => by
-    rw [← preimage_smul_inv]
-    apply H
+  tfae_have 4 → 5; exact fun H c s => by rw [← preimage_smul_inv]; apply H
   tfae_have 5 → 3; exact fun H c s hs => H c s
-  tfae_have 3 → 2;
-  · intro H c s hs
-    rw [preimage_smul]
-    exact H c⁻¹ s hs
+  tfae_have 3 → 2; · intro H c s hs; rw [preimage_smul]; exact H c⁻¹ s hs
   tfae_finish
 #align measure_theory.smul_invariant_measure_tfae MeasureTheory.smulInvariantMeasure_tFAE
 #align measure_theory.vadd_invariant_measure_tfae MeasureTheory.vadd_invariant_measure_tFAE

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

@@ -210,7 +210,7 @@ theorem measure_isOpen_pos_of_smul_invariant_of_compact_ne_zero (hK : IsCompact
   pos_iff_ne_zero.2 fun hμU =>
     hμK <|
       measure_mono_null ht <|
-        (measure_bunionᵢ_null_iff t.countable_toSet).2 fun _ _ => by rwa [measure_smul]
+        (measure_biUnion_null_iff t.countable_toSet).2 fun _ _ => by rwa [measure_smul]
 #align measure_theory.measure_is_open_pos_of_smul_invariant_of_compact_ne_zero MeasureTheory.measure_isOpen_pos_of_smul_invariant_of_compact_ne_zero
 #align measure_theory.measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero MeasureTheory.measure_isOpen_pos_of_vadd_invariant_of_compact_ne_zero
 

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

@@ -84,9 +84,9 @@ instance smul_nNReal [SmulInvariantMeasure M α μ] (c : ℝ≥0) : SmulInvarian
 
 end SmulInvariantMeasure
 
-section HasMeasurableSmul
+section MeasurableSMul
 
-variable {m : MeasurableSpace α} [MeasurableSpace M] [SMul M α] [HasMeasurableSmul M α] (c : M)
+variable {m : MeasurableSpace α} [MeasurableSpace M] [SMul M α] [MeasurableSMul M α] (c : M)
   (μ : Measure α) [SmulInvariantMeasure M α μ]
 
 @[simp, to_additive]
@@ -105,10 +105,10 @@ theorem map_smul : map ((· • ·) c) μ = μ :=
 #align measure_theory.map_smul MeasureTheory.map_smul
 #align measure_theory.map_vadd MeasureTheory.map_vadd
 
-end HasMeasurableSmul
+end MeasurableSMul
 
 variable (G) {m : MeasurableSpace α} [Group G] [MulAction G α] [MeasurableSpace G]
-  [HasMeasurableSmul G α] (c : G) (μ : Measure α)
+  [MeasurableSMul G α] (c : G) (μ : Measure α)
 
 /-- Equivalent definitions of a measure invariant under a multiplicative action of a group.
 
@@ -272,18 +272,18 @@ theorem smul_ae_eq_self_of_mem_zpowers {x y : G} (hs : (x • s : Set α) =ᵐ[
 #align measure_theory.smul_ae_eq_self_of_mem_zpowers MeasureTheory.smul_ae_eq_self_of_mem_zpowers
 
 theorem vadd_ae_eq_self_of_mem_zmultiples {G : Type _} [MeasurableSpace G] [AddGroup G]
-    [AddAction G α] [VaddInvariantMeasure G α μ] [HasMeasurableVadd G α] {x y : G}
+    [AddAction G α] [VaddInvariantMeasure G α μ] [MeasurableVAdd G α] {x y : G}
     (hs : (x +ᵥ s : Set α) =ᵐ[μ] s) (hy : y ∈ AddSubgroup.zmultiples x) :
     (y +ᵥ s : Set α) =ᵐ[μ] s :=
   by
   letI : MeasurableSpace (Multiplicative G) := (by infer_instance : MeasurableSpace G)
   letI : smul_invariant_measure (Multiplicative G) α μ :=
     ⟨fun g => vadd_invariant_measure.measure_preimage_vadd μ (Multiplicative.toAdd g)⟩
-  letI : HasMeasurableSmul (Multiplicative G) α :=
+  letI : MeasurableSMul (Multiplicative G) α :=
     { measurable_const_smul := fun g => measurable_const_vadd (Multiplicative.toAdd g)
       measurable_smul_const := fun a =>
         @measurable_vadd_const (Multiplicative G) α (by infer_instance : VAdd G α) _ _
-          (by infer_instance : HasMeasurableVadd G α) a }
+          (by infer_instance : MeasurableVAdd G α) a }
   exact @smul_ae_eq_self_of_mem_zpowers (Multiplicative G) α _ _ _ _ _ _ _ _ _ _ hs hy
 #align measure_theory.vadd_ae_eq_self_of_mem_zmultiples MeasureTheory.vadd_ae_eq_self_of_mem_zmultiples
 

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

@@ -220,14 +220,14 @@ instead of `μ K ≠ 0`, see `measure_theory.measure_is_open_pos_of_vadd_invaria
 add_decl_doc measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero
 
 @[to_additive]
-theorem isLocallyFiniteMeasure_of_smul_invariant (hU : IsOpen U) (hne : U.Nonempty)
-    (hμU : μ U ≠ ∞) : IsLocallyFiniteMeasure μ :=
+theorem locallyFiniteMeasure_of_smul_invariant (hU : IsOpen U) (hne : U.Nonempty) (hμU : μ U ≠ ∞) :
+    LocallyFiniteMeasure μ :=
   ⟨fun x =>
     let ⟨g, hg⟩ := hU.exists_smul_mem G x hne
     ⟨(· • ·) g ⁻¹' U, (hU.Preimage (continuous_id.const_smul _)).mem_nhds hg,
       Ne.lt_top <| by rwa [measure_preimage_smul]⟩⟩
-#align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.isLocallyFiniteMeasure_of_smul_invariant
-#align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.isLocallyFiniteMeasure_of_vadd_invariant
+#align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.locallyFiniteMeasure_of_smul_invariant
+#align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.locallyFiniteMeasure_of_vadd_invariant
 
 variable [Measure.Regular μ]
 

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

@@ -77,9 +77,9 @@ instance smul [SmulInvariantMeasure M α μ] (c : ℝ≥0∞) : SmulInvariantMea
 #align measure_theory.vadd_invariant_measure.vadd MeasureTheory.VaddInvariantMeasure.vadd
 
 @[to_additive]
-instance smulNnreal [SmulInvariantMeasure M α μ] (c : ℝ≥0) : SmulInvariantMeasure M α (c • μ) :=
+instance smul_nNReal [SmulInvariantMeasure M α μ] (c : ℝ≥0) : SmulInvariantMeasure M α (c • μ) :=
   SmulInvariantMeasure.smul c
-#align measure_theory.smul_invariant_measure.smul_nnreal MeasureTheory.SmulInvariantMeasure.smulNnreal
+#align measure_theory.smul_invariant_measure.smul_nnreal MeasureTheory.SmulInvariantMeasure.smul_nNReal
 #align measure_theory.vadd_invariant_measure.vadd_nnreal MeasureTheory.VaddInvariantMeasure.vadd_nnreal
 
 end SmulInvariantMeasure
@@ -90,18 +90,18 @@ variable {m : MeasurableSpace α} [MeasurableSpace M] [SMul M α] [HasMeasurable
   (μ : Measure α) [SmulInvariantMeasure M α μ]
 
 @[simp, to_additive]
-theorem measurePreservingSmul : MeasurePreserving ((· • ·) c) μ μ :=
+theorem measurePreserving_smul : MeasurePreserving ((· • ·) c) μ μ :=
   { Measurable := measurable_const_smul c
     map_eq := by
       ext1 s hs
       rw [map_apply (measurable_const_smul c) hs]
       exact smul_invariant_measure.measure_preimage_smul μ c hs }
-#align measure_theory.measure_preserving_smul MeasureTheory.measurePreservingSmul
-#align measure_theory.measure_preserving_vadd MeasureTheory.measure_preserving_vadd
+#align measure_theory.measure_preserving_smul MeasureTheory.measurePreserving_smul
+#align measure_theory.measure_preserving_vadd MeasureTheory.measurePreserving_vadd
 
 @[simp, to_additive]
 theorem map_smul : map ((· • ·) c) μ = μ :=
-  (measurePreservingSmul c μ).map_eq
+  (measurePreserving_smul c μ).map_eq
 #align measure_theory.map_smul MeasureTheory.map_smul
 #align measure_theory.map_vadd MeasureTheory.map_vadd
 
@@ -150,7 +150,7 @@ theorem smulInvariantMeasure_tFAE :
     exact H c⁻¹ s hs
   tfae_finish
 #align measure_theory.smul_invariant_measure_tfae MeasureTheory.smulInvariantMeasure_tFAE
-#align measure_theory.vadd_invariant_measure_tfae MeasureTheory.vadd_invariant_measure_tfae
+#align measure_theory.vadd_invariant_measure_tfae MeasureTheory.vadd_invariant_measure_tFAE
 
 /-- Equivalent definitions of a measure invariant under an additive action of a group.
 
@@ -210,9 +210,9 @@ theorem measure_isOpen_pos_of_smul_invariant_of_compact_ne_zero (hK : IsCompact
   pos_iff_ne_zero.2 fun hμU =>
     hμK <|
       measure_mono_null ht <|
-        (measure_bUnion_null_iff t.countable_toSet).2 fun _ _ => by rwa [measure_smul]
+        (measure_bunionᵢ_null_iff t.countable_toSet).2 fun _ _ => by rwa [measure_smul]
 #align measure_theory.measure_is_open_pos_of_smul_invariant_of_compact_ne_zero MeasureTheory.measure_isOpen_pos_of_smul_invariant_of_compact_ne_zero
-#align measure_theory.measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero MeasureTheory.measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero
+#align measure_theory.measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero MeasureTheory.measure_isOpen_pos_of_vadd_invariant_of_compact_ne_zero
 
 /-- If measure `μ` is invariant under an additive group action and is nonzero on a compact set `K`,
 then it is positive on any nonempty open set. In case of a regular measure, one can assume `μ ≠ 0`
@@ -220,14 +220,14 @@ instead of `μ K ≠ 0`, see `measure_theory.measure_is_open_pos_of_vadd_invaria
 add_decl_doc measure_is_open_pos_of_vadd_invariant_of_compact_ne_zero
 
 @[to_additive]
-theorem isLocallyFiniteMeasureOfSmulInvariant (hU : IsOpen U) (hne : U.Nonempty) (hμU : μ U ≠ ∞) :
-    IsLocallyFiniteMeasure μ :=
+theorem isLocallyFiniteMeasure_of_smul_invariant (hU : IsOpen U) (hne : U.Nonempty)
+    (hμU : μ U ≠ ∞) : IsLocallyFiniteMeasure μ :=
   ⟨fun x =>
     let ⟨g, hg⟩ := hU.exists_smul_mem G x hne
     ⟨(· • ·) g ⁻¹' U, (hU.Preimage (continuous_id.const_smul _)).mem_nhds hg,
       Ne.lt_top <| by rwa [measure_preimage_smul]⟩⟩
-#align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.isLocallyFiniteMeasureOfSmulInvariant
-#align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.is_locally_finite_measure_of_vadd_invariant
+#align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.isLocallyFiniteMeasure_of_smul_invariant
+#align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.isLocallyFiniteMeasure_of_vadd_invariant
 
 variable [Measure.Regular μ]
 
@@ -237,7 +237,7 @@ theorem measure_isOpen_pos_of_smul_invariant_of_ne_zero (hμ : μ ≠ 0) (hU : I
   let ⟨K, hK, hμK⟩ := Regular.exists_compact_not_null.mpr hμ
   measure_isOpen_pos_of_smul_invariant_of_compact_ne_zero G hK hμK hU hne
 #align measure_theory.measure_is_open_pos_of_smul_invariant_of_ne_zero MeasureTheory.measure_isOpen_pos_of_smul_invariant_of_ne_zero
-#align measure_theory.measure_is_open_pos_of_vadd_invariant_of_ne_zero MeasureTheory.measure_is_open_pos_of_vadd_invariant_of_ne_zero
+#align measure_theory.measure_is_open_pos_of_vadd_invariant_of_ne_zero MeasureTheory.measure_isOpen_pos_of_vadd_invariant_of_ne_zero
 
 @[to_additive]
 theorem measure_pos_iff_nonempty_of_smul_invariant (hμ : μ ≠ 0) (hU : IsOpen U) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/09079525fd01b3dda35e96adaa08d2f943e1648c

@@ -31,7 +31,7 @@ namespace MeasureTheory
 
 variable {G M α : Type _} {s : Set α}
 
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_vadd] [] -/
 /-- A measure `μ : measure α` is invariant under an additive action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c +ᵥ x` is equal to
 the measure of `s`. -/
@@ -40,7 +40,7 @@ class VaddInvariantMeasure (M α : Type _) [VAdd M α] {_ : MeasurableSpace α}
   measure_preimage_vadd : ∀ (c : M) ⦃s : Set α⦄, MeasurableSet s → μ ((fun x => c +ᵥ x) ⁻¹' s) = μ s
 #align measure_theory.vadd_invariant_measure MeasureTheory.VaddInvariantMeasure
 
-/- ./././Mathport/Syntax/Translate/Command.lean:388:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
+/- ./././Mathport/Syntax/Translate/Command.lean:393:30: infer kinds are unsupported in Lean 4: #[`measure_preimage_smul] [] -/
 /-- A measure `μ : measure α` is invariant under a multiplicative action of `M` on `α` if for any
 measurable set `s : set α` and `c : M`, the measure of its preimage under `λ x, c • x` is equal to
 the measure of `s`. -/

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

@@ -23,7 +23,7 @@ some basic properties of such measures.
 -/
 
 
-open Ennreal NNReal Pointwise Topology
+open ENNReal NNReal Pointwise Topology
 
 open MeasureTheory MeasureTheory.Measure Set Function
 

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

These are changes from #11997, the latest adaptation PR for nightly-2024-04-07, which can be made directly on master.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Ruben Van de Velde <65514131+Ruben-VandeVelde@users.noreply.github.com>

@@ -286,7 +286,7 @@ theorem measure_pos_iff_nonempty_of_smulInvariant (hμ : μ ≠ 0) (hU : IsOpen
 @[to_additive]
 theorem measure_eq_zero_iff_eq_empty_of_smulInvariant (hμ : μ ≠ 0) (hU : IsOpen U) :
     μ U = 0 ↔ U = ∅ := by
-  rw [← not_iff_not, ← Ne.def, ← pos_iff_ne_zero,
+  rw [← not_iff_not, ← Ne, ← pos_iff_ne_zero,
     measure_pos_iff_nonempty_of_smulInvariant G hμ hU, nonempty_iff_ne_empty]
 #align measure_theory.measure_eq_zero_iff_eq_empty_of_smul_invariant MeasureTheory.measure_eq_zero_iff_eq_empty_of_smulInvariant
 #align measure_theory.measure_eq_zero_iff_eq_empty_of_vadd_invariant MeasureTheory.measure_eq_zero_iff_eq_empty_of_vaddInvariant

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

@@ -310,7 +310,7 @@ theorem vadd_ae_eq_self_of_mem_zmultiples {G : Type u} {α : Type w} {s : Set α
     {μ : Measure α} [VAddInvariantMeasure G α μ] {x y : G}
     (hs : (x +ᵥ s : Set α) =ᵐ[μ] s) (hy : y ∈ AddSubgroup.zmultiples x) :
     (y +ᵥ s : Set α) =ᵐ[μ] s := by
-  letI : MeasurableSpace (Multiplicative G) := (inferInstanceAs (MeasurableSpace G))
+  letI : MeasurableSpace (Multiplicative G) := inferInstanceAs (MeasurableSpace G)
   letI : SMulInvariantMeasure (Multiplicative G) α μ :=
     ⟨fun g => VAddInvariantMeasure.measure_preimage_vadd (Multiplicative.toAdd g)⟩
   letI : MeasurableSMul (Multiplicative G) α :=

• Remove manual translations that are now guessed correctly
• Fix some names that were incorrectly guessed by humans (and in one case fix the multiplicative name). Add deprecations for all name changes.
• Remove a couple manually additivized lemmas.

@@ -321,7 +321,7 @@ theorem vadd_ae_eq_self_of_mem_zmultiples {G : Type u} {α : Type w} {s : Set α
   exact smul_ae_eq_self_of_mem_zpowers (G := Multiplicative G) hs hy
 #align measure_theory.vadd_ae_eq_self_of_mem_zmultiples MeasureTheory.vadd_ae_eq_self_of_mem_zmultiples
 
-attribute [to_additive existing vadd_ae_eq_self_of_mem_zmultiples] smul_ae_eq_self_of_mem_zpowers
+attribute [to_additive existing] smul_ae_eq_self_of_mem_zpowers
 
 @[to_additive]
 theorem inv_smul_ae_eq_self {x : G} (hs : (x • s : Set α) =ᵐ[μ] s) : (x⁻¹ • s : Set α) =ᵐ[μ] s :=

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

@@ -301,7 +301,7 @@ theorem smul_ae_eq_self_of_mem_zpowers {x y : G} (hs : (x • s : Set α) =ᵐ[
   have he' : QuasiMeasurePreserving e.symm μ μ :=
     (measurePreserving_smul x⁻¹ μ).quasiMeasurePreserving
   have h := he.image_zpow_ae_eq he' k hs
-  simp only [← MonoidHom.map_zpow] at h
+  simp only [e, ← MonoidHom.map_zpow] at h
   simpa only [MulAction.toPermHom_apply, MulAction.toPerm_apply, image_smul] using h
 #align measure_theory.smul_ae_eq_self_of_mem_zpowers MeasureTheory.smul_ae_eq_self_of_mem_zpowers
 

I used the regex \(\(· (.) ·\) (.)\), replacing with ($2 $1 ·).

@@ -260,7 +260,7 @@ theorem isLocallyFiniteMeasure_of_smulInvariant (hU : IsOpen U) (hne : U.Nonempt
     IsLocallyFiniteMeasure μ :=
   ⟨fun x =>
     let ⟨g, hg⟩ := hU.exists_smul_mem G x hne
-    ⟨(· • ·) g ⁻¹' U, (hU.preimage (continuous_id.const_smul _)).mem_nhds hg,
+    ⟨(g • ·) ⁻¹' U, (hU.preimage (continuous_id.const_smul _)).mem_nhds hg,
       Ne.lt_top <| by rwa [measure_preimage_smul]⟩⟩
 #align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.isLocallyFiniteMeasure_of_smulInvariant
 #align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.isLocallyFiniteMeasure_of_vaddInvariant

Using Lean4's named arguments, we manage to remove a few hard-to-read explicit function calls [@foo](https://github.com/foo) _ _ _ _ _ ... which used to be necessary in Lean3.

Occasionally, this results in slightly longer code. The benefit of named arguments is readability, as well as to reduce the brittleness of the code when the argument order is changed.

Co-authored-by: Michael Rothgang <rothgami@math.hu-berlin.de>

@@ -318,7 +318,7 @@ theorem vadd_ae_eq_self_of_mem_zmultiples {G : Type u} {α : Type w} {s : Set α
       measurable_smul_const := fun a =>
         @measurable_vadd_const (Multiplicative G) α (inferInstanceAs (VAdd G α)) _ _
           (inferInstanceAs (MeasurableVAdd G α)) a }
-  exact @smul_ae_eq_self_of_mem_zpowers (Multiplicative G) α _ _ _ _ _ _ _ _ _ _ hs hy
+  exact smul_ae_eq_self_of_mem_zpowers (G := Multiplicative G) hs hy
 #align measure_theory.vadd_ae_eq_self_of_mem_zmultiples MeasureTheory.vadd_ae_eq_self_of_mem_zmultiples
 
 attribute [to_additive existing vadd_ae_eq_self_of_mem_zmultiples] smul_ae_eq_self_of_mem_zpowers

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

@@ -121,7 +121,7 @@ theorem smulInvariantMeasure_map [SMul M α] [SMul M β]
     _ = μ (f ⁻¹' ((m • ·) ⁻¹' S)) := map_apply hf <| hS.preimage (measurable_const_smul _)
     _ = μ ((m • f ·) ⁻¹' S) := by rw [preimage_preimage]
     _ = μ ((f <| m • ·) ⁻¹' S) := by simp_rw [hsmul]
-    _ = μ ((m • ·) ⁻¹' (f ⁻¹' S)) := by rw [←preimage_preimage]
+    _ = μ ((m • ·) ⁻¹' (f ⁻¹' S)) := by rw [← preimage_preimage]
     _ = μ (f ⁻¹' S) := by rw [SMulInvariantMeasure.measure_preimage_smul m (hS.preimage hf)]
     _ = map f μ S := (map_apply hf hS).symm
 

I believe the file defining a type of morphisms belongs alongside the file defining the structure this morphism works on. So I would like to reorganize the files in the Mathlib.Algebra.Hom folder so that e.g. Mathlib.Algebra.Hom.Ring becomes Mathlib.Algebra.Ring.Hom and Mathlib.Algebra.Hom.NonUnitalAlg becomes Mathlib.Algebra.Algebra.NonUnitalHom.

While fixing the imports I went ahead and sorted them for good luck.

The full list of changes is: renamed: Mathlib/Algebra/Hom/NonUnitalAlg.lean -> Mathlib/Algebra/Algebra/NonUnitalHom.lean renamed: Mathlib/Algebra/Hom/Aut.lean -> Mathlib/Algebra/Group/Aut.lean renamed: Mathlib/Algebra/Hom/Commute.lean -> Mathlib/Algebra/Group/Commute/Hom.lean renamed: Mathlib/Algebra/Hom/Embedding.lean -> Mathlib/Algebra/Group/Embedding.lean renamed: Mathlib/Algebra/Hom/Equiv/Basic.lean -> Mathlib/Algebra/Group/Equiv/Basic.lean renamed: Mathlib/Algebra/Hom/Equiv/TypeTags.lean -> Mathlib/Algebra/Group/Equiv/TypeTags.lean renamed: Mathlib/Algebra/Hom/Equiv/Units/Basic.lean -> Mathlib/Algebra/Group/Units/Equiv.lean renamed: Mathlib/Algebra/Hom/Equiv/Units/GroupWithZero.lean -> Mathlib/Algebra/GroupWithZero/Units/Equiv.lean renamed: Mathlib/Algebra/Hom/Freiman.lean -> Mathlib/Algebra/Group/Freiman.lean renamed: Mathlib/Algebra/Hom/Group/Basic.lean -> Mathlib/Algebra/Group/Hom/Basic.lean renamed: Mathlib/Algebra/Hom/Group/Defs.lean -> Mathlib/Algebra/Group/Hom/Defs.lean renamed: Mathlib/Algebra/Hom/GroupAction.lean -> Mathlib/GroupTheory/GroupAction/Hom.lean renamed: Mathlib/Algebra/Hom/GroupInstances.lean -> Mathlib/Algebra/Group/Hom/Instances.lean renamed: Mathlib/Algebra/Hom/Iterate.lean -> Mathlib/Algebra/GroupPower/IterateHom.lean renamed: Mathlib/Algebra/Hom/Centroid.lean -> Mathlib/Algebra/Ring/CentroidHom.lean renamed: Mathlib/Algebra/Hom/Ring/Basic.lean -> Mathlib/Algebra/Ring/Hom/Basic.lean renamed: Mathlib/Algebra/Hom/Ring/Defs.lean -> Mathlib/Algebra/Ring/Hom/Defs.lean renamed: Mathlib/Algebra/Hom/Units.lean -> Mathlib/Algebra/Group/Units/Hom.lean

Zulip thread: https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Reorganizing.20.60Mathlib.2EAlgebra.2EHom.60

@@ -3,11 +3,11 @@ Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
 -/
-import Mathlib.MeasureTheory.Group.MeasurableEquiv
-import Mathlib.MeasureTheory.Measure.Regular
 import Mathlib.Dynamics.Ergodic.MeasurePreserving
 import Mathlib.Dynamics.Minimal
-import Mathlib.Algebra.Hom.GroupAction
+import Mathlib.GroupTheory.GroupAction.Hom
+import Mathlib.MeasureTheory.Group.MeasurableEquiv
+import Mathlib.MeasureTheory.Measure.Regular
 
 #align_import measure_theory.group.action from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 

Purely cosmetic PR

@@ -123,7 +123,7 @@ theorem smulInvariantMeasure_map [SMul M α] [SMul M β]
     _ = μ ((f <| m • ·) ⁻¹' S) := by simp_rw [hsmul]
     _ = μ ((m • ·) ⁻¹' (f ⁻¹' S)) := by rw [←preimage_preimage]
     _ = μ (f ⁻¹' S) := by rw [SMulInvariantMeasure.measure_preimage_smul m (hS.preimage hf)]
-    _ = map f μ S  := (map_apply hf hS).symm
+    _ = map f μ S := (map_apply hf hS).symm
 
 @[to_additive]
 instance smulInvariantMeasure_map_smul [SMul M α] [SMul N α] [SMulCommClass N M α]

The image of a left invariant measure under right addition is left invariant, and if the measure was a Haar measure it is stays a Haar measure.

Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -7,6 +7,7 @@ import Mathlib.MeasureTheory.Group.MeasurableEquiv
 import Mathlib.MeasureTheory.Measure.Regular
 import Mathlib.Dynamics.Ergodic.MeasurePreserving
 import Mathlib.Dynamics.Minimal
+import Mathlib.Algebra.Hom.GroupAction
 
 #align_import measure_theory.group.action from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
 
@@ -103,6 +104,36 @@ theorem map_smul : map (c • ·) μ = μ :=
 
 end MeasurableSMul
 
+section SMulHomClass
+
+universe uM uN uα uβ
+variable {M : Type uM} {N : Type uN}  {α : Type uα} {β : Type uβ}
+  [MeasurableSpace M] [MeasurableSpace N] [MeasurableSpace α] [MeasurableSpace β]
+
+@[to_additive]
+theorem smulInvariantMeasure_map [SMul M α] [SMul M β]
+    [MeasurableSMul M β]
+    (μ : Measure α) [SMulInvariantMeasure M α μ] (f : α → β)
+    (hsmul : ∀ (m : M) a, f (m • a) = m • f a) (hf : Measurable f) :
+    SMulInvariantMeasure M β (map f μ) where
+  measure_preimage_smul m S hS := calc
+    map f μ ((m • ·) ⁻¹' S)
+    _ = μ (f ⁻¹' ((m • ·) ⁻¹' S)) := map_apply hf <| hS.preimage (measurable_const_smul _)
+    _ = μ ((m • f ·) ⁻¹' S) := by rw [preimage_preimage]
+    _ = μ ((f <| m • ·) ⁻¹' S) := by simp_rw [hsmul]
+    _ = μ ((m • ·) ⁻¹' (f ⁻¹' S)) := by rw [←preimage_preimage]
+    _ = μ (f ⁻¹' S) := by rw [SMulInvariantMeasure.measure_preimage_smul m (hS.preimage hf)]
+    _ = map f μ S  := (map_apply hf hS).symm
+
+@[to_additive]
+instance smulInvariantMeasure_map_smul [SMul M α] [SMul N α] [SMulCommClass N M α]
+    [MeasurableSMul M α] [MeasurableSMul N α]
+    (μ : Measure α) [SMulInvariantMeasure M α μ] (n : N) :
+    SMulInvariantMeasure M α (map (n • ·) μ) :=
+  smulInvariantMeasure_map μ _ (smul_comm n) <| measurable_const_smul _
+
+end SMulHomClass
+
 variable (G) {m : MeasurableSpace α} [Group G] [MulAction G α] [MeasurableSpace G]
   [MeasurableSMul G α] (c : G) (μ : Measure α)
 

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

This has nice performance benefits.

@@ -31,7 +31,7 @@ variable {G : Type u} {M : Type v} {α : Type w} {s : Set α}
 /-- A measure `μ : Measure α` is invariant under an additive action of `M` on `α` if for any
 measurable set `s : Set α` and `c : M`, the measure of its preimage under `fun x => c +ᵥ x` is equal
 to the measure of `s`. -/
-class VAddInvariantMeasure (M α : Type _) [VAdd M α] {_ : MeasurableSpace α} (μ : Measure α) :
+class VAddInvariantMeasure (M α : Type*) [VAdd M α] {_ : MeasurableSpace α} (μ : Measure α) :
   Prop where
   measure_preimage_vadd : ∀ (c : M) ⦃s : Set α⦄, MeasurableSet s → μ ((fun x => c +ᵥ x) ⁻¹' s) = μ s
 #align measure_theory.vadd_invariant_measure MeasureTheory.VAddInvariantMeasure
@@ -41,7 +41,7 @@ class VAddInvariantMeasure (M α : Type _) [VAdd M α] {_ : MeasurableSpace α}
 measurable set `s : Set α` and `c : M`, the measure of its preimage under `fun x => c • x` is equal
 to the measure of `s`. -/
 @[to_additive]
-class SMulInvariantMeasure (M α : Type _) [SMul M α] {_ : MeasurableSpace α} (μ : Measure α) :
+class SMulInvariantMeasure (M α : Type*) [SMul M α] {_ : MeasurableSpace α} (μ : Measure α) :
   Prop where
   measure_preimage_smul : ∀ (c : M) ⦃s : Set α⦄, MeasurableSet s → μ ((fun x => c • x) ⁻¹' s) = μ s
 #align measure_theory.smul_invariant_measure MeasureTheory.SMulInvariantMeasure

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2021 Yury G. Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury G. Kudryashov
-
-! This file was ported from Lean 3 source module measure_theory.group.action
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Group.MeasurableEquiv
 import Mathlib.MeasureTheory.Measure.Regular
 import Mathlib.Dynamics.Ergodic.MeasurePreserving
 import Mathlib.Dynamics.Minimal
 
+#align_import measure_theory.group.action from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Measures invariant under group actions
 

• Add MeasureTheory.inv_smul_ae_eq_self and its additive version.

• Add @[to_additive] to MeasureTheory.measure_smul_null.

• Fix the order of implicit arguments and universes in MeasureTheory.vadd_ae_eq_self_of_mem_zmultiples to match the multiplicative version.

@@ -27,7 +27,9 @@ open ENNReal NNReal Pointwise Topology MeasureTheory MeasureTheory.Measure Set F
 
 namespace MeasureTheory
 
-variable {G M α : Type _} {s : Set α}
+universe u v w
+
+variable {G : Type u} {M : Type v} {α : Type w} {s : Set α}
 
 /-- A measure `μ : Measure α` is invariant under an additive action of `M` on `α` if for any
 measurable set `s : Set α` and `c : M`, the measure of its preimage under `fun x => c +ᵥ x` is equal
@@ -197,6 +199,7 @@ theorem NullMeasurableSet.smul {s} (hs : NullMeasurableSet s μ) (c : G) :
 #align measure_theory.null_measurable_set.smul MeasureTheory.NullMeasurableSet.smul
 #align measure_theory.null_measurable_set.vadd MeasureTheory.NullMeasurableSet.vadd
 
+@[to_additive]
 theorem measure_smul_null {s} (h : μ s = 0) (c : G) : μ (c • s) = 0 := by rwa [measure_smul]
 #align measure_theory.measure_smul_null MeasureTheory.measure_smul_null
 
@@ -274,8 +277,9 @@ theorem smul_ae_eq_self_of_mem_zpowers {x y : G} (hs : (x • s : Set α) =ᵐ[
   simpa only [MulAction.toPermHom_apply, MulAction.toPerm_apply, image_smul] using h
 #align measure_theory.smul_ae_eq_self_of_mem_zpowers MeasureTheory.smul_ae_eq_self_of_mem_zpowers
 
-theorem vadd_ae_eq_self_of_mem_zmultiples {G : Type _} [MeasurableSpace G] [AddGroup G]
-    [AddAction G α] [VAddInvariantMeasure G α μ] [MeasurableVAdd G α] {x y : G}
+theorem vadd_ae_eq_self_of_mem_zmultiples {G : Type u} {α : Type w} {s : Set α}
+    {m : MeasurableSpace α} [AddGroup G] [AddAction G α] [MeasurableSpace G] [MeasurableVAdd G α]
+    {μ : Measure α} [VAddInvariantMeasure G α μ] {x y : G}
     (hs : (x +ᵥ s : Set α) =ᵐ[μ] s) (hy : y ∈ AddSubgroup.zmultiples x) :
     (y +ᵥ s : Set α) =ᵐ[μ] s := by
   letI : MeasurableSpace (Multiplicative G) := (inferInstanceAs (MeasurableSpace G))
@@ -291,4 +295,8 @@ theorem vadd_ae_eq_self_of_mem_zmultiples {G : Type _} [MeasurableSpace G] [AddG
 
 attribute [to_additive existing vadd_ae_eq_self_of_mem_zmultiples] smul_ae_eq_self_of_mem_zpowers
 
+@[to_additive]
+theorem inv_smul_ae_eq_self {x : G} (hs : (x • s : Set α) =ᵐ[μ] s) : (x⁻¹ • s : Set α) =ᵐ[μ] s :=
+  smul_ae_eq_self_of_mem_zpowers hs <| inv_mem (Subgroup.mem_zpowers _)
+
 end MeasureTheory

@@ -23,9 +23,7 @@ some basic properties of such measures.
 -/
 
 
-open ENNReal NNReal Pointwise Topology
-
-open MeasureTheory MeasureTheory.Measure Set Function
+open ENNReal NNReal Pointwise Topology MeasureTheory MeasureTheory.Measure Set Function
 
 namespace MeasureTheory
 
@@ -159,7 +157,7 @@ theorem smulInvariantMeasure_tfae :
 
 /-- Equivalent definitions of a measure invariant under an additive action of a group.
 
-- 0: `vadd_invariant_measure G α μ`;
+- 0: `VAddInvariantMeasure G α μ`;
 
 - 1: for every `c : G` and a measurable set `s`, the measure of the preimage of `s` under
      vector addition `(c +ᵥ ·)` is equal to the measure of `s`;

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.

@@ -227,14 +227,14 @@ instead of `μ K ≠ 0`, see `MeasureTheory.measure_isOpen_pos_of_vaddInvariant_
 add_decl_doc measure_isOpen_pos_of_vaddInvariant_of_compact_ne_zero
 
 @[to_additive]
-theorem locallyFiniteMeasure_of_smulInvariant (hU : IsOpen U) (hne : U.Nonempty) (hμU : μ U ≠ ∞) :
-    LocallyFiniteMeasure μ :=
+theorem isLocallyFiniteMeasure_of_smulInvariant (hU : IsOpen U) (hne : U.Nonempty) (hμU : μ U ≠ ∞) :
+    IsLocallyFiniteMeasure μ :=
   ⟨fun x =>
     let ⟨g, hg⟩ := hU.exists_smul_mem G x hne
     ⟨(· • ·) g ⁻¹' U, (hU.preimage (continuous_id.const_smul _)).mem_nhds hg,
       Ne.lt_top <| by rwa [measure_preimage_smul]⟩⟩
-#align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.locallyFiniteMeasure_of_smulInvariant
-#align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.locallyFiniteMeasure_of_vaddInvariant
+#align measure_theory.is_locally_finite_measure_of_smul_invariant MeasureTheory.isLocallyFiniteMeasure_of_smulInvariant
+#align measure_theory.is_locally_finite_measure_of_vadd_invariant MeasureTheory.isLocallyFiniteMeasure_of_vaddInvariant
 
 variable [Measure.Regular μ]
 

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