measure_theory.group.fundamental_domain

(last sync)

feat(measure_theory/measure/haar_quotient): the Unfolding Trick (#18863)

We prove the "unfolding trick": Given a subgroup Γ of a group G, the integral of a function f on G times the lift to G of a function g on the coset space G ⧸ Γ with respect to a right-invariant measure μ on G, is equal to the integral over the coset space of the automorphization of f times g.

We also prove the following simplified version: Given a subgroup Γ of a group G, the integral of a function f on G with respect to a right-invariant measure μ is equal to the integral over the coset space G ⧸ Γ of the automorphization of f.

A question: is it possible to deduce ae_strongly_measurable (quotient_group.automorphize f) μ_𝓕 from ae_strongly_measurable f μ (as opposed to assuming it as a hypothesis in the main theorem)? It seems quite plausible...

Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com>

Co-authored-by: Alex Kontorovich <58564076+AlexKontorovich@users.noreply.github.com> Co-authored-by: AlexKontorovich <58564076+AlexKontorovich@users.noreply.github.com>

Diff

@@ -212,6 +212,11 @@ calc ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in g • s, f x ∂μ : h.linteg
   tsum_congr $ λ g, ((measure_preserving_smul g⁻¹ μ).set_lintegral_comp_emb
     (measurable_embedding_const_smul _) _ _).symm
 
+
+@[to_additive] lemma lintegral_eq_tsum'' (h : is_fundamental_domain G s μ) (f : α → ℝ≥0∞) :
+  ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in s, f (g • x) ∂μ :=
+(lintegral_eq_tsum' h f).trans ((equiv.inv G).tsum_eq (λ g, ∫⁻ (x : α) in s, f (g • x) ∂μ))
+
 @[to_additive] lemma set_lintegral_eq_tsum (h : is_fundamental_domain G s μ) (f : α → ℝ≥0∞)
   (t : set α) : ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ :=
 calc ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in g • s, f x ∂(μ.restrict t) :
@@ -357,6 +362,10 @@ calc ∫ x, f x ∂μ = ∑' g : G, ∫ x in g • s, f x ∂μ : h.integral_eq_
   tsum_congr $ λ g, (measure_preserving_smul g⁻¹ μ).set_integral_image_emb
     (measurable_embedding_const_smul _) _ _
 
+@[to_additive] lemma integral_eq_tsum'' (h : is_fundamental_domain G s μ)
+  (f : α → E) (hf : integrable f μ) : ∫ x, f x ∂μ = ∑' g : G, ∫ x in s, f (g • x) ∂μ :=
+(integral_eq_tsum' h f hf).trans ((equiv.inv G).tsum_eq (λ g, ∫ (x : α) in s, f (g • x) ∂μ))
+
 @[to_additive] lemma set_integral_eq_tsum (h : is_fundamental_domain G s μ) {f : α → E}
   {t : set α} (hf : integrable_on f t μ) :
   ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ :=

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

bump to nightly-2024-04-19-08

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

a9e81450

Diff

@@ -520,7 +520,7 @@ theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
     _ = ∑' g : G, ∫ x in g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ :=
       tsum_congr fun g =>
-        (measurePreserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
+        (measurePreserving_smul g⁻¹ μ).setIntegral_image_emb (measurableEmbedding_const_smul _) _ _
 #align measure_theory.is_fundamental_domain.integral_eq_tsum' MeasureTheory.IsFundamentalDomain.integral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum'
 -/
@@ -534,37 +534,37 @@ theorem integral_eq_tsum'' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum'' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum''
 -/
 
-#print MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum /-
+#print MeasureTheory.IsFundamentalDomain.setIntegral_eq_tsum /-
 @[to_additive]
-theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
+theorem setIntegral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
     (hf : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ :=
   calc
     ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in g • s, f x ∂μ.restrict t :=
       h.integral_eq_tsum_of_ac restrict_le_self.AbsolutelyContinuous f hf
     _ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := by
       simp only [h.restrict_restrict, measure_smul, inter_comm]
-#align measure_theory.is_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum
-#align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsAddFundamentalDomain.set_integral_eq_tsum
+#align measure_theory.is_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsFundamentalDomain.setIntegral_eq_tsum
+#align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsAddFundamentalDomain.setIntegral_eq_tsum
 -/
 
-#print MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum' /-
+#print MeasureTheory.IsFundamentalDomain.setIntegral_eq_tsum' /-
 @[to_additive]
-theorem set_integral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
+theorem setIntegral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
     (hf : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
   calc
-    ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := h.set_integral_eq_tsum hf
+    ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := h.setIntegral_eq_tsum hf
     _ = ∑' g : G, ∫ x in t ∩ g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫ x in g⁻¹ • (g • t ∩ s), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
     _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
       tsum_congr fun g =>
-        (measurePreserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
-#align measure_theory.is_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum'
-#align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.set_integral_eq_tsum'
+        (measurePreserving_smul g⁻¹ μ).setIntegral_image_emb (measurableEmbedding_const_smul _) _ _
+#align measure_theory.is_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsFundamentalDomain.setIntegral_eq_tsum'
+#align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.setIntegral_eq_tsum'
 -/
 
-#print MeasureTheory.IsFundamentalDomain.set_integral_eq /-
+#print MeasureTheory.IsFundamentalDomain.setIntegral_eq /-
 @[to_additive]
-protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
+protected theorem setIntegral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
     {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) : ∫ x in s, f x ∂μ = ∫ x in t, f x ∂μ :=
   by
   by_cases hfs : integrable_on f s μ
@@ -575,8 +575,8 @@ protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFund
       _ = ∫ x in t, f x ∂μ := (hs.set_integral_eq_tsum' hft).symm
   · rw [integral_undef hfs, integral_undef]
     rwa [hs.integrable_on_iff ht hf] at hfs
-#align measure_theory.is_fundamental_domain.set_integral_eq MeasureTheory.IsFundamentalDomain.set_integral_eq
-#align measure_theory.is_add_fundamental_domain.set_integral_eq MeasureTheory.IsAddFundamentalDomain.set_integral_eq
+#align measure_theory.is_fundamental_domain.set_integral_eq MeasureTheory.IsFundamentalDomain.setIntegral_eq
+#align measure_theory.is_add_fundamental_domain.set_integral_eq MeasureTheory.IsAddFundamentalDomain.setIntegral_eq
 -/
 
 #print MeasureTheory.IsFundamentalDomain.measure_le_of_pairwise_disjoint /-

bump to nightly-2024-04-06-08

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

e34029c9

Diff

@@ -100,7 +100,7 @@ theorem mk' (h_meas : NullMeasurableSet s μ) (h_exists : ∀ x : α, ∃! g : G
 #align measure_theory.is_add_fundamental_domain.mk' MeasureTheory.IsAddFundamentalDomain.mk'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 #print MeasureTheory.IsFundamentalDomain.mk'' /-
 /-- For `s` to be a fundamental domain, it's enough to check `ae_disjoint (g • s) s` for `g ≠ 1`. -/
 @[to_additive
@@ -115,7 +115,7 @@ theorem mk'' (h_meas : NullMeasurableSet s μ) (h_ae_covers : ∀ᵐ x ∂μ, 
 #align measure_theory.is_add_fundamental_domain.mk'' MeasureTheory.IsAddFundamentalDomain.mk''
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 #print MeasureTheory.IsFundamentalDomain.mk_of_measure_univ_le /-
 /-- If a measurable space has a finite measure `μ` and a countable group `G` acts
 quasi-measure-preservingly, then to show that a set `s` is a fundamental domain, it is sufficient
@@ -597,8 +597,8 @@ theorem measure_le_of_pairwise_disjoint (hs : IsFundamentalDomain G s μ)
 #align measure_theory.is_add_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsAddFundamentalDomain.measure_le_of_pairwise_disjoint
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » t) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 #print MeasureTheory.IsFundamentalDomain.exists_ne_one_smul_eq /-
 /-- If the action of a countable group `G` admits an invariant measure `μ` with a fundamental domain
 `s`, then every null-measurable set `t` of measure strictly greater than `μ s` contains two

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -94,7 +94,7 @@ theorem mk' (h_meas : NullMeasurableSet s μ) (h_exists : ∀ x : α, ∃! g : G
       Disjoint.aedisjoint <|
         disjoint_left.2 fun x hxa hxb =>
           by
-          rw [mem_smul_set_iff_inv_smul_mem] at hxa hxb 
+          rw [mem_smul_set_iff_inv_smul_mem] at hxa hxb
           exact hab (inv_injective <| (h_exists x).unique hxa hxb) }
 #align measure_theory.is_fundamental_domain.mk' MeasureTheory.IsFundamentalDomain.mk'
 #align measure_theory.is_add_fundamental_domain.mk' MeasureTheory.IsAddFundamentalDomain.mk'
@@ -574,7 +574,7 @@ protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFund
       _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := by simp only [hf, inter_comm]
       _ = ∫ x in t, f x ∂μ := (hs.set_integral_eq_tsum' hft).symm
   · rw [integral_undef hfs, integral_undef]
-    rwa [hs.integrable_on_iff ht hf] at hfs 
+    rwa [hs.integrable_on_iff ht hf] at hfs
 #align measure_theory.is_fundamental_domain.set_integral_eq MeasureTheory.IsFundamentalDomain.set_integral_eq
 #align measure_theory.is_add_fundamental_domain.set_integral_eq MeasureTheory.IsAddFundamentalDomain.set_integral_eq
 -/
@@ -634,7 +634,7 @@ theorem essSup_measure_restrict (hs : IsFundamentalDomain G s μ) {f : α → 
   rw [essSup_eq_sInf (μ.restrict s) f, essSup_eq_sInf μ f]
   refine' sInf_le_sInf _
   rintro a (ha : (μ.restrict s) {x : α | a < f x} = 0)
-  rw [measure.restrict_apply₀' hs.null_measurable_set] at ha 
+  rw [measure.restrict_apply₀' hs.null_measurable_set] at ha
   refine' measure_zero_of_invariant hs _ _ ha
   intro γ
   ext x
@@ -779,7 +779,7 @@ theorem pairwise_disjoint_fundamentalInterior :
   by
   refine' fun a b hab => disjoint_left.2 _
   rintro _ ⟨x, hx, rfl⟩ ⟨y, hy, hxy⟩
-  rw [mem_fundamental_interior] at hx hy 
+  rw [mem_fundamental_interior] at hx hy
   refine' hx.2 (a⁻¹ * b) _ _
   rwa [Ne.def, inv_mul_eq_iff_eq_mul, mul_one, eq_comm]
   simpa [mul_smul, ← hxy, mem_inv_smul_set_iff] using hy.1

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,8 +3,8 @@ 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.Action
-import Mathbin.MeasureTheory.Integral.SetIntegral
+import MeasureTheory.Group.Action
+import MeasureTheory.Integral.SetIntegral
 
 #align_import measure_theory.group.fundamental_domain from "leanprover-community/mathlib"@"3b52265189f3fb43aa631edffce5d060fafaf82f"
 
@@ -100,7 +100,7 @@ theorem mk' (h_meas : NullMeasurableSet s μ) (h_exists : ∀ x : α, ∃! g : G
 #align measure_theory.is_add_fundamental_domain.mk' MeasureTheory.IsAddFundamentalDomain.mk'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 #print MeasureTheory.IsFundamentalDomain.mk'' /-
 /-- For `s` to be a fundamental domain, it's enough to check `ae_disjoint (g • s) s` for `g ≠ 1`. -/
 @[to_additive
@@ -115,7 +115,7 @@ theorem mk'' (h_meas : NullMeasurableSet s μ) (h_ae_covers : ∀ᵐ x ∂μ, 
 #align measure_theory.is_add_fundamental_domain.mk'' MeasureTheory.IsAddFundamentalDomain.mk''
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 #print MeasureTheory.IsFundamentalDomain.mk_of_measure_univ_le /-
 /-- If a measurable space has a finite measure `μ` and a countable group `G` acts
 quasi-measure-preservingly, then to show that a set `s` is a fundamental domain, it is sufficient
@@ -597,8 +597,8 @@ theorem measure_le_of_pairwise_disjoint (hs : IsFundamentalDomain G s μ)
 #align measure_theory.is_add_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsAddFundamentalDomain.measure_le_of_pairwise_disjoint
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 #print MeasureTheory.IsFundamentalDomain.exists_ne_one_smul_eq /-
 /-- If the action of a countable group `G` admits an invariant measure `μ` with a fundamental domain
 `s`, then every null-measurable set `t` of measure strictly greater than `μ s` contains two

bump to nightly-2023-09-23-06

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

2211bbec

Diff

@@ -300,12 +300,14 @@ theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum'
 -/
 
+#print MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum'' /-
 @[to_additive]
 theorem lintegral_eq_tsum'' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) :
     ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in s, f (g • x) ∂μ :=
   (lintegral_eq_tsum' h f).trans ((Equiv.inv G).tsum_eq fun g => ∫⁻ x : α in s, f (g • x) ∂μ)
 #align measure_theory.is_fundamental_domain.lintegral_eq_tsum'' MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum''
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum'' MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum''
+-/
 
 #print MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum /-
 @[to_additive]
@@ -523,12 +525,14 @@ theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum'
 -/
 
+#print MeasureTheory.IsFundamentalDomain.integral_eq_tsum'' /-
 @[to_additive]
 theorem integral_eq_tsum'' (h : IsFundamentalDomain G s μ) (f : α → E) (hf : Integrable f μ) :
     ∫ x, f x ∂μ = ∑' g : G, ∫ x in s, f (g • x) ∂μ :=
   (integral_eq_tsum' h f hf).trans ((Equiv.inv G).tsum_eq fun g => ∫ x : α in s, f (g • x) ∂μ)
 #align measure_theory.is_fundamental_domain.integral_eq_tsum'' MeasureTheory.IsFundamentalDomain.integral_eq_tsum''
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum'' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum''
+-/
 
 #print MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum /-
 @[to_additive]

bump to nightly-2023-08-02-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

7aca3f15

Diff

@@ -6,7 +6,7 @@ Authors: Yury G. Kudryashov
 import Mathbin.MeasureTheory.Group.Action
 import Mathbin.MeasureTheory.Integral.SetIntegral
 
-#align_import measure_theory.group.fundamental_domain from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+#align_import measure_theory.group.fundamental_domain from "leanprover-community/mathlib"@"3b52265189f3fb43aa631edffce5d060fafaf82f"
 
 /-!
 # Fundamental domain of a group action
@@ -300,6 +300,13 @@ theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum'
 -/
 
+@[to_additive]
+theorem lintegral_eq_tsum'' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) :
+    ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in s, f (g • x) ∂μ :=
+  (lintegral_eq_tsum' h f).trans ((Equiv.inv G).tsum_eq fun g => ∫⁻ x : α in s, f (g • x) ∂μ)
+#align measure_theory.is_fundamental_domain.lintegral_eq_tsum'' MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum''
+#align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum'' MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum''
+
 #print MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum /-
 @[to_additive]
 theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
@@ -516,6 +523,13 @@ theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum'
 -/
 
+@[to_additive]
+theorem integral_eq_tsum'' (h : IsFundamentalDomain G s μ) (f : α → E) (hf : Integrable f μ) :
+    ∫ x, f x ∂μ = ∑' g : G, ∫ x in s, f (g • x) ∂μ :=
+  (integral_eq_tsum' h f hf).trans ((Equiv.inv G).tsum_eq fun g => ∫ x : α in s, f (g • x) ∂μ)
+#align measure_theory.is_fundamental_domain.integral_eq_tsum'' MeasureTheory.IsFundamentalDomain.integral_eq_tsum''
+#align measure_theory.is_add_fundamental_domain.integral_eq_tsum'' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum''
+
 #print MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum /-
 @[to_additive]
 theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,15 +2,12 @@
 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.fundamental_domain
-! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Group.Action
 import Mathbin.MeasureTheory.Integral.SetIntegral
 
+#align_import measure_theory.group.fundamental_domain from "leanprover-community/mathlib"@"c20927220ef87bb4962ba08bf6da2ce3cf50a6dd"
+
 /-!
 # Fundamental domain of a group action
 
@@ -103,7 +100,7 @@ theorem mk' (h_meas : NullMeasurableSet s μ) (h_exists : ∀ x : α, ∃! g : G
 #align measure_theory.is_add_fundamental_domain.mk' MeasureTheory.IsAddFundamentalDomain.mk'
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 #print MeasureTheory.IsFundamentalDomain.mk'' /-
 /-- For `s` to be a fundamental domain, it's enough to check `ae_disjoint (g • s) s` for `g ≠ 1`. -/
 @[to_additive
@@ -118,7 +115,7 @@ theorem mk'' (h_meas : NullMeasurableSet s μ) (h_ae_covers : ∀ᵐ x ∂μ, 
 #align measure_theory.is_add_fundamental_domain.mk'' MeasureTheory.IsAddFundamentalDomain.mk''
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 #print MeasureTheory.IsFundamentalDomain.mk_of_measure_univ_le /-
 /-- If a measurable space has a finite measure `μ` and a countable group `G` acts
 quasi-measure-preservingly, then to show that a set `s` is a fundamental domain, it is sufficient
@@ -582,8 +579,8 @@ theorem measure_le_of_pairwise_disjoint (hs : IsFundamentalDomain G s μ)
 #align measure_theory.is_add_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsAddFundamentalDomain.measure_le_of_pairwise_disjoint
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » t) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 #print MeasureTheory.IsFundamentalDomain.exists_ne_one_smul_eq /-
 /-- If the action of a countable group `G` admits an invariant measure `μ` with a fundamental domain
 `s`, then every null-measurable set `t` of measure strictly greater than `μ s` contains two

bump to nightly-2023-06-19-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

bbb90f4e

Diff

@@ -196,13 +196,13 @@ theorem image_of_equiv {ν : Measure β} (h : IsFundamentalDomain G s μ) (f : 
 #align measure_theory.is_add_fundamental_domain.image_of_equiv MeasureTheory.IsAddFundamentalDomain.image_of_equiv
 -/
 
-#print MeasureTheory.IsFundamentalDomain.pairwise_aEDisjoint_of_ac /-
+#print MeasureTheory.IsFundamentalDomain.pairwise_aedisjoint_of_ac /-
 @[to_additive]
-theorem pairwise_aEDisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
+theorem pairwise_aedisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
     Pairwise fun g₁ g₂ : G => AEDisjoint ν (g₁ • s) (g₂ • s) :=
   h.AEDisjoint.mono fun g₁ g₂ H => hν H
-#align measure_theory.is_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsFundamentalDomain.pairwise_aEDisjoint_of_ac
-#align measure_theory.is_add_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsAddFundamentalDomain.pairwise_aEDisjoint_of_ac
+#align measure_theory.is_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsFundamentalDomain.pairwise_aedisjoint_of_ac
+#align measure_theory.is_add_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsAddFundamentalDomain.pairwise_aedisjoint_of_ac
 -/
 
 #print MeasureTheory.IsFundamentalDomain.smul_of_comm /-

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -84,6 +84,7 @@ namespace IsFundamentalDomain
 variable [Group G] [Group H] [MulAction G α] [MeasurableSpace α] [MulAction H β] [MeasurableSpace β]
   [NormedAddCommGroup E] {s t : Set α} {μ : Measure α}
 
+#print MeasureTheory.IsFundamentalDomain.mk' /-
 /-- If for each `x : α`, exactly one of `g • x`, `g : G`, belongs to a measurable set `s`, then `s`
 is a fundamental domain for the action of `G` on `α`. -/
 @[to_additive
@@ -100,8 +101,10 @@ theorem mk' (h_meas : NullMeasurableSet s μ) (h_exists : ∀ x : α, ∃! g : G
           exact hab (inv_injective <| (h_exists x).unique hxa hxb) }
 #align measure_theory.is_fundamental_domain.mk' MeasureTheory.IsFundamentalDomain.mk'
 #align measure_theory.is_add_fundamental_domain.mk' MeasureTheory.IsAddFundamentalDomain.mk'
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+#print MeasureTheory.IsFundamentalDomain.mk'' /-
 /-- For `s` to be a fundamental domain, it's enough to check `ae_disjoint (g • s) s` for `g ≠ 1`. -/
 @[to_additive
       "For `s` to be a fundamental domain, it's enough to check `ae_disjoint (g +ᵥ s) s` for\n`g ≠ 0`."]
@@ -113,8 +116,10 @@ theorem mk'' (h_meas : NullMeasurableSet s μ) (h_ae_covers : ∀ᵐ x ∂μ, 
     AEDisjoint := pairwise_aedisjoint_of_aedisjoint_forall_ne_one h_ae_disjoint h_qmp }
 #align measure_theory.is_fundamental_domain.mk'' MeasureTheory.IsFundamentalDomain.mk''
 #align measure_theory.is_add_fundamental_domain.mk'' MeasureTheory.IsAddFundamentalDomain.mk''
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+#print MeasureTheory.IsFundamentalDomain.mk_of_measure_univ_le /-
 /-- If a measurable space has a finite measure `μ` and a countable group `G` acts
 quasi-measure-preservingly, then to show that a set `s` is a fundamental domain, it is sufficient
 to check that its translates `g • s` are (almost) disjoint and that the sum `∑' g, μ (g • s)` is
@@ -141,21 +146,27 @@ theorem mk_of_measure_univ_le [IsFiniteMeasure μ] [Countable G] (h_meas : NullM
       exact h_measure_univ_le }
 #align measure_theory.is_fundamental_domain.mk_of_measure_univ_le MeasureTheory.IsFundamentalDomain.mk_of_measure_univ_le
 #align measure_theory.is_add_fundamental_domain.mk_of_measure_univ_le MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_le
+-/
 
+#print MeasureTheory.IsFundamentalDomain.iUnion_smul_ae_eq /-
 @[to_additive]
 theorem iUnion_smul_ae_eq (h : IsFundamentalDomain G s μ) : (⋃ g : G, g • s) =ᵐ[μ] univ :=
   eventuallyEq_univ.2 <|
     h.ae_covers.mono fun x ⟨g, hg⟩ => mem_iUnion.2 ⟨g⁻¹, _, hg, inv_smul_smul _ _⟩
 #align measure_theory.is_fundamental_domain.Union_smul_ae_eq MeasureTheory.IsFundamentalDomain.iUnion_smul_ae_eq
 #align measure_theory.is_add_fundamental_domain.Union_vadd_ae_eq MeasureTheory.IsAddFundamentalDomain.iUnion_vadd_ae_eq
+-/
 
+#print MeasureTheory.IsFundamentalDomain.mono /-
 @[to_additive]
 theorem mono (h : IsFundamentalDomain G s μ) {ν : Measure α} (hle : ν ≪ μ) :
     IsFundamentalDomain G s ν :=
   ⟨h.1.mono_ac hle, hle h.2, h.AEDisjoint.mono fun a b hab => hle hab⟩
 #align measure_theory.is_fundamental_domain.mono MeasureTheory.IsFundamentalDomain.mono
 #align measure_theory.is_add_fundamental_domain.mono MeasureTheory.IsAddFundamentalDomain.mono
+-/
 
+#print MeasureTheory.IsFundamentalDomain.preimage_of_equiv /-
 @[to_additive]
 theorem preimage_of_equiv {ν : Measure β} (h : IsFundamentalDomain G s μ) {f : β → α}
     (hf : QuasiMeasurePreserving f ν μ) {e : G → H} (he : Bijective e)
@@ -169,7 +180,9 @@ theorem preimage_of_equiv {ν : Measure β} (h : IsFundamentalDomain G s μ) {f
       simp only [← preimage_smul_inv, preimage_preimage, ← hef _ _, e.apply_symm_apply, inv_inv] }
 #align measure_theory.is_fundamental_domain.preimage_of_equiv MeasureTheory.IsFundamentalDomain.preimage_of_equiv
 #align measure_theory.is_add_fundamental_domain.preimage_of_equiv MeasureTheory.IsAddFundamentalDomain.preimage_of_equiv
+-/
 
+#print MeasureTheory.IsFundamentalDomain.image_of_equiv /-
 @[to_additive]
 theorem image_of_equiv {ν : Measure β} (h : IsFundamentalDomain G s μ) (f : α ≃ β)
     (hf : QuasiMeasurePreserving f.symm ν μ) (e : H ≃ G)
@@ -181,14 +194,18 @@ theorem image_of_equiv {ν : Measure β} (h : IsFundamentalDomain G s μ) (f : 
   rw [← hef _ _, f.symm_apply_apply, f.symm_apply_apply, e.apply_symm_apply]
 #align measure_theory.is_fundamental_domain.image_of_equiv MeasureTheory.IsFundamentalDomain.image_of_equiv
 #align measure_theory.is_add_fundamental_domain.image_of_equiv MeasureTheory.IsAddFundamentalDomain.image_of_equiv
+-/
 
+#print MeasureTheory.IsFundamentalDomain.pairwise_aEDisjoint_of_ac /-
 @[to_additive]
 theorem pairwise_aEDisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
     Pairwise fun g₁ g₂ : G => AEDisjoint ν (g₁ • s) (g₂ • s) :=
   h.AEDisjoint.mono fun g₁ g₂ H => hν H
 #align measure_theory.is_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsFundamentalDomain.pairwise_aEDisjoint_of_ac
 #align measure_theory.is_add_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsAddFundamentalDomain.pairwise_aEDisjoint_of_ac
+-/
 
+#print MeasureTheory.IsFundamentalDomain.smul_of_comm /-
 @[to_additive]
 theorem smul_of_comm {G' : Type _} [Group G'] [MulAction G' α] [MeasurableSpace G']
     [MeasurableSMul G' α] [SMulInvariantMeasure G' α μ] [SMulCommClass G' G α]
@@ -198,23 +215,29 @@ theorem smul_of_comm {G' : Type _} [Group G'] [MulAction G' α] [MeasurableSpace
     smul_comm g
 #align measure_theory.is_fundamental_domain.smul_of_comm MeasureTheory.IsFundamentalDomain.smul_of_comm
 #align measure_theory.is_add_fundamental_domain.vadd_of_comm MeasureTheory.IsAddFundamentalDomain.vadd_of_comm
+-/
 
 variable [MeasurableSpace G] [MeasurableSMul G α] [SMulInvariantMeasure G α μ]
 
+#print MeasureTheory.IsFundamentalDomain.nullMeasurableSet_smul /-
 @[to_additive]
 theorem nullMeasurableSet_smul (h : IsFundamentalDomain G s μ) (g : G) :
     NullMeasurableSet (g • s) μ :=
   h.NullMeasurableSet.smul g
 #align measure_theory.is_fundamental_domain.null_measurable_set_smul MeasureTheory.IsFundamentalDomain.nullMeasurableSet_smul
 #align measure_theory.is_add_fundamental_domain.null_measurable_set_vadd MeasureTheory.IsAddFundamentalDomain.nullMeasurableSet_vadd
+-/
 
+#print MeasureTheory.IsFundamentalDomain.restrict_restrict /-
 @[to_additive]
 theorem restrict_restrict (h : IsFundamentalDomain G s μ) (g : G) (t : Set α) :
     (μ.restrict t).restrict (g • s) = μ.restrict (g • s ∩ t) :=
   restrict_restrict₀ ((h.nullMeasurableSet_smul g).mono restrict_le_self)
 #align measure_theory.is_fundamental_domain.restrict_restrict MeasureTheory.IsFundamentalDomain.restrict_restrict
 #align measure_theory.is_add_fundamental_domain.restrict_restrict MeasureTheory.IsAddFundamentalDomain.restrict_restrict
+-/
 
+#print MeasureTheory.IsFundamentalDomain.smul /-
 @[to_additive]
 theorem smul (h : IsFundamentalDomain G s μ) (g : G) : IsFundamentalDomain G (g • s) μ :=
   h.image_of_equiv (MulAction.toPerm g) (measurePreserving_smul _ _).QuasiMeasurePreserving
@@ -223,9 +246,11 @@ theorem smul (h : IsFundamentalDomain G s μ) (g : G) : IsFundamentalDomain G (g
     fun g' x => by simp [smul_smul, mul_assoc]
 #align measure_theory.is_fundamental_domain.smul MeasureTheory.IsFundamentalDomain.smul
 #align measure_theory.is_add_fundamental_domain.vadd MeasureTheory.IsAddFundamentalDomain.vadd
+-/
 
 variable [Countable G] {ν : Measure α}
 
+#print MeasureTheory.IsFundamentalDomain.sum_restrict_of_ac /-
 @[to_additive]
 theorem sum_restrict_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
     (Sum fun g : G => ν.restrict (g • s)) = ν := by
@@ -235,27 +260,35 @@ theorem sum_restrict_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
     restrict_congr_set (hν h.Union_smul_ae_eq), restrict_univ]
 #align measure_theory.is_fundamental_domain.sum_restrict_of_ac MeasureTheory.IsFundamentalDomain.sum_restrict_of_ac
 #align measure_theory.is_add_fundamental_domain.sum_restrict_of_ac MeasureTheory.IsAddFundamentalDomain.sum_restrict_of_ac
+-/
 
+#print MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum_of_ac /-
 @[to_additive]
 theorem lintegral_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) (f : α → ℝ≥0∞) :
     ∫⁻ x, f x ∂ν = ∑' g : G, ∫⁻ x in g • s, f x ∂ν := by
   rw [← lintegral_sum_measure, h.sum_restrict_of_ac hν]
 #align measure_theory.is_fundamental_domain.lintegral_eq_tsum_of_ac MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum_of_ac
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum_of_ac MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum_of_ac
+-/
 
+#print MeasureTheory.IsFundamentalDomain.sum_restrict /-
 @[to_additive]
 theorem sum_restrict (h : IsFundamentalDomain G s μ) : (Sum fun g : G => μ.restrict (g • s)) = μ :=
   h.sum_restrict_of_ac (refl _)
 #align measure_theory.is_fundamental_domain.sum_restrict MeasureTheory.IsFundamentalDomain.sum_restrict
 #align measure_theory.is_add_fundamental_domain.sum_restrict MeasureTheory.IsAddFundamentalDomain.sum_restrict
+-/
 
+#print MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum /-
 @[to_additive]
 theorem lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) :
     ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in g • s, f x ∂μ :=
   h.lintegral_eq_tsum_of_ac (refl _) f
 #align measure_theory.is_fundamental_domain.lintegral_eq_tsum MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum
+-/
 
+#print MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum' /-
 @[to_additive]
 theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) :
     ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in s, f (g⁻¹ • x) ∂μ :=
@@ -268,7 +301,9 @@ theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0
             _).symm
 #align measure_theory.is_fundamental_domain.lintegral_eq_tsum' MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum'
+-/
 
+#print MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum /-
 @[to_additive]
 theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
     ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ :=
@@ -278,7 +313,9 @@ theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ
     _ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ := by simp only [h.restrict_restrict, inter_comm]
 #align measure_theory.is_fundamental_domain.set_lintegral_eq_tsum MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum
 #align measure_theory.is_add_fundamental_domain.set_lintegral_eq_tsum MeasureTheory.IsAddFundamentalDomain.set_lintegral_eq_tsum
+-/
 
+#print MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum' /-
 @[to_additive]
 theorem set_lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
     ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
@@ -292,7 +329,9 @@ theorem set_lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ
             _).symm
 #align measure_theory.is_fundamental_domain.set_lintegral_eq_tsum' MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.set_lintegral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.set_lintegral_eq_tsum'
+-/
 
+#print MeasureTheory.IsFundamentalDomain.measure_eq_tsum_of_ac /-
 @[to_additive]
 theorem measure_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) (t : Set α) :
     ν t = ∑' g : G, ν (t ∩ g • s) :=
@@ -303,28 +342,36 @@ theorem measure_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ)
     h.lintegral_eq_tsum_of_ac H 1
 #align measure_theory.is_fundamental_domain.measure_eq_tsum_of_ac MeasureTheory.IsFundamentalDomain.measure_eq_tsum_of_ac
 #align measure_theory.is_add_fundamental_domain.measure_eq_tsum_of_ac MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum_of_ac
+-/
 
+#print MeasureTheory.IsFundamentalDomain.measure_eq_tsum' /-
 @[to_additive]
 theorem measure_eq_tsum' (h : IsFundamentalDomain G s μ) (t : Set α) :
     μ t = ∑' g : G, μ (t ∩ g • s) :=
   h.measure_eq_tsum_of_ac AbsolutelyContinuous.rfl t
 #align measure_theory.is_fundamental_domain.measure_eq_tsum' MeasureTheory.IsFundamentalDomain.measure_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.measure_eq_tsum' MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum'
+-/
 
+#print MeasureTheory.IsFundamentalDomain.measure_eq_tsum /-
 @[to_additive]
 theorem measure_eq_tsum (h : IsFundamentalDomain G s μ) (t : Set α) :
     μ t = ∑' g : G, μ (g • t ∩ s) := by
   simpa only [set_lintegral_one] using h.set_lintegral_eq_tsum' (fun _ => 1) t
 #align measure_theory.is_fundamental_domain.measure_eq_tsum MeasureTheory.IsFundamentalDomain.measure_eq_tsum
 #align measure_theory.is_add_fundamental_domain.measure_eq_tsum MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum
+-/
 
+#print MeasureTheory.IsFundamentalDomain.measure_zero_of_invariant /-
 @[to_additive]
 theorem measure_zero_of_invariant (h : IsFundamentalDomain G s μ) (t : Set α)
     (ht : ∀ g : G, g • t = t) (hts : μ (t ∩ s) = 0) : μ t = 0 := by
   simp [measure_eq_tsum h, ht, hts]
 #align measure_theory.is_fundamental_domain.measure_zero_of_invariant MeasureTheory.IsFundamentalDomain.measure_zero_of_invariant
 #align measure_theory.is_add_fundamental_domain.measure_zero_of_invariant MeasureTheory.IsAddFundamentalDomain.measure_zero_of_invariant
+-/
 
+#print MeasureTheory.IsFundamentalDomain.measure_eq_card_smul_of_smul_ae_eq_self /-
 /-- Given a measure space with an action of a finite group `G`, the measure of any `G`-invariant set
 is determined by the measure of its intersection with a fundamental domain for the action of `G`. -/
 @[to_additive measure_eq_card_smul_of_vadd_ae_eq_self
@@ -340,7 +387,9 @@ theorem measure_eq_card_smul_of_smul_ae_eq_self [Finite G] (h : IsFundamentalDom
     Finset.card_univ]
 #align measure_theory.is_fundamental_domain.measure_eq_card_smul_of_smul_ae_eq_self MeasureTheory.IsFundamentalDomain.measure_eq_card_smul_of_smul_ae_eq_self
 #align measure_theory.is_add_fundamental_domain.measure_eq_card_smul_of_vadd_ae_eq_self MeasureTheory.IsAddFundamentalDomain.measure_eq_card_smul_of_vadd_ae_eq_self
+-/
 
+#print MeasureTheory.IsFundamentalDomain.set_lintegral_eq /-
 @[to_additive]
 protected theorem set_lintegral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
     (f : α → ℝ≥0∞) (hf : ∀ (g : G) (x), f (g • x) = f x) : ∫⁻ x in s, f x ∂μ = ∫⁻ x in t, f x ∂μ :=
@@ -350,7 +399,9 @@ protected theorem set_lintegral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFun
     _ = ∫⁻ x in t, f x ∂μ := (hs.set_lintegral_eq_tsum' _ _).symm
 #align measure_theory.is_fundamental_domain.set_lintegral_eq MeasureTheory.IsFundamentalDomain.set_lintegral_eq
 #align measure_theory.is_add_fundamental_domain.set_lintegral_eq MeasureTheory.IsAddFundamentalDomain.set_lintegral_eq
+-/
 
+#print MeasureTheory.IsFundamentalDomain.measure_set_eq /-
 @[to_additive]
 theorem measure_set_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ) {A : Set α}
     (hA₀ : MeasurableSet A) (hA : ∀ g : G, (fun x => g • x) ⁻¹' A = A) : μ (A ∩ s) = μ (A ∩ t) :=
@@ -364,7 +415,9 @@ theorem measure_set_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDoma
   simpa [measure.restrict_apply hA₀, lintegral_indicator _ hA₀] using this
 #align measure_theory.is_fundamental_domain.measure_set_eq MeasureTheory.IsFundamentalDomain.measure_set_eq
 #align measure_theory.is_add_fundamental_domain.measure_set_eq MeasureTheory.IsAddFundamentalDomain.measure_set_eq
+-/
 
+#print MeasureTheory.IsFundamentalDomain.measure_eq /-
 /-- If `s` and `t` are two fundamental domains of the same action, then their measures are equal. -/
 @[to_additive
       "If `s` and `t` are two fundamental domains of the same action, then their measures\nare equal."]
@@ -373,7 +426,9 @@ protected theorem measure_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundament
   simpa only [set_lintegral_one] using hs.set_lintegral_eq ht (fun _ => 1) fun _ _ => rfl
 #align measure_theory.is_fundamental_domain.measure_eq MeasureTheory.IsFundamentalDomain.measure_eq
 #align measure_theory.is_add_fundamental_domain.measure_eq MeasureTheory.IsAddFundamentalDomain.measure_eq
+-/
 
+#print MeasureTheory.IsFundamentalDomain.aEStronglyMeasurable_on_iff /-
 @[to_additive]
 protected theorem aEStronglyMeasurable_on_iff {β : Type _} [TopologicalSpace β]
     [PseudoMetrizableSpace β] (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
@@ -402,7 +457,9 @@ protected theorem aEStronglyMeasurable_on_iff {β : Type _} [TopologicalSpace β
         hs.sum_restrict_of_ac restrict_le_self.absolutely_continuous]
 #align measure_theory.is_fundamental_domain.ae_strongly_measurable_on_iff MeasureTheory.IsFundamentalDomain.aEStronglyMeasurable_on_iff
 #align measure_theory.is_add_fundamental_domain.ae_strongly_measurable_on_iff MeasureTheory.IsAddFundamentalDomain.aEStronglyMeasurable_on_iff
+-/
 
+#print MeasureTheory.IsFundamentalDomain.hasFiniteIntegral_on_iff /-
 @[to_additive]
 protected theorem hasFiniteIntegral_on_iff (hs : IsFundamentalDomain G s μ)
     (ht : IsFundamentalDomain G t μ) {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) :
@@ -413,16 +470,20 @@ protected theorem hasFiniteIntegral_on_iff (hs : IsFundamentalDomain G s μ)
   intro g x; rw [hf]
 #align measure_theory.is_fundamental_domain.has_finite_integral_on_iff MeasureTheory.IsFundamentalDomain.hasFiniteIntegral_on_iff
 #align measure_theory.is_add_fundamental_domain.has_finite_integral_on_iff MeasureTheory.IsAddFundamentalDomain.hasFiniteIntegral_on_iff
+-/
 
+#print MeasureTheory.IsFundamentalDomain.integrableOn_iff /-
 @[to_additive]
 protected theorem integrableOn_iff (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
     {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) : IntegrableOn f s μ ↔ IntegrableOn f t μ :=
   and_congr (hs.aEStronglyMeasurable_on_iff ht hf) (hs.hasFiniteIntegral_on_iff ht hf)
 #align measure_theory.is_fundamental_domain.integrable_on_iff MeasureTheory.IsFundamentalDomain.integrableOn_iff
 #align measure_theory.is_add_fundamental_domain.integrable_on_iff MeasureTheory.IsAddFundamentalDomain.integrableOn_iff
+-/
 
 variable [NormedSpace ℝ E] [CompleteSpace E]
 
+#print MeasureTheory.IsFundamentalDomain.integral_eq_tsum_of_ac /-
 @[to_additive]
 theorem integral_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) (f : α → E)
     (hf : Integrable f ν) : ∫ x, f x ∂ν = ∑' g : G, ∫ x in g • s, f x ∂ν :=
@@ -433,14 +494,18 @@ theorem integral_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ
   exact hf
 #align measure_theory.is_fundamental_domain.integral_eq_tsum_of_ac MeasureTheory.IsFundamentalDomain.integral_eq_tsum_of_ac
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum_of_ac MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum_of_ac
+-/
 
+#print MeasureTheory.IsFundamentalDomain.integral_eq_tsum /-
 @[to_additive]
 theorem integral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → E) (hf : Integrable f μ) :
     ∫ x, f x ∂μ = ∑' g : G, ∫ x in g • s, f x ∂μ :=
   integral_eq_tsum_of_ac h (by rfl) f hf
 #align measure_theory.is_fundamental_domain.integral_eq_tsum MeasureTheory.IsFundamentalDomain.integral_eq_tsum
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum
+-/
 
+#print MeasureTheory.IsFundamentalDomain.integral_eq_tsum' /-
 @[to_additive]
 theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf : Integrable f μ) :
     ∫ x, f x ∂μ = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ :=
@@ -452,7 +517,9 @@ theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
         (measurePreserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
 #align measure_theory.is_fundamental_domain.integral_eq_tsum' MeasureTheory.IsFundamentalDomain.integral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum'
+-/
 
+#print MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum /-
 @[to_additive]
 theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
     (hf : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ :=
@@ -463,7 +530,9 @@ theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t
       simp only [h.restrict_restrict, measure_smul, inter_comm]
 #align measure_theory.is_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum
 #align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsAddFundamentalDomain.set_integral_eq_tsum
+-/
 
+#print MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum' /-
 @[to_additive]
 theorem set_integral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
     (hf : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
@@ -476,7 +545,9 @@ theorem set_integral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t
         (measurePreserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
 #align measure_theory.is_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.set_integral_eq_tsum'
+-/
 
+#print MeasureTheory.IsFundamentalDomain.set_integral_eq /-
 @[to_additive]
 protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
     {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) : ∫ x in s, f x ∂μ = ∫ x in t, f x ∂μ :=
@@ -491,7 +562,9 @@ protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFund
     rwa [hs.integrable_on_iff ht hf] at hfs 
 #align measure_theory.is_fundamental_domain.set_integral_eq MeasureTheory.IsFundamentalDomain.set_integral_eq
 #align measure_theory.is_add_fundamental_domain.set_integral_eq MeasureTheory.IsAddFundamentalDomain.set_integral_eq
+-/
 
+#print MeasureTheory.IsFundamentalDomain.measure_le_of_pairwise_disjoint /-
 /-- If the action of a countable group `G` admits an invariant measure `μ` with a fundamental domain
 `s`, then every null-measurable set `t` such that the sets `g • t ∩ s` are pairwise a.e.-disjoint
 has measure at most `μ s`. -/
@@ -507,9 +580,11 @@ theorem measure_le_of_pairwise_disjoint (hs : IsFundamentalDomain G s μ)
     _ ≤ μ s := measure_mono (iUnion_subset fun g => inter_subset_right _ _)
 #align measure_theory.is_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsFundamentalDomain.measure_le_of_pairwise_disjoint
 #align measure_theory.is_add_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsAddFundamentalDomain.measure_le_of_pairwise_disjoint
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+#print MeasureTheory.IsFundamentalDomain.exists_ne_one_smul_eq /-
 /-- If the action of a countable group `G` admits an invariant measure `μ` with a fundamental domain
 `s`, then every null-measurable set `t` of measure strictly greater than `μ s` contains two
 points `x y` such that `g • x = y` for some `g ≠ 1`. -/
@@ -529,7 +604,9 @@ theorem exists_ne_one_smul_eq (hs : IsFundamentalDomain G s μ) (htm : NullMeasu
   rw [mul_smul, ← hxy, inv_smul_smul]
 #align measure_theory.is_fundamental_domain.exists_ne_one_smul_eq MeasureTheory.IsFundamentalDomain.exists_ne_one_smul_eq
 #align measure_theory.is_add_fundamental_domain.exists_ne_zero_vadd_eq MeasureTheory.IsAddFundamentalDomain.exists_ne_zero_vadd_eq
+-/
 
+#print MeasureTheory.IsFundamentalDomain.essSup_measure_restrict /-
 /-- If `f` is invariant under the action of a countable group `G`, and `μ` is a `G`-invariant
   measure with a fundamental domain `s`, then the `ess_sup` of `f` restricted to `s` is the same as
   that of `f` on all of its domain. -/
@@ -550,6 +627,7 @@ theorem essSup_measure_restrict (hs : IsFundamentalDomain G s μ) {f : α → 
   simp only [mem_set_of_eq, hf γ⁻¹ x]
 #align measure_theory.is_fundamental_domain.ess_sup_measure_restrict MeasureTheory.IsFundamentalDomain.essSup_measure_restrict
 #align measure_theory.is_add_fundamental_domain.ess_sup_measure_restrict MeasureTheory.IsAddFundamentalDomain.essSup_measure_restrict
+-/
 
 end IsFundamentalDomain
 
@@ -583,19 +661,23 @@ def fundamentalInterior : Set α :=
 
 variable {G s}
 
+#print MeasureTheory.mem_fundamentalFrontier /-
 @[simp, to_additive MeasureTheory.mem_addFundamentalFrontier]
 theorem mem_fundamentalFrontier :
     x ∈ fundamentalFrontier G s ↔ x ∈ s ∧ ∃ (g : G) (hg : g ≠ 1), x ∈ g • s := by
   simp [fundamental_frontier]
 #align measure_theory.mem_fundamental_frontier MeasureTheory.mem_fundamentalFrontier
 #align measure_theory.mem_add_fundamental_frontier MeasureTheory.mem_addFundamentalFrontier
+-/
 
+#print MeasureTheory.mem_fundamentalInterior /-
 @[simp, to_additive MeasureTheory.mem_addFundamentalInterior]
 theorem mem_fundamentalInterior :
     x ∈ fundamentalInterior G s ↔ x ∈ s ∧ ∀ (g : G) (hg : g ≠ 1), x ∉ g • s := by
   simp [fundamental_interior]
 #align measure_theory.mem_fundamental_interior MeasureTheory.mem_fundamentalInterior
 #align measure_theory.mem_add_fundamental_interior MeasureTheory.mem_addFundamentalInterior
+-/
 
 #print MeasureTheory.fundamentalFrontier_subset /-
 @[to_additive MeasureTheory.addFundamentalFrontier_subset]
@@ -615,52 +697,67 @@ theorem fundamentalInterior_subset : fundamentalInterior G s ⊆ s :=
 
 variable (G s)
 
+#print MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier /-
 @[to_additive MeasureTheory.disjoint_addFundamentalInterior_addFundamentalFrontier]
 theorem disjoint_fundamentalInterior_fundamentalFrontier :
     Disjoint (fundamentalInterior G s) (fundamentalFrontier G s) :=
   disjoint_sdiff_self_left.mono_right inf_le_right
 #align measure_theory.disjoint_fundamental_interior_fundamental_frontier MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier
 #align measure_theory.disjoint_add_fundamental_interior_add_fundamental_frontier MeasureTheory.disjoint_addFundamentalInterior_addFundamentalFrontier
+-/
 
+#print MeasureTheory.fundamentalInterior_union_fundamentalFrontier /-
 @[simp, to_additive MeasureTheory.addFundamentalInterior_union_addFundamentalFrontier]
 theorem fundamentalInterior_union_fundamentalFrontier :
     fundamentalInterior G s ∪ fundamentalFrontier G s = s :=
   diff_union_inter _ _
 #align measure_theory.fundamental_interior_union_fundamental_frontier MeasureTheory.fundamentalInterior_union_fundamentalFrontier
 #align measure_theory.add_fundamental_interior_union_add_fundamental_frontier MeasureTheory.addFundamentalInterior_union_addFundamentalFrontier
+-/
 
+#print MeasureTheory.fundamentalFrontier_union_fundamentalInterior /-
 @[simp, to_additive MeasureTheory.addFundamentalInterior_union_addFundamentalFrontier]
 theorem fundamentalFrontier_union_fundamentalInterior :
     fundamentalFrontier G s ∪ fundamentalInterior G s = s :=
   inter_union_diff _ _
 #align measure_theory.fundamental_frontier_union_fundamental_interior MeasureTheory.fundamentalFrontier_union_fundamentalInterior
+-/
 
+#print MeasureTheory.sdiff_fundamentalInterior /-
 @[simp, to_additive MeasureTheory.sdiff_addFundamentalInterior]
 theorem sdiff_fundamentalInterior : s \ fundamentalInterior G s = fundamentalFrontier G s :=
   sdiff_sdiff_right_self
 #align measure_theory.sdiff_fundamental_interior MeasureTheory.sdiff_fundamentalInterior
 #align measure_theory.sdiff_add_fundamental_interior MeasureTheory.sdiff_addFundamentalInterior
+-/
 
+#print MeasureTheory.sdiff_fundamentalFrontier /-
 @[simp, to_additive MeasureTheory.sdiff_addFundamentalFrontier]
 theorem sdiff_fundamentalFrontier : s \ fundamentalFrontier G s = fundamentalInterior G s :=
   diff_self_inter
 #align measure_theory.sdiff_fundamental_frontier MeasureTheory.sdiff_fundamentalFrontier
 #align measure_theory.sdiff_add_fundamental_frontier MeasureTheory.sdiff_addFundamentalFrontier
+-/
 
+#print MeasureTheory.fundamentalFrontier_smul /-
 @[simp, to_additive MeasureTheory.addFundamentalFrontier_vadd]
 theorem fundamentalFrontier_smul [Group H] [MulAction H α] [SMulCommClass H G α] (g : H) :
     fundamentalFrontier G (g • s) = g • fundamentalFrontier G s := by
   simp_rw [fundamental_frontier, smul_set_inter, smul_set_Union, smul_comm g]
 #align measure_theory.fundamental_frontier_smul MeasureTheory.fundamentalFrontier_smul
 #align measure_theory.add_fundamental_frontier_vadd MeasureTheory.addFundamentalFrontier_vadd
+-/
 
+#print MeasureTheory.fundamentalInterior_smul /-
 @[simp, to_additive MeasureTheory.addFundamentalInterior_vadd]
 theorem fundamentalInterior_smul [Group H] [MulAction H α] [SMulCommClass H G α] (g : H) :
     fundamentalInterior G (g • s) = g • fundamentalInterior G s := by
   simp_rw [fundamental_interior, smul_set_sdiff, smul_set_Union, smul_comm g]
 #align measure_theory.fundamental_interior_smul MeasureTheory.fundamentalInterior_smul
 #align measure_theory.add_fundamental_interior_vadd MeasureTheory.addFundamentalInterior_vadd
+-/
 
+#print MeasureTheory.pairwise_disjoint_fundamentalInterior /-
 @[to_additive MeasureTheory.pairwise_disjoint_addFundamentalInterior]
 theorem pairwise_disjoint_fundamentalInterior :
     Pairwise (Disjoint on fun g : G => g • fundamentalInterior G s) :=
@@ -673,6 +770,7 @@ theorem pairwise_disjoint_fundamentalInterior :
   simpa [mul_smul, ← hxy, mem_inv_smul_set_iff] using hy.1
 #align measure_theory.pairwise_disjoint_fundamental_interior MeasureTheory.pairwise_disjoint_fundamentalInterior
 #align measure_theory.pairwise_disjoint_add_fundamental_interior MeasureTheory.pairwise_disjoint_addFundamentalInterior
+-/
 
 variable [Countable G] [MeasurableSpace G] [MeasurableSpace α] [MeasurableSMul G α] {μ : Measure α}
   [SMulInvariantMeasure G α μ]
@@ -704,8 +802,7 @@ section Group
 variable [Countable G] [Group G] [MulAction G α] [MeasurableSpace α] {μ : Measure α} {s : Set α}
   (hs : IsFundamentalDomain G s μ)
 
-include hs
-
+#print MeasureTheory.IsFundamentalDomain.measure_fundamentalFrontier /-
 @[to_additive MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalFrontier]
 theorem measure_fundamentalFrontier : μ (fundamentalFrontier G s) = 0 := by
   simpa only [fundamental_frontier, Union₂_inter, measure_Union_null_iff', one_smul,
@@ -713,12 +810,15 @@ theorem measure_fundamentalFrontier : μ (fundamentalFrontier G s) = 0 := by
     hs.ae_disjoint hg
 #align measure_theory.is_fundamental_domain.measure_fundamental_frontier MeasureTheory.IsFundamentalDomain.measure_fundamentalFrontier
 #align measure_theory.is_add_fundamental_domain.measure_add_fundamental_frontier MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalFrontier
+-/
 
+#print MeasureTheory.IsFundamentalDomain.measure_fundamentalInterior /-
 @[to_additive MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalInterior]
 theorem measure_fundamentalInterior : μ (fundamentalInterior G s) = μ s :=
   measure_diff_null' hs.measure_fundamentalFrontier
 #align measure_theory.is_fundamental_domain.measure_fundamental_interior MeasureTheory.IsFundamentalDomain.measure_fundamentalInterior
 #align measure_theory.is_add_fundamental_domain.measure_add_fundamental_interior MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalInterior
+-/
 
 end Group
 
@@ -726,8 +826,7 @@ variable [Countable G] [Group G] [MulAction G α] [MeasurableSpace α] {μ : Mea
   (hs : IsFundamentalDomain G s μ) [MeasurableSpace G] [MeasurableSMul G α]
   [SMulInvariantMeasure G α μ]
 
-include hs
-
+#print MeasureTheory.IsFundamentalDomain.fundamentalInterior /-
 protected theorem fundamentalInterior : IsFundamentalDomain G (fundamentalInterior G s) μ :=
   { NullMeasurableSet := hs.NullMeasurableSet.fundamentalInterior _ _
     ae_covers :=
@@ -749,6 +848,7 @@ protected theorem fundamentalInterior : IsFundamentalDomain G (fundamentalInteri
           hs.ae_covers
     AEDisjoint := (pairwise_disjoint_fundamentalInterior _ _).mono fun _ _ => Disjoint.aedisjoint }
 #align measure_theory.is_fundamental_domain.fundamental_interior MeasureTheory.IsFundamentalDomain.fundamentalInterior
+-/
 
 end IsFundamentalDomain

bump to nightly-2023-06-10-07

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

3fdc57bc

Diff

@@ -238,7 +238,7 @@ theorem sum_restrict_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
 
 @[to_additive]
 theorem lintegral_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) (f : α → ℝ≥0∞) :
-    (∫⁻ x, f x ∂ν) = ∑' g : G, ∫⁻ x in g • s, f x ∂ν := by
+    ∫⁻ x, f x ∂ν = ∑' g : G, ∫⁻ x in g • s, f x ∂ν := by
   rw [← lintegral_sum_measure, h.sum_restrict_of_ac hν]
 #align measure_theory.is_fundamental_domain.lintegral_eq_tsum_of_ac MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum_of_ac
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum_of_ac MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum_of_ac
@@ -251,16 +251,16 @@ theorem sum_restrict (h : IsFundamentalDomain G s μ) : (Sum fun g : G => μ.res
 
 @[to_additive]
 theorem lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) :
-    (∫⁻ x, f x ∂μ) = ∑' g : G, ∫⁻ x in g • s, f x ∂μ :=
+    ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in g • s, f x ∂μ :=
   h.lintegral_eq_tsum_of_ac (refl _) f
 #align measure_theory.is_fundamental_domain.lintegral_eq_tsum MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum
 
 @[to_additive]
 theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) :
-    (∫⁻ x, f x ∂μ) = ∑' g : G, ∫⁻ x in s, f (g⁻¹ • x) ∂μ :=
+    ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in s, f (g⁻¹ • x) ∂μ :=
   calc
-    (∫⁻ x, f x ∂μ) = ∑' g : G, ∫⁻ x in g • s, f x ∂μ := h.lintegral_eq_tsum f
+    ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in g • s, f x ∂μ := h.lintegral_eq_tsum f
     _ = ∑' g : G, ∫⁻ x in g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫⁻ x in s, f (g⁻¹ • x) ∂μ :=
       tsum_congr fun g =>
@@ -271,9 +271,9 @@ theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0
 
 @[to_additive]
 theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
-    (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ :=
+    ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ :=
   calc
-    (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in g • s, f x ∂μ.restrict t :=
+    ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in g • s, f x ∂μ.restrict t :=
       h.lintegral_eq_tsum_of_ac restrict_le_self.AbsolutelyContinuous _
     _ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ := by simp only [h.restrict_restrict, inter_comm]
 #align measure_theory.is_fundamental_domain.set_lintegral_eq_tsum MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum
@@ -281,9 +281,9 @@ theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ
 
 @[to_additive]
 theorem set_lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
-    (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
+    ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
   calc
-    (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ := h.set_lintegral_eq_tsum f t
+    ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ := h.set_lintegral_eq_tsum f t
     _ = ∑' g : G, ∫⁻ x in t ∩ g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫⁻ x in g⁻¹ • (g • t ∩ s), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
     _ = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
@@ -343,10 +343,9 @@ theorem measure_eq_card_smul_of_smul_ae_eq_self [Finite G] (h : IsFundamentalDom
 
 @[to_additive]
 protected theorem set_lintegral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
-    (f : α → ℝ≥0∞) (hf : ∀ (g : G) (x), f (g • x) = f x) :
-    (∫⁻ x in s, f x ∂μ) = ∫⁻ x in t, f x ∂μ :=
+    (f : α → ℝ≥0∞) (hf : ∀ (g : G) (x), f (g • x) = f x) : ∫⁻ x in s, f x ∂μ = ∫⁻ x in t, f x ∂μ :=
   calc
-    (∫⁻ x in s, f x ∂μ) = ∑' g : G, ∫⁻ x in s ∩ g • t, f x ∂μ := ht.set_lintegral_eq_tsum _ _
+    ∫⁻ x in s, f x ∂μ = ∑' g : G, ∫⁻ x in s ∩ g • t, f x ∂μ := ht.set_lintegral_eq_tsum _ _
     _ = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := by simp only [hf, inter_comm]
     _ = ∫⁻ x in t, f x ∂μ := (hs.set_lintegral_eq_tsum' _ _).symm
 #align measure_theory.is_fundamental_domain.set_lintegral_eq MeasureTheory.IsFundamentalDomain.set_lintegral_eq
@@ -356,7 +355,7 @@ protected theorem set_lintegral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFun
 theorem measure_set_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ) {A : Set α}
     (hA₀ : MeasurableSet A) (hA : ∀ g : G, (fun x => g • x) ⁻¹' A = A) : μ (A ∩ s) = μ (A ∩ t) :=
   by
-  have : (∫⁻ x in s, A.indicator 1 x ∂μ) = ∫⁻ x in t, A.indicator 1 x ∂μ :=
+  have : ∫⁻ x in s, A.indicator 1 x ∂μ = ∫⁻ x in t, A.indicator 1 x ∂μ :=
     by
     refine' hs.set_lintegral_eq ht (Set.indicator A fun _ => 1) _
     intro g x
@@ -426,7 +425,7 @@ variable [NormedSpace ℝ E] [CompleteSpace E]
 
 @[to_additive]
 theorem integral_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) (f : α → E)
-    (hf : Integrable f ν) : (∫ x, f x ∂ν) = ∑' g : G, ∫ x in g • s, f x ∂ν :=
+    (hf : Integrable f ν) : ∫ x, f x ∂ν = ∑' g : G, ∫ x in g • s, f x ∂ν :=
   by
   rw [← MeasureTheory.integral_sum_measure, h.sum_restrict_of_ac hν]
   rw [h.sum_restrict_of_ac hν]
@@ -437,16 +436,16 @@ theorem integral_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ
 
 @[to_additive]
 theorem integral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → E) (hf : Integrable f μ) :
-    (∫ x, f x ∂μ) = ∑' g : G, ∫ x in g • s, f x ∂μ :=
+    ∫ x, f x ∂μ = ∑' g : G, ∫ x in g • s, f x ∂μ :=
   integral_eq_tsum_of_ac h (by rfl) f hf
 #align measure_theory.is_fundamental_domain.integral_eq_tsum MeasureTheory.IsFundamentalDomain.integral_eq_tsum
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum
 
 @[to_additive]
 theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf : Integrable f μ) :
-    (∫ x, f x ∂μ) = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ :=
+    ∫ x, f x ∂μ = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ :=
   calc
-    (∫ x, f x ∂μ) = ∑' g : G, ∫ x in g • s, f x ∂μ := h.integral_eq_tsum f hf
+    ∫ x, f x ∂μ = ∑' g : G, ∫ x in g • s, f x ∂μ := h.integral_eq_tsum f hf
     _ = ∑' g : G, ∫ x in g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ :=
       tsum_congr fun g =>
@@ -456,9 +455,9 @@ theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
 
 @[to_additive]
 theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
-    (hf : IntegrableOn f t μ) : (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ :=
+    (hf : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ :=
   calc
-    (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in g • s, f x ∂μ.restrict t :=
+    ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in g • s, f x ∂μ.restrict t :=
       h.integral_eq_tsum_of_ac restrict_le_self.AbsolutelyContinuous f hf
     _ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := by
       simp only [h.restrict_restrict, measure_smul, inter_comm]
@@ -467,9 +466,9 @@ theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t
 
 @[to_additive]
 theorem set_integral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
-    (hf : IntegrableOn f t μ) : (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
+    (hf : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
   calc
-    (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := h.set_integral_eq_tsum hf
+    ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := h.set_integral_eq_tsum hf
     _ = ∑' g : G, ∫ x in t ∩ g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫ x in g⁻¹ • (g • t ∩ s), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
     _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
@@ -480,12 +479,12 @@ theorem set_integral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t
 
 @[to_additive]
 protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
-    {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) : (∫ x in s, f x ∂μ) = ∫ x in t, f x ∂μ :=
+    {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) : ∫ x in s, f x ∂μ = ∫ x in t, f x ∂μ :=
   by
   by_cases hfs : integrable_on f s μ
   · have hft : integrable_on f t μ := by rwa [ht.integrable_on_iff hs hf]
     calc
-      (∫ x in s, f x ∂μ) = ∑' g : G, ∫ x in s ∩ g • t, f x ∂μ := ht.set_integral_eq_tsum hfs
+      ∫ x in s, f x ∂μ = ∑' g : G, ∫ x in s ∩ g • t, f x ∂μ := ht.set_integral_eq_tsum hfs
       _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := by simp only [hf, inter_comm]
       _ = ∫ x in t, f x ∂μ := (hs.set_integral_eq_tsum' hft).symm
   · rw [integral_undef hfs, integral_undef]

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -266,7 +266,6 @@ theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0
       tsum_congr fun g =>
         ((measurePreserving_smul g⁻¹ μ).set_lintegral_comp_emb (measurableEmbedding_const_smul _) _
             _).symm
-    
 #align measure_theory.is_fundamental_domain.lintegral_eq_tsum' MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum'
 
@@ -277,7 +276,6 @@ theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ
     (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in g • s, f x ∂μ.restrict t :=
       h.lintegral_eq_tsum_of_ac restrict_le_self.AbsolutelyContinuous _
     _ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ := by simp only [h.restrict_restrict, inter_comm]
-    
 #align measure_theory.is_fundamental_domain.set_lintegral_eq_tsum MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum
 #align measure_theory.is_add_fundamental_domain.set_lintegral_eq_tsum MeasureTheory.IsAddFundamentalDomain.set_lintegral_eq_tsum
 
@@ -292,7 +290,6 @@ theorem set_lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ
       tsum_congr fun g =>
         ((measurePreserving_smul g⁻¹ μ).set_lintegral_comp_emb (measurableEmbedding_const_smul _) _
             _).symm
-    
 #align measure_theory.is_fundamental_domain.set_lintegral_eq_tsum' MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.set_lintegral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.set_lintegral_eq_tsum'
 
@@ -352,7 +349,6 @@ protected theorem set_lintegral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFun
     (∫⁻ x in s, f x ∂μ) = ∑' g : G, ∫⁻ x in s ∩ g • t, f x ∂μ := ht.set_lintegral_eq_tsum _ _
     _ = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := by simp only [hf, inter_comm]
     _ = ∫⁻ x in t, f x ∂μ := (hs.set_lintegral_eq_tsum' _ _).symm
-    
 #align measure_theory.is_fundamental_domain.set_lintegral_eq MeasureTheory.IsFundamentalDomain.set_lintegral_eq
 #align measure_theory.is_add_fundamental_domain.set_lintegral_eq MeasureTheory.IsAddFundamentalDomain.set_lintegral_eq
 
@@ -405,7 +401,6 @@ protected theorem aEStronglyMeasurable_on_iff {β : Type _} [TopologicalSpace β
     _ ↔ AEStronglyMeasurable f (μ.restrict t) := by
       simp only [← aestronglyMeasurable_sum_measure_iff, ← hs.restrict_restrict,
         hs.sum_restrict_of_ac restrict_le_self.absolutely_continuous]
-    
 #align measure_theory.is_fundamental_domain.ae_strongly_measurable_on_iff MeasureTheory.IsFundamentalDomain.aEStronglyMeasurable_on_iff
 #align measure_theory.is_add_fundamental_domain.ae_strongly_measurable_on_iff MeasureTheory.IsAddFundamentalDomain.aEStronglyMeasurable_on_iff
 
@@ -456,7 +451,6 @@ theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
     _ = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ :=
       tsum_congr fun g =>
         (measurePreserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
-    
 #align measure_theory.is_fundamental_domain.integral_eq_tsum' MeasureTheory.IsFundamentalDomain.integral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum'
 
@@ -468,7 +462,6 @@ theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t
       h.integral_eq_tsum_of_ac restrict_le_self.AbsolutelyContinuous f hf
     _ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := by
       simp only [h.restrict_restrict, measure_smul, inter_comm]
-    
 #align measure_theory.is_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum
 #align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsAddFundamentalDomain.set_integral_eq_tsum
 
@@ -482,7 +475,6 @@ theorem set_integral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t
     _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
       tsum_congr fun g =>
         (measurePreserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
-    
 #align measure_theory.is_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.set_integral_eq_tsum'
 
@@ -496,7 +488,6 @@ protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFund
       (∫ x in s, f x ∂μ) = ∑' g : G, ∫ x in s ∩ g • t, f x ∂μ := ht.set_integral_eq_tsum hfs
       _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := by simp only [hf, inter_comm]
       _ = ∫ x in t, f x ∂μ := (hs.set_integral_eq_tsum' hft).symm
-      
   · rw [integral_undef hfs, integral_undef]
     rwa [hs.integrable_on_iff ht hf] at hfs 
 #align measure_theory.is_fundamental_domain.set_integral_eq MeasureTheory.IsFundamentalDomain.set_integral_eq
@@ -515,7 +506,6 @@ theorem measure_le_of_pairwise_disjoint (hs : IsFundamentalDomain G s μ)
     _ = μ (⋃ g : G, g • t ∩ s) :=
       (Eq.symm <| measure_iUnion₀ hd fun g => (ht.smul _).inter hs.NullMeasurableSet)
     _ ≤ μ s := measure_mono (iUnion_subset fun g => inter_subset_right _ _)
-    
 #align measure_theory.is_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsFundamentalDomain.measure_le_of_pairwise_disjoint
 #align measure_theory.is_add_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsAddFundamentalDomain.measure_le_of_pairwise_disjoint

bump to nightly-2023-06-08-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

d3cfe2e3

Diff

@@ -101,7 +101,7 @@ theorem mk' (h_meas : NullMeasurableSet s μ) (h_exists : ∀ x : α, ∃! g : G
 #align measure_theory.is_fundamental_domain.mk' MeasureTheory.IsFundamentalDomain.mk'
 #align measure_theory.is_add_fundamental_domain.mk' MeasureTheory.IsAddFundamentalDomain.mk'
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 /-- For `s` to be a fundamental domain, it's enough to check `ae_disjoint (g • s) s` for `g ≠ 1`. -/
 @[to_additive
       "For `s` to be a fundamental domain, it's enough to check `ae_disjoint (g +ᵥ s) s` for\n`g ≠ 0`."]
@@ -114,7 +114,7 @@ theorem mk'' (h_meas : NullMeasurableSet s μ) (h_ae_covers : ∀ᵐ x ∂μ, 
 #align measure_theory.is_fundamental_domain.mk'' MeasureTheory.IsFundamentalDomain.mk''
 #align measure_theory.is_add_fundamental_domain.mk'' MeasureTheory.IsAddFundamentalDomain.mk''
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 /-- If a measurable space has a finite measure `μ` and a countable group `G` acts
 quasi-measure-preservingly, then to show that a set `s` is a fundamental domain, it is sufficient
 to check that its translates `g • s` are (almost) disjoint and that the sum `∑' g, μ (g • s)` is
@@ -519,8 +519,8 @@ theorem measure_le_of_pairwise_disjoint (hs : IsFundamentalDomain G s μ)
 #align measure_theory.is_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsFundamentalDomain.measure_le_of_pairwise_disjoint
 #align measure_theory.is_add_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsAddFundamentalDomain.measure_le_of_pairwise_disjoint
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 /-- If the action of a countable group `G` admits an invariant measure `μ` with a fundamental domain
 `s`, then every null-measurable set `t` of measure strictly greater than `μ s` contains two
 points `x y` such that `g • x = y` for some `g ≠ 1`. -/

bump to nightly-2023-06-08-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

8f04dc2b

Diff

@@ -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.fundamental_domain
-! leanprover-community/mathlib commit eb810cf549db839dadf13353dbe69bac55acdbbc
+! leanprover-community/mathlib commit c20927220ef87bb4962ba08bf6da2ce3cf50a6dd
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.MeasureTheory.Integral.SetIntegral
 /-!
 # Fundamental domain of a group action
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A set `s` is said to be a *fundamental domain* of an action of a group `G` on a measurable space `α`
 with respect to a measure `μ` if

bump to nightly-2023-06-06-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3209ddf94136d36e5e5c624b10b2a347cc9d090

fa2ed17c

Diff

@@ -47,6 +47,7 @@ open MeasureTheory MeasureTheory.Measure Set Function TopologicalSpace Filter
 
 namespace MeasureTheory
 
+#print MeasureTheory.IsAddFundamentalDomain /-
 /-- A measurable set `s` is a *fundamental domain* for an additive action of an additive group `G`
 on a measurable space `α` with respect to a measure `α` if the sets `g +ᵥ s`, `g : G`, are pairwise
 a.e. disjoint and cover the whole space. -/
@@ -57,7 +58,9 @@ structure IsAddFundamentalDomain (G : Type _) {α : Type _} [Zero G] [VAdd G α]
   ae_covers : ∀ᵐ x ∂μ, ∃ g : G, g +ᵥ x ∈ s
   AEDisjoint : Pairwise <| (AEDisjoint μ on fun g : G => g +ᵥ s)
 #align measure_theory.is_add_fundamental_domain MeasureTheory.IsAddFundamentalDomain
+-/
 
+#print MeasureTheory.IsFundamentalDomain /-
 /-- A measurable set `s` is a *fundamental domain* for an action of a group `G` on a measurable
 space `α` with respect to a measure `α` if the sets `g • s`, `g : G`, are pairwise a.e. disjoint and
 cover the whole space. -/
@@ -69,6 +72,7 @@ structure IsFundamentalDomain (G : Type _) {α : Type _} [One G] [SMul G α] [Me
   AEDisjoint : Pairwise <| (AEDisjoint μ on fun g : G => g • s)
 #align measure_theory.is_fundamental_domain MeasureTheory.IsFundamentalDomain
 #align measure_theory.is_add_fundamental_domain MeasureTheory.IsAddFundamentalDomain
+-/
 
 variable {G H α β E : Type _}
 
@@ -564,6 +568,7 @@ section MeasurableSpace
 
 variable (G) [Group G] [MulAction G α] (s : Set α) {x : α}
 
+#print MeasureTheory.fundamentalFrontier /-
 /-- The boundary of a fundamental domain, those points of the domain that also lie in a nontrivial
 translate. -/
 @[to_additive MeasureTheory.addFundamentalFrontier
@@ -572,7 +577,9 @@ def fundamentalFrontier : Set α :=
   s ∩ ⋃ (g : G) (hg : g ≠ 1), g • s
 #align measure_theory.fundamental_frontier MeasureTheory.fundamentalFrontier
 #align measure_theory.add_fundamental_frontier MeasureTheory.addFundamentalFrontier
+-/
 
+#print MeasureTheory.fundamentalInterior /-
 /-- The interior of a fundamental domain, those points of the domain not lying in any translate. -/
 @[to_additive MeasureTheory.addFundamentalInterior
       "The interior of a fundamental domain, those\npoints of the domain not lying in any translate."]
@@ -580,85 +587,89 @@ def fundamentalInterior : Set α :=
   s \ ⋃ (g : G) (hg : g ≠ 1), g • s
 #align measure_theory.fundamental_interior MeasureTheory.fundamentalInterior
 #align measure_theory.add_fundamental_interior MeasureTheory.addFundamentalInterior
+-/
 
 variable {G s}
 
-@[simp, to_additive MeasureTheory.mem_add_fundamentalFrontier]
+@[simp, to_additive MeasureTheory.mem_addFundamentalFrontier]
 theorem mem_fundamentalFrontier :
     x ∈ fundamentalFrontier G s ↔ x ∈ s ∧ ∃ (g : G) (hg : g ≠ 1), x ∈ g • s := by
   simp [fundamental_frontier]
 #align measure_theory.mem_fundamental_frontier MeasureTheory.mem_fundamentalFrontier
-#align measure_theory.mem_add_fundamental_frontier MeasureTheory.mem_add_fundamentalFrontier
+#align measure_theory.mem_add_fundamental_frontier MeasureTheory.mem_addFundamentalFrontier
 
-@[simp, to_additive MeasureTheory.mem_add_fundamentalInterior]
+@[simp, to_additive MeasureTheory.mem_addFundamentalInterior]
 theorem mem_fundamentalInterior :
     x ∈ fundamentalInterior G s ↔ x ∈ s ∧ ∀ (g : G) (hg : g ≠ 1), x ∉ g • s := by
   simp [fundamental_interior]
 #align measure_theory.mem_fundamental_interior MeasureTheory.mem_fundamentalInterior
-#align measure_theory.mem_add_fundamental_interior MeasureTheory.mem_add_fundamentalInterior
+#align measure_theory.mem_add_fundamental_interior MeasureTheory.mem_addFundamentalInterior
 
-@[to_additive MeasureTheory.add_fundamentalFrontier_subset]
+#print MeasureTheory.fundamentalFrontier_subset /-
+@[to_additive MeasureTheory.addFundamentalFrontier_subset]
 theorem fundamentalFrontier_subset : fundamentalFrontier G s ⊆ s :=
   inter_subset_left _ _
 #align measure_theory.fundamental_frontier_subset MeasureTheory.fundamentalFrontier_subset
-#align measure_theory.add_fundamental_frontier_subset MeasureTheory.add_fundamentalFrontier_subset
+#align measure_theory.add_fundamental_frontier_subset MeasureTheory.addFundamentalFrontier_subset
+-/
 
-@[to_additive MeasureTheory.add_fundamentalInterior_subset]
+#print MeasureTheory.fundamentalInterior_subset /-
+@[to_additive MeasureTheory.addFundamentalInterior_subset]
 theorem fundamentalInterior_subset : fundamentalInterior G s ⊆ s :=
   diff_subset _ _
 #align measure_theory.fundamental_interior_subset MeasureTheory.fundamentalInterior_subset
-#align measure_theory.add_fundamental_interior_subset MeasureTheory.add_fundamentalInterior_subset
+#align measure_theory.add_fundamental_interior_subset MeasureTheory.addFundamentalInterior_subset
+-/
 
 variable (G s)
 
-@[to_additive MeasureTheory.disjoint_add_fundamental_interior_add_fundamental_frontier]
+@[to_additive MeasureTheory.disjoint_addFundamentalInterior_addFundamentalFrontier]
 theorem disjoint_fundamentalInterior_fundamentalFrontier :
     Disjoint (fundamentalInterior G s) (fundamentalFrontier G s) :=
   disjoint_sdiff_self_left.mono_right inf_le_right
 #align measure_theory.disjoint_fundamental_interior_fundamental_frontier MeasureTheory.disjoint_fundamentalInterior_fundamentalFrontier
-#align measure_theory.disjoint_add_fundamental_interior_add_fundamental_frontier MeasureTheory.disjoint_add_fundamental_interior_add_fundamental_frontier
+#align measure_theory.disjoint_add_fundamental_interior_add_fundamental_frontier MeasureTheory.disjoint_addFundamentalInterior_addFundamentalFrontier
 
-@[simp, to_additive MeasureTheory.add_fundamentalInterior_union_add_fundamentalFrontier]
+@[simp, to_additive MeasureTheory.addFundamentalInterior_union_addFundamentalFrontier]
 theorem fundamentalInterior_union_fundamentalFrontier :
     fundamentalInterior G s ∪ fundamentalFrontier G s = s :=
   diff_union_inter _ _
 #align measure_theory.fundamental_interior_union_fundamental_frontier MeasureTheory.fundamentalInterior_union_fundamentalFrontier
-#align measure_theory.add_fundamental_interior_union_add_fundamental_frontier MeasureTheory.add_fundamentalInterior_union_add_fundamentalFrontier
+#align measure_theory.add_fundamental_interior_union_add_fundamental_frontier MeasureTheory.addFundamentalInterior_union_addFundamentalFrontier
 
-@[simp, to_additive MeasureTheory.add_fundamentalInterior_union_add_fundamentalFrontier]
+@[simp, to_additive MeasureTheory.addFundamentalInterior_union_addFundamentalFrontier]
 theorem fundamentalFrontier_union_fundamentalInterior :
     fundamentalFrontier G s ∪ fundamentalInterior G s = s :=
   inter_union_diff _ _
 #align measure_theory.fundamental_frontier_union_fundamental_interior MeasureTheory.fundamentalFrontier_union_fundamentalInterior
-#align measure_theory.add_fundamental_interior_union_add_fundamental_frontier MeasureTheory.add_fundamentalInterior_union_add_fundamentalFrontier
 
-@[simp, to_additive MeasureTheory.sdiff_add_fundamentalInterior]
+@[simp, to_additive MeasureTheory.sdiff_addFundamentalInterior]
 theorem sdiff_fundamentalInterior : s \ fundamentalInterior G s = fundamentalFrontier G s :=
   sdiff_sdiff_right_self
 #align measure_theory.sdiff_fundamental_interior MeasureTheory.sdiff_fundamentalInterior
-#align measure_theory.sdiff_add_fundamental_interior MeasureTheory.sdiff_add_fundamentalInterior
+#align measure_theory.sdiff_add_fundamental_interior MeasureTheory.sdiff_addFundamentalInterior
 
-@[simp, to_additive MeasureTheory.sdiff_add_fundamentalFrontier]
+@[simp, to_additive MeasureTheory.sdiff_addFundamentalFrontier]
 theorem sdiff_fundamentalFrontier : s \ fundamentalFrontier G s = fundamentalInterior G s :=
   diff_self_inter
 #align measure_theory.sdiff_fundamental_frontier MeasureTheory.sdiff_fundamentalFrontier
-#align measure_theory.sdiff_add_fundamental_frontier MeasureTheory.sdiff_add_fundamentalFrontier
+#align measure_theory.sdiff_add_fundamental_frontier MeasureTheory.sdiff_addFundamentalFrontier
 
-@[simp, to_additive MeasureTheory.add_fundamentalFrontier_vadd]
+@[simp, to_additive MeasureTheory.addFundamentalFrontier_vadd]
 theorem fundamentalFrontier_smul [Group H] [MulAction H α] [SMulCommClass H G α] (g : H) :
     fundamentalFrontier G (g • s) = g • fundamentalFrontier G s := by
   simp_rw [fundamental_frontier, smul_set_inter, smul_set_Union, smul_comm g]
 #align measure_theory.fundamental_frontier_smul MeasureTheory.fundamentalFrontier_smul
-#align measure_theory.add_fundamental_frontier_vadd MeasureTheory.add_fundamentalFrontier_vadd
+#align measure_theory.add_fundamental_frontier_vadd MeasureTheory.addFundamentalFrontier_vadd
 
-@[simp, to_additive MeasureTheory.add_fundamentalInterior_vadd]
+@[simp, to_additive MeasureTheory.addFundamentalInterior_vadd]
 theorem fundamentalInterior_smul [Group H] [MulAction H α] [SMulCommClass H G α] (g : H) :
     fundamentalInterior G (g • s) = g • fundamentalInterior G s := by
   simp_rw [fundamental_interior, smul_set_sdiff, smul_set_Union, smul_comm g]
 #align measure_theory.fundamental_interior_smul MeasureTheory.fundamentalInterior_smul
-#align measure_theory.add_fundamental_interior_vadd MeasureTheory.add_fundamentalInterior_vadd
+#align measure_theory.add_fundamental_interior_vadd MeasureTheory.addFundamentalInterior_vadd
 
-@[to_additive MeasureTheory.pairwise_disjoint_add_fundamental_interior]
+@[to_additive MeasureTheory.pairwise_disjoint_addFundamentalInterior]
 theorem pairwise_disjoint_fundamentalInterior :
     Pairwise (Disjoint on fun g : G => g • fundamentalInterior G s) :=
   by
@@ -669,24 +680,28 @@ theorem pairwise_disjoint_fundamentalInterior :
   rwa [Ne.def, inv_mul_eq_iff_eq_mul, mul_one, eq_comm]
   simpa [mul_smul, ← hxy, mem_inv_smul_set_iff] using hy.1
 #align measure_theory.pairwise_disjoint_fundamental_interior MeasureTheory.pairwise_disjoint_fundamentalInterior
-#align measure_theory.pairwise_disjoint_add_fundamental_interior MeasureTheory.pairwise_disjoint_add_fundamental_interior
+#align measure_theory.pairwise_disjoint_add_fundamental_interior MeasureTheory.pairwise_disjoint_addFundamentalInterior
 
 variable [Countable G] [MeasurableSpace G] [MeasurableSpace α] [MeasurableSMul G α] {μ : Measure α}
   [SMulInvariantMeasure G α μ]
 
-@[to_additive MeasureTheory.NullMeasurableSet.add_fundamentalFrontier]
+#print MeasureTheory.NullMeasurableSet.fundamentalFrontier /-
+@[to_additive MeasureTheory.NullMeasurableSet.addFundamentalFrontier]
 protected theorem NullMeasurableSet.fundamentalFrontier (hs : NullMeasurableSet s μ) :
     NullMeasurableSet (fundamentalFrontier G s) μ :=
   hs.inter <| NullMeasurableSet.iUnion fun g => NullMeasurableSet.iUnion fun hg => hs.smul _
 #align measure_theory.null_measurable_set.fundamental_frontier MeasureTheory.NullMeasurableSet.fundamentalFrontier
-#align measure_theory.null_measurable_set.add_fundamental_frontier MeasureTheory.NullMeasurableSet.add_fundamentalFrontier
+#align measure_theory.null_measurable_set.add_fundamental_frontier MeasureTheory.NullMeasurableSet.addFundamentalFrontier
+-/
 
-@[to_additive MeasureTheory.NullMeasurableSet.add_fundamentalInterior]
+#print MeasureTheory.NullMeasurableSet.fundamentalInterior /-
+@[to_additive MeasureTheory.NullMeasurableSet.addFundamentalInterior]
 protected theorem NullMeasurableSet.fundamentalInterior (hs : NullMeasurableSet s μ) :
     NullMeasurableSet (fundamentalInterior G s) μ :=
   hs.diffₓ <| NullMeasurableSet.iUnion fun g => NullMeasurableSet.iUnion fun hg => hs.smul _
 #align measure_theory.null_measurable_set.fundamental_interior MeasureTheory.NullMeasurableSet.fundamentalInterior
-#align measure_theory.null_measurable_set.add_fundamental_interior MeasureTheory.NullMeasurableSet.add_fundamentalInterior
+#align measure_theory.null_measurable_set.add_fundamental_interior MeasureTheory.NullMeasurableSet.addFundamentalInterior
+-/
 
 end MeasurableSpace
 
@@ -699,19 +714,19 @@ variable [Countable G] [Group G] [MulAction G α] [MeasurableSpace α] {μ : Mea
 
 include hs
 
-@[to_additive MeasureTheory.IsAddFundamentalDomain.measure_add_fundamentalFrontier]
+@[to_additive MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalFrontier]
 theorem measure_fundamentalFrontier : μ (fundamentalFrontier G s) = 0 := by
   simpa only [fundamental_frontier, Union₂_inter, measure_Union_null_iff', one_smul,
     measure_Union_null_iff, inter_comm s, Function.onFun] using fun g (hg : g ≠ 1) =>
     hs.ae_disjoint hg
 #align measure_theory.is_fundamental_domain.measure_fundamental_frontier MeasureTheory.IsFundamentalDomain.measure_fundamentalFrontier
-#align measure_theory.is_add_fundamental_domain.measure_add_fundamental_frontier MeasureTheory.IsAddFundamentalDomain.measure_add_fundamentalFrontier
+#align measure_theory.is_add_fundamental_domain.measure_add_fundamental_frontier MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalFrontier
 
-@[to_additive MeasureTheory.IsAddFundamentalDomain.measure_add_fundamentalInterior]
+@[to_additive MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalInterior]
 theorem measure_fundamentalInterior : μ (fundamentalInterior G s) = μ s :=
   measure_diff_null' hs.measure_fundamentalFrontier
 #align measure_theory.is_fundamental_domain.measure_fundamental_interior MeasureTheory.IsFundamentalDomain.measure_fundamentalInterior
-#align measure_theory.is_add_fundamental_domain.measure_add_fundamental_interior MeasureTheory.IsAddFundamentalDomain.measure_add_fundamentalInterior
+#align measure_theory.is_add_fundamental_domain.measure_add_fundamental_interior MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalInterior
 
 end Group

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -114,7 +114,7 @@ to check that its translates `g • s` are (almost) disjoint and that the sum `
 sufficiently large. -/
 @[to_additive MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_le
       "\nIf a measurable space has a finite measure `μ` and a countable additive group `G` acts\nquasi-measure-preservingly, then to show that a set `s` is a fundamental domain, it is sufficient\nto check that its translates `g +ᵥ s` are (almost) disjoint and that the sum `∑' g, μ (g +ᵥ s)` is\nsufficiently large."]
-theorem mk_of_measure_univ_le [FiniteMeasure μ] [Countable G] (h_meas : NullMeasurableSet s μ)
+theorem mk_of_measure_univ_le [IsFiniteMeasure μ] [Countable G] (h_meas : NullMeasurableSet s μ)
     (h_ae_disjoint : ∀ (g) (_ : g ≠ (1 : G)), AEDisjoint μ (g • s) s)
     (h_qmp : ∀ g : G, QuasiMeasurePreserving ((· • ·) g : α → α) μ μ)
     (h_measure_univ_le : μ (univ : Set α) ≤ ∑' g : G, μ (g • s)) : IsFundamentalDomain G s μ :=
@@ -126,7 +126,7 @@ theorem mk_of_measure_univ_le [FiniteMeasure μ] [Countable G] (h_meas : NullMea
       by
       replace h_meas : ∀ g : G, null_measurable_set (g • s) μ := fun g => by
         rw [← inv_inv g, ← preimage_smul]; exact h_meas.preimage (h_qmp g⁻¹)
-      have h_meas' : null_measurable_set { a | ∃ g : G, g • a ∈ s } μ := by
+      have h_meas' : null_measurable_set {a | ∃ g : G, g • a ∈ s} μ := by
         rw [← Union_smul_eq_set_of_exists]; exact null_measurable_set.Union h_meas
       rw [ae_iff_measure_eq h_meas', ← Union_smul_eq_set_of_exists]
       refine' le_antisymm (measure_mono <| subset_univ _) _
@@ -158,7 +158,7 @@ theorem preimage_of_equiv {ν : Measure β} (h : IsFundamentalDomain G s μ) {f
     AEDisjoint := fun a b hab => by
       lift e to G ≃ H using he
       have : (e.symm a⁻¹)⁻¹ ≠ (e.symm b⁻¹)⁻¹ := by simp [hab]
-      convert(h.ae_disjoint this).Preimage hf using 1
+      convert (h.ae_disjoint this).Preimage hf using 1
       simp only [← preimage_smul_inv, preimage_preimage, ← hef _ _, e.apply_symm_apply, inv_inv] }
 #align measure_theory.is_fundamental_domain.preimage_of_equiv MeasureTheory.IsFundamentalDomain.preimage_of_equiv
 #align measure_theory.is_add_fundamental_domain.preimage_of_equiv MeasureTheory.IsAddFundamentalDomain.preimage_of_equiv
@@ -357,7 +357,7 @@ theorem measure_set_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDoma
     by
     refine' hs.set_lintegral_eq ht (Set.indicator A fun _ => 1) _
     intro g x
-    convert(Set.indicator_comp_right fun x : α => g • x).symm
+    convert (Set.indicator_comp_right fun x : α => g • x).symm
     rw [hA g]
   simpa [measure.restrict_apply hA₀, lintegral_indicator _ hA₀] using this
 #align measure_theory.is_fundamental_domain.measure_set_eq MeasureTheory.IsFundamentalDomain.measure_set_eq
@@ -545,7 +545,7 @@ theorem essSup_measure_restrict (hs : IsFundamentalDomain G s μ) {f : α → 
   refine' le_antisymm (essSup_mono_measure' measure.restrict_le_self) _
   rw [essSup_eq_sInf (μ.restrict s) f, essSup_eq_sInf μ f]
   refine' sInf_le_sInf _
-  rintro a (ha : (μ.restrict s) { x : α | a < f x } = 0)
+  rintro a (ha : (μ.restrict s) {x : α | a < f x} = 0)
   rw [measure.restrict_apply₀' hs.null_measurable_set] at ha 
   refine' measure_zero_of_invariant hs _ _ ha
   intro γ

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -52,7 +52,7 @@ on a measurable space `α` with respect to a measure `α` if the sets `g +ᵥ s`
 a.e. disjoint and cover the whole space. -/
 @[protect_proj]
 structure IsAddFundamentalDomain (G : Type _) {α : Type _} [Zero G] [VAdd G α] [MeasurableSpace α]
-  (s : Set α) (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) : Prop where
+    (s : Set α) (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) : Prop where
   NullMeasurableSet : NullMeasurableSet s μ
   ae_covers : ∀ᵐ x ∂μ, ∃ g : G, g +ᵥ x ∈ s
   AEDisjoint : Pairwise <| (AEDisjoint μ on fun g : G => g +ᵥ s)
@@ -63,7 +63,7 @@ space `α` with respect to a measure `α` if the sets `g • s`, `g : G`, are pa
 cover the whole space. -/
 @[protect_proj, to_additive is_add_fundamental_domain]
 structure IsFundamentalDomain (G : Type _) {α : Type _} [One G] [SMul G α] [MeasurableSpace α]
-  (s : Set α) (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) : Prop where
+    (s : Set α) (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) : Prop where
   NullMeasurableSet : NullMeasurableSet s μ
   ae_covers : ∀ᵐ x ∂μ, ∃ g : G, g • x ∈ s
   AEDisjoint : Pairwise <| (AEDisjoint μ on fun g : G => g • s)
@@ -89,7 +89,7 @@ theorem mk' (h_meas : NullMeasurableSet s μ) (h_exists : ∀ x : α, ∃! g : G
       Disjoint.aedisjoint <|
         disjoint_left.2 fun x hxa hxb =>
           by
-          rw [mem_smul_set_iff_inv_smul_mem] at hxa hxb
+          rw [mem_smul_set_iff_inv_smul_mem] at hxa hxb 
           exact hab (inv_injective <| (h_exists x).unique hxa hxb) }
 #align measure_theory.is_fundamental_domain.mk' MeasureTheory.IsFundamentalDomain.mk'
 #align measure_theory.is_add_fundamental_domain.mk' MeasureTheory.IsAddFundamentalDomain.mk'
@@ -491,7 +491,7 @@ protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFund
       _ = ∫ x in t, f x ∂μ := (hs.set_integral_eq_tsum' hft).symm
       
   · rw [integral_undef hfs, integral_undef]
-    rwa [hs.integrable_on_iff ht hf] at hfs
+    rwa [hs.integrable_on_iff ht hf] at hfs 
 #align measure_theory.is_fundamental_domain.set_integral_eq MeasureTheory.IsFundamentalDomain.set_integral_eq
 #align measure_theory.is_add_fundamental_domain.set_integral_eq MeasureTheory.IsAddFundamentalDomain.set_integral_eq
 
@@ -520,7 +520,8 @@ points `x y` such that `g • x = y` for some `g ≠ 1`. -/
 @[to_additive
       "If the additive action of a countable group `G` admits an invariant measure `μ` with\na fundamental domain `s`, then every null-measurable set `t` of measure strictly greater than `μ s`\ncontains two points `x y` such that `g +ᵥ x = y` for some `g ≠ 0`."]
 theorem exists_ne_one_smul_eq (hs : IsFundamentalDomain G s μ) (htm : NullMeasurableSet t μ)
-    (ht : μ s < μ t) : ∃ (x : _)(_ : x ∈ t)(y : _)(_ : y ∈ t)(g : _)(_ : g ≠ (1 : G)), g • x = y :=
+    (ht : μ s < μ t) :
+    ∃ (x : _) (_ : x ∈ t) (y : _) (_ : y ∈ t) (g : _) (_ : g ≠ (1 : G)), g • x = y :=
   by
   contrapose! ht
   refine' hs.measure_le_of_pairwise_disjoint htm (Pairwise.aedisjoint fun g₁ g₂ hne => _)
@@ -545,7 +546,7 @@ theorem essSup_measure_restrict (hs : IsFundamentalDomain G s μ) {f : α → 
   rw [essSup_eq_sInf (μ.restrict s) f, essSup_eq_sInf μ f]
   refine' sInf_le_sInf _
   rintro a (ha : (μ.restrict s) { x : α | a < f x } = 0)
-  rw [measure.restrict_apply₀' hs.null_measurable_set] at ha
+  rw [measure.restrict_apply₀' hs.null_measurable_set] at ha 
   refine' measure_zero_of_invariant hs _ _ ha
   intro γ
   ext x
@@ -584,7 +585,7 @@ variable {G s}
 
 @[simp, to_additive MeasureTheory.mem_add_fundamentalFrontier]
 theorem mem_fundamentalFrontier :
-    x ∈ fundamentalFrontier G s ↔ x ∈ s ∧ ∃ (g : G)(hg : g ≠ 1), x ∈ g • s := by
+    x ∈ fundamentalFrontier G s ↔ x ∈ s ∧ ∃ (g : G) (hg : g ≠ 1), x ∈ g • s := by
   simp [fundamental_frontier]
 #align measure_theory.mem_fundamental_frontier MeasureTheory.mem_fundamentalFrontier
 #align measure_theory.mem_add_fundamental_frontier MeasureTheory.mem_add_fundamentalFrontier
@@ -663,7 +664,7 @@ theorem pairwise_disjoint_fundamentalInterior :
   by
   refine' fun a b hab => disjoint_left.2 _
   rintro _ ⟨x, hx, rfl⟩ ⟨y, hy, hxy⟩
-  rw [mem_fundamental_interior] at hx hy
+  rw [mem_fundamental_interior] at hx hy 
   refine' hx.2 (a⁻¹ * b) _ _
   rwa [Ne.def, inv_mul_eq_iff_eq_mul, mul_one, eq_comm]
   simpa [mul_smul, ← hxy, mem_inv_smul_set_iff] using hy.1

bump to nightly-2023-06-01-04

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

4d9eaa85

Diff

@@ -184,7 +184,7 @@ theorem pairwise_aEDisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : 
 
 @[to_additive]
 theorem smul_of_comm {G' : Type _} [Group G'] [MulAction G' α] [MeasurableSpace G']
-    [MeasurableSMul G' α] [SmulInvariantMeasure G' α μ] [SMulCommClass G' G α]
+    [MeasurableSMul G' α] [SMulInvariantMeasure G' α μ] [SMulCommClass G' G α]
     (h : IsFundamentalDomain G s μ) (g : G') : IsFundamentalDomain G (g • s) μ :=
   h.image_of_equiv (MulAction.toPerm g) (measurePreserving_smul _ _).QuasiMeasurePreserving
       (Equiv.refl _) <|
@@ -192,7 +192,7 @@ theorem smul_of_comm {G' : Type _} [Group G'] [MulAction G' α] [MeasurableSpace
 #align measure_theory.is_fundamental_domain.smul_of_comm MeasureTheory.IsFundamentalDomain.smul_of_comm
 #align measure_theory.is_add_fundamental_domain.vadd_of_comm MeasureTheory.IsAddFundamentalDomain.vadd_of_comm
 
-variable [MeasurableSpace G] [MeasurableSMul G α] [SmulInvariantMeasure G α μ]
+variable [MeasurableSpace G] [MeasurableSMul G α] [SMulInvariantMeasure G α μ]
 
 @[to_additive]
 theorem nullMeasurableSet_smul (h : IsFundamentalDomain G s μ) (g : G) :
@@ -671,7 +671,7 @@ theorem pairwise_disjoint_fundamentalInterior :
 #align measure_theory.pairwise_disjoint_add_fundamental_interior MeasureTheory.pairwise_disjoint_add_fundamental_interior
 
 variable [Countable G] [MeasurableSpace G] [MeasurableSpace α] [MeasurableSMul G α] {μ : Measure α}
-  [SmulInvariantMeasure G α μ]
+  [SMulInvariantMeasure G α μ]
 
 @[to_additive MeasureTheory.NullMeasurableSet.add_fundamentalFrontier]
 protected theorem NullMeasurableSet.fundamentalFrontier (hs : NullMeasurableSet s μ) :
@@ -716,7 +716,7 @@ end Group
 
 variable [Countable G] [Group G] [MulAction G α] [MeasurableSpace α] {μ : Measure α} {s : Set α}
   (hs : IsFundamentalDomain G s μ) [MeasurableSpace G] [MeasurableSMul G α]
-  [SmulInvariantMeasure G α μ]
+  [SMulInvariantMeasure G α μ]
 
 include hs

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -41,7 +41,7 @@ We also generate additive versions of all theorems in this file using the `to_ad
 -/
 
 
-open ENNReal Pointwise Topology NNReal ENNReal MeasureTheory
+open scoped ENNReal Pointwise Topology NNReal ENNReal MeasureTheory
 
 open MeasureTheory MeasureTheory.Measure Set Function TopologicalSpace Filter

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -124,14 +124,10 @@ theorem mk_of_measure_univ_le [FiniteMeasure μ] [Countable G] (h_meas : NullMea
     AEDisjoint
     ae_covers :=
       by
-      replace h_meas : ∀ g : G, null_measurable_set (g • s) μ := fun g =>
-        by
-        rw [← inv_inv g, ← preimage_smul]
-        exact h_meas.preimage (h_qmp g⁻¹)
-      have h_meas' : null_measurable_set { a | ∃ g : G, g • a ∈ s } μ :=
-        by
-        rw [← Union_smul_eq_set_of_exists]
-        exact null_measurable_set.Union h_meas
+      replace h_meas : ∀ g : G, null_measurable_set (g • s) μ := fun g => by
+        rw [← inv_inv g, ← preimage_smul]; exact h_meas.preimage (h_qmp g⁻¹)
+      have h_meas' : null_measurable_set { a | ∃ g : G, g • a ∈ s } μ := by
+        rw [← Union_smul_eq_set_of_exists]; exact null_measurable_set.Union h_meas
       rw [ae_iff_measure_eq h_meas', ← Union_smul_eq_set_of_exists]
       refine' le_antisymm (measure_mono <| subset_univ _) _
       rw [measure_Union₀ ae_disjoint h_meas]

bump to nightly-2023-05-23-20

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

4d066d3b

Diff

@@ -377,34 +377,34 @@ protected theorem measure_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundament
 #align measure_theory.is_add_fundamental_domain.measure_eq MeasureTheory.IsAddFundamentalDomain.measure_eq
 
 @[to_additive]
-protected theorem aeStronglyMeasurable_on_iff {β : Type _} [TopologicalSpace β]
+protected theorem aEStronglyMeasurable_on_iff {β : Type _} [TopologicalSpace β]
     [PseudoMetrizableSpace β] (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
     {f : α → β} (hf : ∀ (g : G) (x), f (g • x) = f x) :
-    AeStronglyMeasurable f (μ.restrict s) ↔ AeStronglyMeasurable f (μ.restrict t) :=
+    AEStronglyMeasurable f (μ.restrict s) ↔ AEStronglyMeasurable f (μ.restrict t) :=
   calc
-    AeStronglyMeasurable f (μ.restrict s) ↔
-        AeStronglyMeasurable f (Measure.sum fun g : G => μ.restrict (g • t ∩ s)) :=
+    AEStronglyMeasurable f (μ.restrict s) ↔
+        AEStronglyMeasurable f (Measure.sum fun g : G => μ.restrict (g • t ∩ s)) :=
       by
       simp only [← ht.restrict_restrict,
         ht.sum_restrict_of_ac restrict_le_self.absolutely_continuous]
-    _ ↔ ∀ g : G, AeStronglyMeasurable f (μ.restrict (g • (g⁻¹ • s ∩ t))) := by
-      simp only [smul_set_inter, inter_comm, smul_inv_smul, aeStronglyMeasurable_sum_measure_iff]
-    _ ↔ ∀ g : G, AeStronglyMeasurable f (μ.restrict (g⁻¹ • (g⁻¹⁻¹ • s ∩ t))) :=
+    _ ↔ ∀ g : G, AEStronglyMeasurable f (μ.restrict (g • (g⁻¹ • s ∩ t))) := by
+      simp only [smul_set_inter, inter_comm, smul_inv_smul, aestronglyMeasurable_sum_measure_iff]
+    _ ↔ ∀ g : G, AEStronglyMeasurable f (μ.restrict (g⁻¹ • (g⁻¹⁻¹ • s ∩ t))) :=
       inv_surjective.forall
-    _ ↔ ∀ g : G, AeStronglyMeasurable f (μ.restrict (g⁻¹ • (g • s ∩ t))) := by simp only [inv_inv]
-    _ ↔ ∀ g : G, AeStronglyMeasurable f (μ.restrict (g • s ∩ t)) :=
+    _ ↔ ∀ g : G, AEStronglyMeasurable f (μ.restrict (g⁻¹ • (g • s ∩ t))) := by simp only [inv_inv]
+    _ ↔ ∀ g : G, AEStronglyMeasurable f (μ.restrict (g • s ∩ t)) :=
       by
       refine' forall_congr' fun g => _
       have he : MeasurableEmbedding ((· • ·) g⁻¹ : α → α) := measurableEmbedding_const_smul _
       rw [← image_smul, ←
-        ((measure_preserving_smul g⁻¹ μ).restrict_image_emb he _).aeStronglyMeasurable_comp_iff he]
+        ((measure_preserving_smul g⁻¹ μ).restrict_image_emb he _).aestronglyMeasurable_comp_iff he]
       simp only [(· ∘ ·), hf]
-    _ ↔ AeStronglyMeasurable f (μ.restrict t) := by
-      simp only [← aeStronglyMeasurable_sum_measure_iff, ← hs.restrict_restrict,
+    _ ↔ AEStronglyMeasurable f (μ.restrict t) := by
+      simp only [← aestronglyMeasurable_sum_measure_iff, ← hs.restrict_restrict,
         hs.sum_restrict_of_ac restrict_le_self.absolutely_continuous]
     
-#align measure_theory.is_fundamental_domain.ae_strongly_measurable_on_iff MeasureTheory.IsFundamentalDomain.aeStronglyMeasurable_on_iff
-#align measure_theory.is_add_fundamental_domain.ae_strongly_measurable_on_iff MeasureTheory.IsAddFundamentalDomain.aeStronglyMeasurable_on_iff
+#align measure_theory.is_fundamental_domain.ae_strongly_measurable_on_iff MeasureTheory.IsFundamentalDomain.aEStronglyMeasurable_on_iff
+#align measure_theory.is_add_fundamental_domain.ae_strongly_measurable_on_iff MeasureTheory.IsAddFundamentalDomain.aEStronglyMeasurable_on_iff
 
 @[to_additive]
 protected theorem hasFiniteIntegral_on_iff (hs : IsFundamentalDomain G s μ)
@@ -420,7 +420,7 @@ protected theorem hasFiniteIntegral_on_iff (hs : IsFundamentalDomain G s μ)
 @[to_additive]
 protected theorem integrableOn_iff (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
     {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) : IntegrableOn f s μ ↔ IntegrableOn f t μ :=
-  and_congr (hs.aeStronglyMeasurable_on_iff ht hf) (hs.hasFiniteIntegral_on_iff ht hf)
+  and_congr (hs.aEStronglyMeasurable_on_iff ht hf) (hs.hasFiniteIntegral_on_iff ht hf)
 #align measure_theory.is_fundamental_domain.integrable_on_iff MeasureTheory.IsFundamentalDomain.integrableOn_iff
 #align measure_theory.is_add_fundamental_domain.integrable_on_iff MeasureTheory.IsAddFundamentalDomain.integrableOn_iff

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -140,11 +140,11 @@ theorem mk_of_measure_univ_le [FiniteMeasure μ] [Countable G] (h_meas : NullMea
 #align measure_theory.is_add_fundamental_domain.mk_of_measure_univ_le MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_le
 
 @[to_additive]
-theorem unionᵢ_smul_ae_eq (h : IsFundamentalDomain G s μ) : (⋃ g : G, g • s) =ᵐ[μ] univ :=
+theorem iUnion_smul_ae_eq (h : IsFundamentalDomain G s μ) : (⋃ g : G, g • s) =ᵐ[μ] univ :=
   eventuallyEq_univ.2 <|
-    h.ae_covers.mono fun x ⟨g, hg⟩ => mem_unionᵢ.2 ⟨g⁻¹, _, hg, inv_smul_smul _ _⟩
-#align measure_theory.is_fundamental_domain.Union_smul_ae_eq MeasureTheory.IsFundamentalDomain.unionᵢ_smul_ae_eq
-#align measure_theory.is_add_fundamental_domain.Union_vadd_ae_eq MeasureTheory.IsAddFundamentalDomain.unionᵢ_vadd_ae_eq
+    h.ae_covers.mono fun x ⟨g, hg⟩ => mem_iUnion.2 ⟨g⁻¹, _, hg, inv_smul_smul _ _⟩
+#align measure_theory.is_fundamental_domain.Union_smul_ae_eq MeasureTheory.IsFundamentalDomain.iUnion_smul_ae_eq
+#align measure_theory.is_add_fundamental_domain.Union_vadd_ae_eq MeasureTheory.IsAddFundamentalDomain.iUnion_vadd_ae_eq
 
 @[to_additive]
 theorem mono (h : IsFundamentalDomain G s μ) {ν : Measure α} (hle : ν ≪ μ) :
@@ -510,8 +510,8 @@ theorem measure_le_of_pairwise_disjoint (hs : IsFundamentalDomain G s μ)
   calc
     μ t = ∑' g : G, μ (g • t ∩ s) := hs.measure_eq_tsum t
     _ = μ (⋃ g : G, g • t ∩ s) :=
-      (Eq.symm <| measure_unionᵢ₀ hd fun g => (ht.smul _).inter hs.NullMeasurableSet)
-    _ ≤ μ s := measure_mono (unionᵢ_subset fun g => inter_subset_right _ _)
+      (Eq.symm <| measure_iUnion₀ hd fun g => (ht.smul _).inter hs.NullMeasurableSet)
+    _ ≤ μ s := measure_mono (iUnion_subset fun g => inter_subset_right _ _)
     
 #align measure_theory.is_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsFundamentalDomain.measure_le_of_pairwise_disjoint
 #align measure_theory.is_add_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsAddFundamentalDomain.measure_le_of_pairwise_disjoint
@@ -546,8 +546,8 @@ theorem essSup_measure_restrict (hs : IsFundamentalDomain G s μ) {f : α → 
     (hf : ∀ γ : G, ∀ x : α, f (γ • x) = f x) : essSup f (μ.restrict s) = essSup f μ :=
   by
   refine' le_antisymm (essSup_mono_measure' measure.restrict_le_self) _
-  rw [essSup_eq_infₛ (μ.restrict s) f, essSup_eq_infₛ μ f]
-  refine' infₛ_le_infₛ _
+  rw [essSup_eq_sInf (μ.restrict s) f, essSup_eq_sInf μ f]
+  refine' sInf_le_sInf _
   rintro a (ha : (μ.restrict s) { x : α | a < f x } = 0)
   rw [measure.restrict_apply₀' hs.null_measurable_set] at ha
   refine' measure_zero_of_invariant hs _ _ ha
@@ -680,14 +680,14 @@ variable [Countable G] [MeasurableSpace G] [MeasurableSpace α] [MeasurableSMul
 @[to_additive MeasureTheory.NullMeasurableSet.add_fundamentalFrontier]
 protected theorem NullMeasurableSet.fundamentalFrontier (hs : NullMeasurableSet s μ) :
     NullMeasurableSet (fundamentalFrontier G s) μ :=
-  hs.inter <| NullMeasurableSet.unionᵢ fun g => NullMeasurableSet.unionᵢ fun hg => hs.smul _
+  hs.inter <| NullMeasurableSet.iUnion fun g => NullMeasurableSet.iUnion fun hg => hs.smul _
 #align measure_theory.null_measurable_set.fundamental_frontier MeasureTheory.NullMeasurableSet.fundamentalFrontier
 #align measure_theory.null_measurable_set.add_fundamental_frontier MeasureTheory.NullMeasurableSet.add_fundamentalFrontier
 
 @[to_additive MeasureTheory.NullMeasurableSet.add_fundamentalInterior]
 protected theorem NullMeasurableSet.fundamentalInterior (hs : NullMeasurableSet s μ) :
     NullMeasurableSet (fundamentalInterior G s) μ :=
-  hs.diffₓ <| NullMeasurableSet.unionᵢ fun g => NullMeasurableSet.unionᵢ fun hg => hs.smul _
+  hs.diffₓ <| NullMeasurableSet.iUnion fun g => NullMeasurableSet.iUnion fun hg => hs.smul _
 #align measure_theory.null_measurable_set.fundamental_interior MeasureTheory.NullMeasurableSet.fundamentalInterior
 #align measure_theory.null_measurable_set.add_fundamental_interior MeasureTheory.NullMeasurableSet.add_fundamentalInterior

bump to nightly-2023-05-10-10

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

d51144ae

Diff

@@ -188,7 +188,7 @@ theorem pairwise_aEDisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : 
 
 @[to_additive]
 theorem smul_of_comm {G' : Type _} [Group G'] [MulAction G' α] [MeasurableSpace G']
-    [HasMeasurableSmul G' α] [SmulInvariantMeasure G' α μ] [SMulCommClass G' G α]
+    [MeasurableSMul G' α] [SmulInvariantMeasure G' α μ] [SMulCommClass G' G α]
     (h : IsFundamentalDomain G s μ) (g : G') : IsFundamentalDomain G (g • s) μ :=
   h.image_of_equiv (MulAction.toPerm g) (measurePreserving_smul _ _).QuasiMeasurePreserving
       (Equiv.refl _) <|
@@ -196,7 +196,7 @@ theorem smul_of_comm {G' : Type _} [Group G'] [MulAction G' α] [MeasurableSpace
 #align measure_theory.is_fundamental_domain.smul_of_comm MeasureTheory.IsFundamentalDomain.smul_of_comm
 #align measure_theory.is_add_fundamental_domain.vadd_of_comm MeasureTheory.IsAddFundamentalDomain.vadd_of_comm
 
-variable [MeasurableSpace G] [HasMeasurableSmul G α] [SmulInvariantMeasure G α μ]
+variable [MeasurableSpace G] [MeasurableSMul G α] [SmulInvariantMeasure G α μ]
 
 @[to_additive]
 theorem nullMeasurableSet_smul (h : IsFundamentalDomain G s μ) (g : G) :
@@ -674,8 +674,8 @@ theorem pairwise_disjoint_fundamentalInterior :
 #align measure_theory.pairwise_disjoint_fundamental_interior MeasureTheory.pairwise_disjoint_fundamentalInterior
 #align measure_theory.pairwise_disjoint_add_fundamental_interior MeasureTheory.pairwise_disjoint_add_fundamental_interior
 
-variable [Countable G] [MeasurableSpace G] [MeasurableSpace α] [HasMeasurableSmul G α]
-  {μ : Measure α} [SmulInvariantMeasure G α μ]
+variable [Countable G] [MeasurableSpace G] [MeasurableSpace α] [MeasurableSMul G α] {μ : Measure α}
+  [SmulInvariantMeasure G α μ]
 
 @[to_additive MeasureTheory.NullMeasurableSet.add_fundamentalFrontier]
 protected theorem NullMeasurableSet.fundamentalFrontier (hs : NullMeasurableSet s μ) :
@@ -719,7 +719,7 @@ theorem measure_fundamentalInterior : μ (fundamentalInterior G s) = μ s :=
 end Group
 
 variable [Countable G] [Group G] [MulAction G α] [MeasurableSpace α] {μ : Measure α} {s : Set α}
-  (hs : IsFundamentalDomain G s μ) [MeasurableSpace G] [HasMeasurableSmul G α]
+  (hs : IsFundamentalDomain G s μ) [MeasurableSpace G] [MeasurableSMul G α]
   [SmulInvariantMeasure G α μ]
 
 include hs

bump to nightly-2023-05-09-08

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

244524af

Diff

@@ -103,7 +103,7 @@ theorem mk'' (h_meas : NullMeasurableSet s μ) (h_ae_covers : ∀ᵐ x ∂μ, 
     (h_qmp : ∀ g : G, QuasiMeasurePreserving ((· • ·) g : α → α) μ μ) : IsFundamentalDomain G s μ :=
   { NullMeasurableSet := h_meas
     ae_covers := h_ae_covers
-    AEDisjoint := pairwise_aEDisjoint_of_aEDisjoint_forall_ne_one h_ae_disjoint h_qmp }
+    AEDisjoint := pairwise_aedisjoint_of_aedisjoint_forall_ne_one h_ae_disjoint h_qmp }
 #align measure_theory.is_fundamental_domain.mk'' MeasureTheory.IsFundamentalDomain.mk''
 #align measure_theory.is_add_fundamental_domain.mk'' MeasureTheory.IsAddFundamentalDomain.mk''
 
@@ -114,12 +114,12 @@ to check that its translates `g • s` are (almost) disjoint and that the sum `
 sufficiently large. -/
 @[to_additive MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_le
       "\nIf a measurable space has a finite measure `μ` and a countable additive group `G` acts\nquasi-measure-preservingly, then to show that a set `s` is a fundamental domain, it is sufficient\nto check that its translates `g +ᵥ s` are (almost) disjoint and that the sum `∑' g, μ (g +ᵥ s)` is\nsufficiently large."]
-theorem mk_of_measure_univ_le [IsFiniteMeasure μ] [Countable G] (h_meas : NullMeasurableSet s μ)
+theorem mk_of_measure_univ_le [FiniteMeasure μ] [Countable G] (h_meas : NullMeasurableSet s μ)
     (h_ae_disjoint : ∀ (g) (_ : g ≠ (1 : G)), AEDisjoint μ (g • s) s)
     (h_qmp : ∀ g : G, QuasiMeasurePreserving ((· • ·) g : α → α) μ μ)
     (h_measure_univ_le : μ (univ : Set α) ≤ ∑' g : G, μ (g • s)) : IsFundamentalDomain G s μ :=
   have ae_disjoint : Pairwise (AEDisjoint μ on fun g : G => g • s) :=
-    pairwise_aEDisjoint_of_aEDisjoint_forall_ne_one h_ae_disjoint h_qmp
+    pairwise_aedisjoint_of_aedisjoint_forall_ne_one h_ae_disjoint h_qmp
   { NullMeasurableSet := h_meas
     AEDisjoint
     ae_covers :=

bump to nightly-2023-05-06-14

mathlib commit https://github.com/leanprover-community/mathlib/commit/3905fa80e62c0898131285baab35559fbc4e5cda

2f9b6e15

Diff

@@ -510,7 +510,7 @@ theorem measure_le_of_pairwise_disjoint (hs : IsFundamentalDomain G s μ)
   calc
     μ t = ∑' g : G, μ (g • t ∩ s) := hs.measure_eq_tsum t
     _ = μ (⋃ g : G, g • t ∩ s) :=
-      (Eq.symm <| measure_Union₀ hd fun g => (ht.smul _).inter hs.NullMeasurableSet)
+      (Eq.symm <| measure_unionᵢ₀ hd fun g => (ht.smul _).inter hs.NullMeasurableSet)
     _ ≤ μ s := measure_mono (unionᵢ_subset fun g => inter_subset_right _ _)
     
 #align measure_theory.is_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsFundamentalDomain.measure_le_of_pairwise_disjoint

bump to nightly-2023-05-06-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/3905fa80e62c0898131285baab35559fbc4e5cda

e8904d96

Diff

@@ -55,7 +55,7 @@ structure IsAddFundamentalDomain (G : Type _) {α : Type _} [Zero G] [VAdd G α]
   (s : Set α) (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) : Prop where
   NullMeasurableSet : NullMeasurableSet s μ
   ae_covers : ∀ᵐ x ∂μ, ∃ g : G, g +ᵥ x ∈ s
-  AeDisjoint : Pairwise <| (AeDisjoint μ on fun g : G => g +ᵥ s)
+  AEDisjoint : Pairwise <| (AEDisjoint μ on fun g : G => g +ᵥ s)
 #align measure_theory.is_add_fundamental_domain MeasureTheory.IsAddFundamentalDomain
 
 /-- A measurable set `s` is a *fundamental domain* for an action of a group `G` on a measurable
@@ -66,7 +66,7 @@ structure IsFundamentalDomain (G : Type _) {α : Type _} [One G] [SMul G α] [Me
   (s : Set α) (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) : Prop where
   NullMeasurableSet : NullMeasurableSet s μ
   ae_covers : ∀ᵐ x ∂μ, ∃ g : G, g • x ∈ s
-  AeDisjoint : Pairwise <| (AeDisjoint μ on fun g : G => g • s)
+  AEDisjoint : Pairwise <| (AEDisjoint μ on fun g : G => g • s)
 #align measure_theory.is_fundamental_domain MeasureTheory.IsFundamentalDomain
 #align measure_theory.is_add_fundamental_domain MeasureTheory.IsAddFundamentalDomain
 
@@ -85,8 +85,8 @@ theorem mk' (h_meas : NullMeasurableSet s μ) (h_exists : ∀ x : α, ∃! g : G
     IsFundamentalDomain G s μ :=
   { NullMeasurableSet := h_meas
     ae_covers := eventually_of_forall fun x => (h_exists x).exists
-    AeDisjoint := fun a b hab =>
-      Disjoint.aeDisjoint <|
+    AEDisjoint := fun a b hab =>
+      Disjoint.aedisjoint <|
         disjoint_left.2 fun x hxa hxb =>
           by
           rw [mem_smul_set_iff_inv_smul_mem] at hxa hxb
@@ -99,11 +99,11 @@ theorem mk' (h_meas : NullMeasurableSet s μ) (h_exists : ∀ x : α, ∃! g : G
 @[to_additive
       "For `s` to be a fundamental domain, it's enough to check `ae_disjoint (g +ᵥ s) s` for\n`g ≠ 0`."]
 theorem mk'' (h_meas : NullMeasurableSet s μ) (h_ae_covers : ∀ᵐ x ∂μ, ∃ g : G, g • x ∈ s)
-    (h_ae_disjoint : ∀ (g) (_ : g ≠ (1 : G)), AeDisjoint μ (g • s) s)
+    (h_ae_disjoint : ∀ (g) (_ : g ≠ (1 : G)), AEDisjoint μ (g • s) s)
     (h_qmp : ∀ g : G, QuasiMeasurePreserving ((· • ·) g : α → α) μ μ) : IsFundamentalDomain G s μ :=
   { NullMeasurableSet := h_meas
     ae_covers := h_ae_covers
-    AeDisjoint := pairwise_aeDisjoint_of_aeDisjoint_forall_ne_one h_ae_disjoint h_qmp }
+    AEDisjoint := pairwise_aEDisjoint_of_aEDisjoint_forall_ne_one h_ae_disjoint h_qmp }
 #align measure_theory.is_fundamental_domain.mk'' MeasureTheory.IsFundamentalDomain.mk''
 #align measure_theory.is_add_fundamental_domain.mk'' MeasureTheory.IsAddFundamentalDomain.mk''
 
@@ -115,13 +115,13 @@ sufficiently large. -/
 @[to_additive MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_le
       "\nIf a measurable space has a finite measure `μ` and a countable additive group `G` acts\nquasi-measure-preservingly, then to show that a set `s` is a fundamental domain, it is sufficient\nto check that its translates `g +ᵥ s` are (almost) disjoint and that the sum `∑' g, μ (g +ᵥ s)` is\nsufficiently large."]
 theorem mk_of_measure_univ_le [IsFiniteMeasure μ] [Countable G] (h_meas : NullMeasurableSet s μ)
-    (h_ae_disjoint : ∀ (g) (_ : g ≠ (1 : G)), AeDisjoint μ (g • s) s)
+    (h_ae_disjoint : ∀ (g) (_ : g ≠ (1 : G)), AEDisjoint μ (g • s) s)
     (h_qmp : ∀ g : G, QuasiMeasurePreserving ((· • ·) g : α → α) μ μ)
     (h_measure_univ_le : μ (univ : Set α) ≤ ∑' g : G, μ (g • s)) : IsFundamentalDomain G s μ :=
-  have ae_disjoint : Pairwise (AeDisjoint μ on fun g : G => g • s) :=
-    pairwise_aeDisjoint_of_aeDisjoint_forall_ne_one h_ae_disjoint h_qmp
+  have ae_disjoint : Pairwise (AEDisjoint μ on fun g : G => g • s) :=
+    pairwise_aEDisjoint_of_aEDisjoint_forall_ne_one h_ae_disjoint h_qmp
   { NullMeasurableSet := h_meas
-    AeDisjoint
+    AEDisjoint
     ae_covers :=
       by
       replace h_meas : ∀ g : G, null_measurable_set (g • s) μ := fun g =>
@@ -149,7 +149,7 @@ theorem unionᵢ_smul_ae_eq (h : IsFundamentalDomain G s μ) : (⋃ g : G, g •
 @[to_additive]
 theorem mono (h : IsFundamentalDomain G s μ) {ν : Measure α} (hle : ν ≪ μ) :
     IsFundamentalDomain G s ν :=
-  ⟨h.1.mono_ac hle, hle h.2, h.AeDisjoint.mono fun a b hab => hle hab⟩
+  ⟨h.1.mono_ac hle, hle h.2, h.AEDisjoint.mono fun a b hab => hle hab⟩
 #align measure_theory.is_fundamental_domain.mono MeasureTheory.IsFundamentalDomain.mono
 #align measure_theory.is_add_fundamental_domain.mono MeasureTheory.IsAddFundamentalDomain.mono
 
@@ -159,7 +159,7 @@ theorem preimage_of_equiv {ν : Measure β} (h : IsFundamentalDomain G s μ) {f
     (hef : ∀ g, Semiconj f ((· • ·) (e g)) ((· • ·) g)) : IsFundamentalDomain H (f ⁻¹' s) ν :=
   { NullMeasurableSet := h.NullMeasurableSet.Preimage hf
     ae_covers := (hf.ae h.ae_covers).mono fun x ⟨g, hg⟩ => ⟨e g, by rwa [mem_preimage, hef g x]⟩
-    AeDisjoint := fun a b hab => by
+    AEDisjoint := fun a b hab => by
       lift e to G ≃ H using he
       have : (e.symm a⁻¹)⁻¹ ≠ (e.symm b⁻¹)⁻¹ := by simp [hab]
       convert(h.ae_disjoint this).Preimage hf using 1
@@ -180,11 +180,11 @@ theorem image_of_equiv {ν : Measure β} (h : IsFundamentalDomain G s μ) (f : 
 #align measure_theory.is_add_fundamental_domain.image_of_equiv MeasureTheory.IsAddFundamentalDomain.image_of_equiv
 
 @[to_additive]
-theorem pairwise_aeDisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
-    Pairwise fun g₁ g₂ : G => AeDisjoint ν (g₁ • s) (g₂ • s) :=
-  h.AeDisjoint.mono fun g₁ g₂ H => hν H
-#align measure_theory.is_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsFundamentalDomain.pairwise_aeDisjoint_of_ac
-#align measure_theory.is_add_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsAddFundamentalDomain.pairwise_aeDisjoint_of_ac
+theorem pairwise_aEDisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
+    Pairwise fun g₁ g₂ : G => AEDisjoint ν (g₁ • s) (g₂ • s) :=
+  h.AEDisjoint.mono fun g₁ g₂ H => hν H
+#align measure_theory.is_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsFundamentalDomain.pairwise_aEDisjoint_of_ac
+#align measure_theory.is_add_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsAddFundamentalDomain.pairwise_aEDisjoint_of_ac
 
 @[to_additive]
 theorem smul_of_comm {G' : Type _} [Group G'] [MulAction G' α] [MeasurableSpace G']
@@ -505,7 +505,7 @@ has measure at most `μ s`. -/
 @[to_additive
       "If the additive action of a countable group `G` admits an invariant measure `μ` with\na fundamental domain `s`, then every null-measurable set `t` such that the sets `g +ᵥ t ∩ s` are\npairwise a.e.-disjoint has measure at most `μ s`."]
 theorem measure_le_of_pairwise_disjoint (hs : IsFundamentalDomain G s μ)
-    (ht : NullMeasurableSet t μ) (hd : Pairwise (AeDisjoint μ on fun g : G => g • t ∩ s)) :
+    (ht : NullMeasurableSet t μ) (hd : Pairwise (AEDisjoint μ on fun g : G => g • t ∩ s)) :
     μ t ≤ μ s :=
   calc
     μ t = ∑' g : G, μ (g • t ∩ s) := hs.measure_eq_tsum t
@@ -527,7 +527,7 @@ theorem exists_ne_one_smul_eq (hs : IsFundamentalDomain G s μ) (htm : NullMeasu
     (ht : μ s < μ t) : ∃ (x : _)(_ : x ∈ t)(y : _)(_ : y ∈ t)(g : _)(_ : g ≠ (1 : G)), g • x = y :=
   by
   contrapose! ht
-  refine' hs.measure_le_of_pairwise_disjoint htm (Pairwise.aeDisjoint fun g₁ g₂ hne => _)
+  refine' hs.measure_le_of_pairwise_disjoint htm (Pairwise.aedisjoint fun g₁ g₂ hne => _)
   dsimp [Function.onFun]
   refine' (Disjoint.inf_left _ _).inf_right _
   rw [Set.disjoint_left]
@@ -743,7 +743,7 @@ protected theorem fundamentalInterior : IsFundamentalDomain G (fundamentalInteri
         measure_union_null
           (measure_Union_null fun _ => measure_smul_null hs.measure_fundamental_frontier _)
           hs.ae_covers
-    AeDisjoint := (pairwise_disjoint_fundamentalInterior _ _).mono fun _ _ => Disjoint.aeDisjoint }
+    AEDisjoint := (pairwise_disjoint_fundamentalInterior _ _).mono fun _ _ => Disjoint.aedisjoint }
 #align measure_theory.is_fundamental_domain.fundamental_interior MeasureTheory.IsFundamentalDomain.fundamentalInterior
 
 end IsFundamentalDomain

bump to nightly-2023-05-04-10

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

3d8894bd

Diff

@@ -114,7 +114,7 @@ to check that its translates `g • s` are (almost) disjoint and that the sum `
 sufficiently large. -/
 @[to_additive MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_le
       "\nIf a measurable space has a finite measure `μ` and a countable additive group `G` acts\nquasi-measure-preservingly, then to show that a set `s` is a fundamental domain, it is sufficient\nto check that its translates `g +ᵥ s` are (almost) disjoint and that the sum `∑' g, μ (g +ᵥ s)` is\nsufficiently large."]
-theorem mkOfMeasureUnivLe [IsFiniteMeasure μ] [Countable G] (h_meas : NullMeasurableSet s μ)
+theorem mk_of_measure_univ_le [IsFiniteMeasure μ] [Countable G] (h_meas : NullMeasurableSet s μ)
     (h_ae_disjoint : ∀ (g) (_ : g ≠ (1 : G)), AeDisjoint μ (g • s) s)
     (h_qmp : ∀ g : G, QuasiMeasurePreserving ((· • ·) g : α → α) μ μ)
     (h_measure_univ_le : μ (univ : Set α) ≤ ∑' g : G, μ (g • s)) : IsFundamentalDomain G s μ :=
@@ -136,7 +136,7 @@ theorem mkOfMeasureUnivLe [IsFiniteMeasure μ] [Countable G] (h_meas : NullMeasu
       refine' le_antisymm (measure_mono <| subset_univ _) _
       rw [measure_Union₀ ae_disjoint h_meas]
       exact h_measure_univ_le }
-#align measure_theory.is_fundamental_domain.mk_of_measure_univ_le MeasureTheory.IsFundamentalDomain.mkOfMeasureUnivLe
+#align measure_theory.is_fundamental_domain.mk_of_measure_univ_le MeasureTheory.IsFundamentalDomain.mk_of_measure_univ_le
 #align measure_theory.is_add_fundamental_domain.mk_of_measure_univ_le MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_le
 
 @[to_additive]
@@ -144,17 +144,17 @@ theorem unionᵢ_smul_ae_eq (h : IsFundamentalDomain G s μ) : (⋃ g : G, g •
   eventuallyEq_univ.2 <|
     h.ae_covers.mono fun x ⟨g, hg⟩ => mem_unionᵢ.2 ⟨g⁻¹, _, hg, inv_smul_smul _ _⟩
 #align measure_theory.is_fundamental_domain.Union_smul_ae_eq MeasureTheory.IsFundamentalDomain.unionᵢ_smul_ae_eq
-#align measure_theory.is_add_fundamental_domain.Union_vadd_ae_eq MeasureTheory.IsAddFundamentalDomain.Union_vadd_ae_eq
+#align measure_theory.is_add_fundamental_domain.Union_vadd_ae_eq MeasureTheory.IsAddFundamentalDomain.unionᵢ_vadd_ae_eq
 
 @[to_additive]
 theorem mono (h : IsFundamentalDomain G s μ) {ν : Measure α} (hle : ν ≪ μ) :
     IsFundamentalDomain G s ν :=
-  ⟨h.1.monoAc hle, hle h.2, h.AeDisjoint.mono fun a b hab => hle hab⟩
+  ⟨h.1.mono_ac hle, hle h.2, h.AeDisjoint.mono fun a b hab => hle hab⟩
 #align measure_theory.is_fundamental_domain.mono MeasureTheory.IsFundamentalDomain.mono
 #align measure_theory.is_add_fundamental_domain.mono MeasureTheory.IsAddFundamentalDomain.mono
 
 @[to_additive]
-theorem preimageOfEquiv {ν : Measure β} (h : IsFundamentalDomain G s μ) {f : β → α}
+theorem preimage_of_equiv {ν : Measure β} (h : IsFundamentalDomain G s μ) {f : β → α}
     (hf : QuasiMeasurePreserving f ν μ) {e : G → H} (he : Bijective e)
     (hef : ∀ g, Semiconj f ((· • ·) (e g)) ((· • ·) g)) : IsFundamentalDomain H (f ⁻¹' s) ν :=
   { NullMeasurableSet := h.NullMeasurableSet.Preimage hf
@@ -164,11 +164,11 @@ theorem preimageOfEquiv {ν : Measure β} (h : IsFundamentalDomain G s μ) {f :
       have : (e.symm a⁻¹)⁻¹ ≠ (e.symm b⁻¹)⁻¹ := by simp [hab]
       convert(h.ae_disjoint this).Preimage hf using 1
       simp only [← preimage_smul_inv, preimage_preimage, ← hef _ _, e.apply_symm_apply, inv_inv] }
-#align measure_theory.is_fundamental_domain.preimage_of_equiv MeasureTheory.IsFundamentalDomain.preimageOfEquiv
+#align measure_theory.is_fundamental_domain.preimage_of_equiv MeasureTheory.IsFundamentalDomain.preimage_of_equiv
 #align measure_theory.is_add_fundamental_domain.preimage_of_equiv MeasureTheory.IsAddFundamentalDomain.preimage_of_equiv
 
 @[to_additive]
-theorem imageOfEquiv {ν : Measure β} (h : IsFundamentalDomain G s μ) (f : α ≃ β)
+theorem image_of_equiv {ν : Measure β} (h : IsFundamentalDomain G s μ) (f : α ≃ β)
     (hf : QuasiMeasurePreserving f.symm ν μ) (e : H ≃ G)
     (hef : ∀ g, Semiconj f ((· • ·) (e g)) ((· • ·) g)) : IsFundamentalDomain H (f '' s) ν :=
   by
@@ -176,7 +176,7 @@ theorem imageOfEquiv {ν : Measure β} (h : IsFundamentalDomain G s μ) (f : α
   refine' h.preimage_of_equiv hf e.symm.bijective fun g x => _
   rcases f.surjective x with ⟨x, rfl⟩
   rw [← hef _ _, f.symm_apply_apply, f.symm_apply_apply, e.apply_symm_apply]
-#align measure_theory.is_fundamental_domain.image_of_equiv MeasureTheory.IsFundamentalDomain.imageOfEquiv
+#align measure_theory.is_fundamental_domain.image_of_equiv MeasureTheory.IsFundamentalDomain.image_of_equiv
 #align measure_theory.is_add_fundamental_domain.image_of_equiv MeasureTheory.IsAddFundamentalDomain.image_of_equiv
 
 @[to_additive]
@@ -184,37 +184,37 @@ theorem pairwise_aeDisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : 
     Pairwise fun g₁ g₂ : G => AeDisjoint ν (g₁ • s) (g₂ • s) :=
   h.AeDisjoint.mono fun g₁ g₂ H => hν H
 #align measure_theory.is_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsFundamentalDomain.pairwise_aeDisjoint_of_ac
-#align measure_theory.is_add_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsAddFundamentalDomain.pairwise_ae_disjoint_of_ac
+#align measure_theory.is_add_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsAddFundamentalDomain.pairwise_aeDisjoint_of_ac
 
 @[to_additive]
-theorem smulOfComm {G' : Type _} [Group G'] [MulAction G' α] [MeasurableSpace G']
+theorem smul_of_comm {G' : Type _} [Group G'] [MulAction G' α] [MeasurableSpace G']
     [HasMeasurableSmul G' α] [SmulInvariantMeasure G' α μ] [SMulCommClass G' G α]
     (h : IsFundamentalDomain G s μ) (g : G') : IsFundamentalDomain G (g • s) μ :=
-  h.imageOfEquiv (MulAction.toPerm g) (measurePreservingSmul _ _).QuasiMeasurePreserving
+  h.image_of_equiv (MulAction.toPerm g) (measurePreserving_smul _ _).QuasiMeasurePreserving
       (Equiv.refl _) <|
     smul_comm g
-#align measure_theory.is_fundamental_domain.smul_of_comm MeasureTheory.IsFundamentalDomain.smulOfComm
+#align measure_theory.is_fundamental_domain.smul_of_comm MeasureTheory.IsFundamentalDomain.smul_of_comm
 #align measure_theory.is_add_fundamental_domain.vadd_of_comm MeasureTheory.IsAddFundamentalDomain.vadd_of_comm
 
 variable [MeasurableSpace G] [HasMeasurableSmul G α] [SmulInvariantMeasure G α μ]
 
 @[to_additive]
-theorem nullMeasurableSetSmul (h : IsFundamentalDomain G s μ) (g : G) :
+theorem nullMeasurableSet_smul (h : IsFundamentalDomain G s μ) (g : G) :
     NullMeasurableSet (g • s) μ :=
   h.NullMeasurableSet.smul g
-#align measure_theory.is_fundamental_domain.null_measurable_set_smul MeasureTheory.IsFundamentalDomain.nullMeasurableSetSmul
-#align measure_theory.is_add_fundamental_domain.null_measurable_set_vadd MeasureTheory.IsAddFundamentalDomain.null_measurable_set_vadd
+#align measure_theory.is_fundamental_domain.null_measurable_set_smul MeasureTheory.IsFundamentalDomain.nullMeasurableSet_smul
+#align measure_theory.is_add_fundamental_domain.null_measurable_set_vadd MeasureTheory.IsAddFundamentalDomain.nullMeasurableSet_vadd
 
 @[to_additive]
 theorem restrict_restrict (h : IsFundamentalDomain G s μ) (g : G) (t : Set α) :
     (μ.restrict t).restrict (g • s) = μ.restrict (g • s ∩ t) :=
-  restrict_restrict₀ ((h.nullMeasurableSetSmul g).mono restrict_le_self)
+  restrict_restrict₀ ((h.nullMeasurableSet_smul g).mono restrict_le_self)
 #align measure_theory.is_fundamental_domain.restrict_restrict MeasureTheory.IsFundamentalDomain.restrict_restrict
 #align measure_theory.is_add_fundamental_domain.restrict_restrict MeasureTheory.IsAddFundamentalDomain.restrict_restrict
 
 @[to_additive]
 theorem smul (h : IsFundamentalDomain G s μ) (g : G) : IsFundamentalDomain G (g • s) μ :=
-  h.imageOfEquiv (MulAction.toPerm g) (measurePreservingSmul _ _).QuasiMeasurePreserving
+  h.image_of_equiv (MulAction.toPerm g) (measurePreserving_smul _ _).QuasiMeasurePreserving
     ⟨fun g' => g⁻¹ * g' * g, fun g' => g * g' * g⁻¹, fun g' => by simp [mul_assoc], fun g' => by
       simp [mul_assoc]⟩
     fun g' x => by simp [smul_smul, mul_assoc]
@@ -228,7 +228,7 @@ theorem sum_restrict_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
     (Sum fun g : G => ν.restrict (g • s)) = ν := by
   rw [←
     restrict_Union_ae (h.ae_disjoint.mono fun i j h => hν h) fun g =>
-      (h.null_measurable_set_smul g).monoAc hν,
+      (h.null_measurable_set_smul g).mono_ac hν,
     restrict_congr_set (hν h.Union_smul_ae_eq), restrict_univ]
 #align measure_theory.is_fundamental_domain.sum_restrict_of_ac MeasureTheory.IsFundamentalDomain.sum_restrict_of_ac
 #align measure_theory.is_add_fundamental_domain.sum_restrict_of_ac MeasureTheory.IsAddFundamentalDomain.sum_restrict_of_ac
@@ -261,7 +261,7 @@ theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0
     _ = ∑' g : G, ∫⁻ x in g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫⁻ x in s, f (g⁻¹ • x) ∂μ :=
       tsum_congr fun g =>
-        ((measurePreservingSmul g⁻¹ μ).set_lintegral_comp_emb (measurableEmbedding_const_smul _) _
+        ((measurePreserving_smul g⁻¹ μ).set_lintegral_comp_emb (measurableEmbedding_const_smul _) _
             _).symm
     
 #align measure_theory.is_fundamental_domain.lintegral_eq_tsum' MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum'
@@ -287,7 +287,7 @@ theorem set_lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ
     _ = ∑' g : G, ∫⁻ x in g⁻¹ • (g • t ∩ s), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
     _ = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
       tsum_congr fun g =>
-        ((measurePreservingSmul g⁻¹ μ).set_lintegral_comp_emb (measurableEmbedding_const_smul _) _
+        ((measurePreserving_smul g⁻¹ μ).set_lintegral_comp_emb (measurableEmbedding_const_smul _) _
             _).symm
     
 #align measure_theory.is_fundamental_domain.set_lintegral_eq_tsum' MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum'
@@ -299,7 +299,7 @@ theorem measure_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ)
   by
   have H : ν.restrict t ≪ μ := Measure.restrict_le_self.AbsolutelyContinuous.trans hν
   simpa only [set_lintegral_one, Pi.one_def,
-    measure.restrict_apply₀ ((h.null_measurable_set_smul _).monoAc H), inter_comm] using
+    measure.restrict_apply₀ ((h.null_measurable_set_smul _).mono_ac H), inter_comm] using
     h.lintegral_eq_tsum_of_ac H 1
 #align measure_theory.is_fundamental_domain.measure_eq_tsum_of_ac MeasureTheory.IsFundamentalDomain.measure_eq_tsum_of_ac
 #align measure_theory.is_add_fundamental_domain.measure_eq_tsum_of_ac MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum_of_ac
@@ -397,14 +397,14 @@ protected theorem aeStronglyMeasurable_on_iff {β : Type _} [TopologicalSpace β
       refine' forall_congr' fun g => _
       have he : MeasurableEmbedding ((· • ·) g⁻¹ : α → α) := measurableEmbedding_const_smul _
       rw [← image_smul, ←
-        ((measure_preserving_smul g⁻¹ μ).restrictImageEmb he _).aeStronglyMeasurable_comp_iff he]
+        ((measure_preserving_smul g⁻¹ μ).restrict_image_emb he _).aeStronglyMeasurable_comp_iff he]
       simp only [(· ∘ ·), hf]
     _ ↔ AeStronglyMeasurable f (μ.restrict t) := by
       simp only [← aeStronglyMeasurable_sum_measure_iff, ← hs.restrict_restrict,
         hs.sum_restrict_of_ac restrict_le_self.absolutely_continuous]
     
 #align measure_theory.is_fundamental_domain.ae_strongly_measurable_on_iff MeasureTheory.IsFundamentalDomain.aeStronglyMeasurable_on_iff
-#align measure_theory.is_add_fundamental_domain.ae_strongly_measurable_on_iff MeasureTheory.IsAddFundamentalDomain.ae_strongly_measurable_on_iff
+#align measure_theory.is_add_fundamental_domain.ae_strongly_measurable_on_iff MeasureTheory.IsAddFundamentalDomain.aeStronglyMeasurable_on_iff
 
 @[to_additive]
 protected theorem hasFiniteIntegral_on_iff (hs : IsFundamentalDomain G s μ)
@@ -415,14 +415,14 @@ protected theorem hasFiniteIntegral_on_iff (hs : IsFundamentalDomain G s μ)
   rw [hs.set_lintegral_eq ht]
   intro g x; rw [hf]
 #align measure_theory.is_fundamental_domain.has_finite_integral_on_iff MeasureTheory.IsFundamentalDomain.hasFiniteIntegral_on_iff
-#align measure_theory.is_add_fundamental_domain.has_finite_integral_on_iff MeasureTheory.IsAddFundamentalDomain.has_finite_integral_on_iff
+#align measure_theory.is_add_fundamental_domain.has_finite_integral_on_iff MeasureTheory.IsAddFundamentalDomain.hasFiniteIntegral_on_iff
 
 @[to_additive]
 protected theorem integrableOn_iff (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
     {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) : IntegrableOn f s μ ↔ IntegrableOn f t μ :=
   and_congr (hs.aeStronglyMeasurable_on_iff ht hf) (hs.hasFiniteIntegral_on_iff ht hf)
 #align measure_theory.is_fundamental_domain.integrable_on_iff MeasureTheory.IsFundamentalDomain.integrableOn_iff
-#align measure_theory.is_add_fundamental_domain.integrable_on_iff MeasureTheory.IsAddFundamentalDomain.integrable_on_iff
+#align measure_theory.is_add_fundamental_domain.integrable_on_iff MeasureTheory.IsAddFundamentalDomain.integrableOn_iff
 
 variable [NormedSpace ℝ E] [CompleteSpace E]
 
@@ -452,7 +452,7 @@ theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
     _ = ∑' g : G, ∫ x in g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ :=
       tsum_congr fun g =>
-        (measurePreservingSmul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
+        (measurePreserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
     
 #align measure_theory.is_fundamental_domain.integral_eq_tsum' MeasureTheory.IsFundamentalDomain.integral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum'
@@ -478,7 +478,7 @@ theorem set_integral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t
     _ = ∑' g : G, ∫ x in g⁻¹ • (g • t ∩ s), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
     _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
       tsum_congr fun g =>
-        (measurePreservingSmul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
+        (measurePreserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
     
 #align measure_theory.is_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.set_integral_eq_tsum'
@@ -556,7 +556,7 @@ theorem essSup_measure_restrict (hs : IsFundamentalDomain G s μ) {f : α → 
   rw [mem_smul_set_iff_inv_smul_mem]
   simp only [mem_set_of_eq, hf γ⁻¹ x]
 #align measure_theory.is_fundamental_domain.ess_sup_measure_restrict MeasureTheory.IsFundamentalDomain.essSup_measure_restrict
-#align measure_theory.is_add_fundamental_domain.ess_sup_measure_restrict MeasureTheory.IsAddFundamentalDomain.ess_sup_measure_restrict
+#align measure_theory.is_add_fundamental_domain.ess_sup_measure_restrict MeasureTheory.IsAddFundamentalDomain.essSup_measure_restrict
 
 end IsFundamentalDomain
 
@@ -677,19 +677,19 @@ theorem pairwise_disjoint_fundamentalInterior :
 variable [Countable G] [MeasurableSpace G] [MeasurableSpace α] [HasMeasurableSmul G α]
   {μ : Measure α} [SmulInvariantMeasure G α μ]
 
-@[to_additive MeasureTheory.NullMeasurableSet.add_fundamental_frontier]
+@[to_additive MeasureTheory.NullMeasurableSet.add_fundamentalFrontier]
 protected theorem NullMeasurableSet.fundamentalFrontier (hs : NullMeasurableSet s μ) :
     NullMeasurableSet (fundamentalFrontier G s) μ :=
-  hs.inter <| NullMeasurableSet.union fun g => NullMeasurableSet.union fun hg => hs.smul _
+  hs.inter <| NullMeasurableSet.unionᵢ fun g => NullMeasurableSet.unionᵢ fun hg => hs.smul _
 #align measure_theory.null_measurable_set.fundamental_frontier MeasureTheory.NullMeasurableSet.fundamentalFrontier
-#align measure_theory.null_measurable_set.add_fundamental_frontier MeasureTheory.NullMeasurableSet.add_fundamental_frontier
+#align measure_theory.null_measurable_set.add_fundamental_frontier MeasureTheory.NullMeasurableSet.add_fundamentalFrontier
 
-@[to_additive MeasureTheory.NullMeasurableSet.add_fundamental_interior]
+@[to_additive MeasureTheory.NullMeasurableSet.add_fundamentalInterior]
 protected theorem NullMeasurableSet.fundamentalInterior (hs : NullMeasurableSet s μ) :
     NullMeasurableSet (fundamentalInterior G s) μ :=
-  hs.diffₓ <| NullMeasurableSet.union fun g => NullMeasurableSet.union fun hg => hs.smul _
+  hs.diffₓ <| NullMeasurableSet.unionᵢ fun g => NullMeasurableSet.unionᵢ fun hg => hs.smul _
 #align measure_theory.null_measurable_set.fundamental_interior MeasureTheory.NullMeasurableSet.fundamentalInterior
-#align measure_theory.null_measurable_set.add_fundamental_interior MeasureTheory.NullMeasurableSet.add_fundamental_interior
+#align measure_theory.null_measurable_set.add_fundamental_interior MeasureTheory.NullMeasurableSet.add_fundamentalInterior
 
 end MeasurableSpace
 
@@ -702,19 +702,19 @@ variable [Countable G] [Group G] [MulAction G α] [MeasurableSpace α] {μ : Mea
 
 include hs
 
-@[to_additive MeasureTheory.IsAddFundamentalDomain.measure_add_fundamental_frontier]
+@[to_additive MeasureTheory.IsAddFundamentalDomain.measure_add_fundamentalFrontier]
 theorem measure_fundamentalFrontier : μ (fundamentalFrontier G s) = 0 := by
   simpa only [fundamental_frontier, Union₂_inter, measure_Union_null_iff', one_smul,
     measure_Union_null_iff, inter_comm s, Function.onFun] using fun g (hg : g ≠ 1) =>
     hs.ae_disjoint hg
 #align measure_theory.is_fundamental_domain.measure_fundamental_frontier MeasureTheory.IsFundamentalDomain.measure_fundamentalFrontier
-#align measure_theory.is_add_fundamental_domain.measure_add_fundamental_frontier MeasureTheory.IsAddFundamentalDomain.measure_add_fundamental_frontier
+#align measure_theory.is_add_fundamental_domain.measure_add_fundamental_frontier MeasureTheory.IsAddFundamentalDomain.measure_add_fundamentalFrontier
 
-@[to_additive MeasureTheory.IsAddFundamentalDomain.measure_add_fundamental_interior]
+@[to_additive MeasureTheory.IsAddFundamentalDomain.measure_add_fundamentalInterior]
 theorem measure_fundamentalInterior : μ (fundamentalInterior G s) = μ s :=
   measure_diff_null' hs.measure_fundamentalFrontier
 #align measure_theory.is_fundamental_domain.measure_fundamental_interior MeasureTheory.IsFundamentalDomain.measure_fundamentalInterior
-#align measure_theory.is_add_fundamental_domain.measure_add_fundamental_interior MeasureTheory.IsAddFundamentalDomain.measure_add_fundamental_interior
+#align measure_theory.is_add_fundamental_domain.measure_add_fundamental_interior MeasureTheory.IsAddFundamentalDomain.measure_add_fundamentalInterior
 
 end Group

bump to nightly-2023-03-30-02

mathlib commit https://github.com/leanprover-community/mathlib/commit/b685f506164f8d17a6404048bc4d696739c5d976

af7dd13c

Diff

@@ -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.fundamental_domain
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit eb810cf549db839dadf13353dbe69bac55acdbbc
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -254,21 +254,35 @@ theorem lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum
 
 @[to_additive]
-theorem set_lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
+theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) :
+    (∫⁻ x, f x ∂μ) = ∑' g : G, ∫⁻ x in s, f (g⁻¹ • x) ∂μ :=
+  calc
+    (∫⁻ x, f x ∂μ) = ∑' g : G, ∫⁻ x in g • s, f x ∂μ := h.lintegral_eq_tsum f
+    _ = ∑' g : G, ∫⁻ x in g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
+    _ = ∑' g : G, ∫⁻ x in s, f (g⁻¹ • x) ∂μ :=
+      tsum_congr fun g =>
+        ((measurePreservingSmul g⁻¹ μ).set_lintegral_comp_emb (measurableEmbedding_const_smul _) _
+            _).symm
+    
+#align measure_theory.is_fundamental_domain.lintegral_eq_tsum' MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum'
+#align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum'
+
+@[to_additive]
+theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
     (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ :=
   calc
     (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in g • s, f x ∂μ.restrict t :=
       h.lintegral_eq_tsum_of_ac restrict_le_self.AbsolutelyContinuous _
     _ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ := by simp only [h.restrict_restrict, inter_comm]
     
-#align measure_theory.is_fundamental_domain.set_lintegral_eq_tsum' MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum'
-#align measure_theory.is_add_fundamental_domain.set_lintegral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.set_lintegral_eq_tsum'
+#align measure_theory.is_fundamental_domain.set_lintegral_eq_tsum MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum
+#align measure_theory.is_add_fundamental_domain.set_lintegral_eq_tsum MeasureTheory.IsAddFundamentalDomain.set_lintegral_eq_tsum
 
 @[to_additive]
-theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
+theorem set_lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
     (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
   calc
-    (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ := h.set_lintegral_eq_tsum' f t
+    (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ := h.set_lintegral_eq_tsum f t
     _ = ∑' g : G, ∫⁻ x in t ∩ g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫⁻ x in g⁻¹ • (g • t ∩ s), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
     _ = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
@@ -276,8 +290,8 @@ theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ
         ((measurePreservingSmul g⁻¹ μ).set_lintegral_comp_emb (measurableEmbedding_const_smul _) _
             _).symm
     
-#align measure_theory.is_fundamental_domain.set_lintegral_eq_tsum MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum
-#align measure_theory.is_add_fundamental_domain.set_lintegral_eq_tsum MeasureTheory.IsAddFundamentalDomain.set_lintegral_eq_tsum
+#align measure_theory.is_fundamental_domain.set_lintegral_eq_tsum' MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum'
+#align measure_theory.is_add_fundamental_domain.set_lintegral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.set_lintegral_eq_tsum'
 
 @[to_additive]
 theorem measure_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) (t : Set α) :
@@ -300,7 +314,7 @@ theorem measure_eq_tsum' (h : IsFundamentalDomain G s μ) (t : Set α) :
 @[to_additive]
 theorem measure_eq_tsum (h : IsFundamentalDomain G s μ) (t : Set α) :
     μ t = ∑' g : G, μ (g • t ∩ s) := by
-  simpa only [set_lintegral_one] using h.set_lintegral_eq_tsum (fun _ => 1) t
+  simpa only [set_lintegral_one] using h.set_lintegral_eq_tsum' (fun _ => 1) t
 #align measure_theory.is_fundamental_domain.measure_eq_tsum MeasureTheory.IsFundamentalDomain.measure_eq_tsum
 #align measure_theory.is_add_fundamental_domain.measure_eq_tsum MeasureTheory.IsAddFundamentalDomain.measure_eq_tsum
 
@@ -332,9 +346,9 @@ protected theorem set_lintegral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFun
     (f : α → ℝ≥0∞) (hf : ∀ (g : G) (x), f (g • x) = f x) :
     (∫⁻ x in s, f x ∂μ) = ∫⁻ x in t, f x ∂μ :=
   calc
-    (∫⁻ x in s, f x ∂μ) = ∑' g : G, ∫⁻ x in s ∩ g • t, f x ∂μ := ht.set_lintegral_eq_tsum' _ _
+    (∫⁻ x in s, f x ∂μ) = ∑' g : G, ∫⁻ x in s ∩ g • t, f x ∂μ := ht.set_lintegral_eq_tsum _ _
     _ = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := by simp only [hf, inter_comm]
-    _ = ∫⁻ x in t, f x ∂μ := (hs.set_lintegral_eq_tsum _ _).symm
+    _ = ∫⁻ x in t, f x ∂μ := (hs.set_lintegral_eq_tsum' _ _).symm
     
 #align measure_theory.is_fundamental_domain.set_lintegral_eq MeasureTheory.IsFundamentalDomain.set_lintegral_eq
 #align measure_theory.is_add_fundamental_domain.set_lintegral_eq MeasureTheory.IsAddFundamentalDomain.set_lintegral_eq
@@ -412,31 +426,73 @@ protected theorem integrableOn_iff (hs : IsFundamentalDomain G s μ) (ht : IsFun
 
 variable [NormedSpace ℝ E] [CompleteSpace E]
 
+@[to_additive]
+theorem integral_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) (f : α → E)
+    (hf : Integrable f ν) : (∫ x, f x ∂ν) = ∑' g : G, ∫ x in g • s, f x ∂ν :=
+  by
+  rw [← MeasureTheory.integral_sum_measure, h.sum_restrict_of_ac hν]
+  rw [h.sum_restrict_of_ac hν]
+  -- Weirdly, these rewrites seem not to be combinable
+  exact hf
+#align measure_theory.is_fundamental_domain.integral_eq_tsum_of_ac MeasureTheory.IsFundamentalDomain.integral_eq_tsum_of_ac
+#align measure_theory.is_add_fundamental_domain.integral_eq_tsum_of_ac MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum_of_ac
+
+@[to_additive]
+theorem integral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → E) (hf : Integrable f μ) :
+    (∫ x, f x ∂μ) = ∑' g : G, ∫ x in g • s, f x ∂μ :=
+  integral_eq_tsum_of_ac h (by rfl) f hf
+#align measure_theory.is_fundamental_domain.integral_eq_tsum MeasureTheory.IsFundamentalDomain.integral_eq_tsum
+#align measure_theory.is_add_fundamental_domain.integral_eq_tsum MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum
+
+@[to_additive]
+theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf : Integrable f μ) :
+    (∫ x, f x ∂μ) = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ :=
+  calc
+    (∫ x, f x ∂μ) = ∑' g : G, ∫ x in g • s, f x ∂μ := h.integral_eq_tsum f hf
+    _ = ∑' g : G, ∫ x in g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
+    _ = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ :=
+      tsum_congr fun g =>
+        (measurePreservingSmul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
+    
+#align measure_theory.is_fundamental_domain.integral_eq_tsum' MeasureTheory.IsFundamentalDomain.integral_eq_tsum'
+#align measure_theory.is_add_fundamental_domain.integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum'
+
+@[to_additive]
+theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
+    (hf : IntegrableOn f t μ) : (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ :=
+  calc
+    (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in g • s, f x ∂μ.restrict t :=
+      h.integral_eq_tsum_of_ac restrict_le_self.AbsolutelyContinuous f hf
+    _ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := by
+      simp only [h.restrict_restrict, measure_smul, inter_comm]
+    
+#align measure_theory.is_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum
+#align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsAddFundamentalDomain.set_integral_eq_tsum
+
+@[to_additive]
+theorem set_integral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
+    (hf : IntegrableOn f t μ) : (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
+  calc
+    (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := h.set_integral_eq_tsum hf
+    _ = ∑' g : G, ∫ x in t ∩ g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
+    _ = ∑' g : G, ∫ x in g⁻¹ • (g • t ∩ s), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
+    _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
+      tsum_congr fun g =>
+        (measurePreservingSmul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
+    
+#align measure_theory.is_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum'
+#align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.set_integral_eq_tsum'
+
 @[to_additive]
 protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
     {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) : (∫ x in s, f x ∂μ) = ∫ x in t, f x ∂μ :=
   by
   by_cases hfs : integrable_on f s μ
   · have hft : integrable_on f t μ := by rwa [ht.integrable_on_iff hs hf]
-    have hac : ∀ {u}, μ.restrict u ≪ μ := fun u => restrict_le_self.absolutely_continuous
     calc
-      (∫ x in s, f x ∂μ) = ∫ x in ⋃ g : G, g • t, f x ∂μ.restrict s := by
-        rw [restrict_congr_set (hac ht.Union_smul_ae_eq), restrict_univ]
-      _ = ∑' g : G, ∫ x in g • t, f x ∂μ.restrict s :=
-        (integral_Union_ae (fun g => (ht.null_measurable_set_smul g).monoAc hac)
-          (ht.pairwise_ae_disjoint_of_ac hac) hfs.integrable.integrable_on)
-      _ = ∑' g : G, ∫ x in s ∩ g • t, f x ∂μ := by simp only [ht.restrict_restrict, inter_comm]
-      _ = ∑' g : G, ∫ x in s ∩ g⁻¹ • t, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
-      _ = ∑' g : G, ∫ x in g⁻¹ • (g • s ∩ t), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
-      _ = ∑' g : G, ∫ x in g • s ∩ t, f (g⁻¹ • x) ∂μ :=
-        (tsum_congr fun g =>
-          (measure_preserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _)
-            _ _)
-      _ = ∑' g : G, ∫ x in g • s, f x ∂μ.restrict t := by simp only [hf, hs.restrict_restrict]
-      _ = ∫ x in ⋃ g : G, g • s, f x ∂μ.restrict t :=
-        (integral_Union_ae (fun g => (hs.null_measurable_set_smul g).monoAc hac)
-            (hs.ae_disjoint.mono fun i j h => hac h) hft.integrable.integrable_on).symm
-      _ = ∫ x in t, f x ∂μ := by rw [restrict_congr_set (hac hs.Union_smul_ae_eq), restrict_univ]
+      (∫ x in s, f x ∂μ) = ∑' g : G, ∫ x in s ∩ g • t, f x ∂μ := ht.set_integral_eq_tsum hfs
+      _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := by simp only [hf, inter_comm]
+      _ = ∫ x in t, f x ∂μ := (hs.set_integral_eq_tsum' hft).symm
       
   · rw [integral_undef hfs, integral_undef]
     rwa [hs.integrable_on_iff ht hf] at hfs

bump to nightly-2023-03-17-00

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

c85864d4

Diff

@@ -162,7 +162,7 @@ theorem preimageOfEquiv {ν : Measure β} (h : IsFundamentalDomain G s μ) {f :
     AeDisjoint := fun a b hab => by
       lift e to G ≃ H using he
       have : (e.symm a⁻¹)⁻¹ ≠ (e.symm b⁻¹)⁻¹ := by simp [hab]
-      convert (h.ae_disjoint this).Preimage hf using 1
+      convert(h.ae_disjoint this).Preimage hf using 1
       simp only [← preimage_smul_inv, preimage_preimage, ← hef _ _, e.apply_symm_apply, inv_inv] }
 #align measure_theory.is_fundamental_domain.preimage_of_equiv MeasureTheory.IsFundamentalDomain.preimageOfEquiv
 #align measure_theory.is_add_fundamental_domain.preimage_of_equiv MeasureTheory.IsAddFundamentalDomain.preimage_of_equiv
@@ -347,7 +347,7 @@ theorem measure_set_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDoma
     by
     refine' hs.set_lintegral_eq ht (Set.indicator A fun _ => 1) _
     intro g x
-    convert (Set.indicator_comp_right fun x : α => g • x).symm
+    convert(Set.indicator_comp_right fun x : α => g • x).symm
     rw [hA g]
   simpa [measure.restrict_apply hA₀, lintegral_indicator _ hA₀] using this
 #align measure_theory.is_fundamental_domain.measure_set_eq MeasureTheory.IsFundamentalDomain.measure_set_eq

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -94,7 +94,7 @@ theorem mk' (h_meas : NullMeasurableSet s μ) (h_exists : ∀ x : α, ∃! g : G
 #align measure_theory.is_fundamental_domain.mk' MeasureTheory.IsFundamentalDomain.mk'
 #align measure_theory.is_add_fundamental_domain.mk' MeasureTheory.IsAddFundamentalDomain.mk'
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 /-- For `s` to be a fundamental domain, it's enough to check `ae_disjoint (g • s) s` for `g ≠ 1`. -/
 @[to_additive
       "For `s` to be a fundamental domain, it's enough to check `ae_disjoint (g +ᵥ s) s` for\n`g ≠ 0`."]
@@ -107,7 +107,7 @@ theorem mk'' (h_meas : NullMeasurableSet s μ) (h_ae_covers : ∀ᵐ x ∂μ, 
 #align measure_theory.is_fundamental_domain.mk'' MeasureTheory.IsFundamentalDomain.mk''
 #align measure_theory.is_add_fundamental_domain.mk'' MeasureTheory.IsAddFundamentalDomain.mk''
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 /-- If a measurable space has a finite measure `μ` and a countable group `G` acts
 quasi-measure-preservingly, then to show that a set `s` is a fundamental domain, it is sufficient
 to check that its translates `g • s` are (almost) disjoint and that the sum `∑' g, μ (g • s)` is
@@ -423,15 +423,15 @@ protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFund
       (∫ x in s, f x ∂μ) = ∫ x in ⋃ g : G, g • t, f x ∂μ.restrict s := by
         rw [restrict_congr_set (hac ht.Union_smul_ae_eq), restrict_univ]
       _ = ∑' g : G, ∫ x in g • t, f x ∂μ.restrict s :=
-        integral_Union_ae (fun g => (ht.null_measurable_set_smul g).monoAc hac)
-          (ht.pairwise_ae_disjoint_of_ac hac) hfs.integrable.integrable_on
+        (integral_Union_ae (fun g => (ht.null_measurable_set_smul g).monoAc hac)
+          (ht.pairwise_ae_disjoint_of_ac hac) hfs.integrable.integrable_on)
       _ = ∑' g : G, ∫ x in s ∩ g • t, f x ∂μ := by simp only [ht.restrict_restrict, inter_comm]
       _ = ∑' g : G, ∫ x in s ∩ g⁻¹ • t, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
       _ = ∑' g : G, ∫ x in g⁻¹ • (g • s ∩ t), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
       _ = ∑' g : G, ∫ x in g • s ∩ t, f (g⁻¹ • x) ∂μ :=
-        tsum_congr fun g =>
+        (tsum_congr fun g =>
           (measure_preserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _)
-            _ _
+            _ _)
       _ = ∑' g : G, ∫ x in g • s, f x ∂μ.restrict t := by simp only [hf, hs.restrict_restrict]
       _ = ∫ x in ⋃ g : G, g • s, f x ∂μ.restrict t :=
         (integral_Union_ae (fun g => (hs.null_measurable_set_smul g).monoAc hac)
@@ -454,14 +454,14 @@ theorem measure_le_of_pairwise_disjoint (hs : IsFundamentalDomain G s μ)
   calc
     μ t = ∑' g : G, μ (g • t ∩ s) := hs.measure_eq_tsum t
     _ = μ (⋃ g : G, g • t ∩ s) :=
-      Eq.symm <| measure_Union₀ hd fun g => (ht.smul _).inter hs.NullMeasurableSet
+      (Eq.symm <| measure_Union₀ hd fun g => (ht.smul _).inter hs.NullMeasurableSet)
     _ ≤ μ s := measure_mono (unionᵢ_subset fun g => inter_subset_right _ _)
     
 #align measure_theory.is_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsFundamentalDomain.measure_le_of_pairwise_disjoint
 #align measure_theory.is_add_fundamental_domain.measure_le_of_pairwise_disjoint MeasureTheory.IsAddFundamentalDomain.measure_le_of_pairwise_disjoint
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » t) -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (g «expr ≠ » (1 : G)) -/
 /-- If the action of a countable group `G` admits an invariant measure `μ` with a fundamental domain
 `s`, then every null-measurable set `t` of measure strictly greater than `μ s` contains two
 points `x y` such that `g • x = y` for some `g ≠ 1`. -/

bump to nightly-2023-02-27-10

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

49ff026a

Diff

@@ -41,7 +41,7 @@ We also generate additive versions of all theorems in this file using the `to_ad
 -/
 
 
-open Ennreal Pointwise Topology NNReal Ennreal MeasureTheory
+open ENNReal Pointwise Topology NNReal ENNReal MeasureTheory
 
 open MeasureTheory MeasureTheory.Measure Set Function TopologicalSpace Filter
 
@@ -682,7 +682,7 @@ protected theorem fundamentalInterior : IsFundamentalDomain G (fundamentalInteri
           fundamental_frontier_union_fundamental_interior]
       refine' eq_bot_mono (μ.mono <| compl_subset_compl.2 this) _
       simp only [Union_inv_smul, outer_measure.measure_of_eq_coe, coe_to_outer_measure, compl_sdiff,
-        Ennreal.bot_eq_zero, himp_eq, sup_eq_union, @Union_smul_eq_set_of_exists _ _ _ _ s]
+        ENNReal.bot_eq_zero, himp_eq, sup_eq_union, @Union_smul_eq_set_of_exists _ _ _ _ s]
       exact
         measure_union_null
           (measure_Union_null fun _ => measure_smul_null hs.measure_fundamental_frontier _)

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

This file has an open sync PR:
#7506 awaiting-author mathlib3-pair t-measure-probability

mathlib3

mathlib4

chore: adapt to multiple goal linter 1 (#12338)

A PR accompanying #12339.

Zulip discussion

45f93f3f

Diff

@@ -669,8 +669,8 @@ theorem pairwise_disjoint_fundamentalInterior :
   rintro _ ⟨x, hx, rfl⟩ ⟨y, hy, hxy⟩
   rw [mem_fundamentalInterior] at hx hy
   refine' hx.2 (a⁻¹ * b) _ _
-  rwa [Ne, inv_mul_eq_iff_eq_mul, mul_one, eq_comm]
-  simpa [mul_smul, ← hxy, mem_inv_smul_set_iff] using hy.1
+  · rwa [Ne, inv_mul_eq_iff_eq_mul, mul_one, eq_comm]
+  · simpa [mul_smul, ← hxy, mem_inv_smul_set_iff] using hy.1
 #align measure_theory.pairwise_disjoint_fundamental_interior MeasureTheory.pairwise_disjoint_fundamentalInterior
 #align measure_theory.pairwise_disjoint_add_fundamental_interior MeasureTheory.pairwise_disjoint_addFundamentalInterior

chore: tidy various files (#12213)

1c5029c0

Diff

@@ -875,8 +875,7 @@ local notation "π" => @Quotient.mk _ α_mod_G
   `U` of the quotient, `μ U = ν ((π ⁻¹' U) ∩ t)`. -/
 class QuotientMeasureEqMeasurePreimage (ν : Measure α := by volume_tac)
     (μ : Measure (Quotient α_mod_G)) : Prop where
-  projection_respects_measure' : ∀ (t : Set α) (_ : IsFundamentalDomain G t ν),
-    μ = (ν.restrict t).map π
+  projection_respects_measure' (t : Set α) : IsFundamentalDomain G t ν → μ = (ν.restrict t).map π
 
 attribute [to_additive]
   MeasureTheory.QuotientMeasureEqMeasurePreimage
@@ -904,9 +903,7 @@ an artificial way to generate a measure downstairs such that the pair satisfies
 lemma IsFundamentalDomain.quotientMeasureEqMeasurePreimage_quotientMeasure
     {s : Set α} (fund_dom_s : IsFundamentalDomain G s ν) :
     QuotientMeasureEqMeasurePreimage ν ((ν.restrict s).map π) where
-  projection_respects_measure' := by
-    intro t fund_dom_t
-    rw [fund_dom_s.quotientMeasure_eq _ fund_dom_t]
+  projection_respects_measure' t fund_dom_t := by rw [fund_dom_s.quotientMeasure_eq _ fund_dom_t]
 
 /-- One can prove `QuotientMeasureEqMeasurePreimage` by checking behavior with respect to a single
 fundamental domain. -/
@@ -1019,8 +1016,8 @@ sigma-finite measure, then it is itself `SigmaFinite`. -/
 @[to_additive MeasureTheory.instSigmaFiniteAddQuotientOrbitRelInstMeasurableSpaceToMeasurableSpace]
 instance [SigmaFinite (volume : Measure α)] [HasFundamentalDomain G α]
     (μ : Measure (Quotient α_mod_G)) [QuotientMeasureEqMeasurePreimage volume μ] :
-    SigmaFinite μ := by
-  exact QuotientMeasureEqMeasurePreimage.sigmaFiniteQuotient (ν := (volume : Measure α)) (μ := μ)
+    SigmaFinite μ :=
+  QuotientMeasureEqMeasurePreimage.sigmaFiniteQuotient (ν := (volume : Measure α)) (μ := μ)
 
 end QuotientMeasureEqMeasurePreimage

chore: replace set_integral with setIntegral (#12215)

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

f4b4298b

Diff

@@ -445,7 +445,7 @@ theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
     ∫ x, f x ∂μ = ∑' g : G, ∫ x in g • s, f x ∂μ := h.integral_eq_tsum f hf
     _ = ∑' g : G, ∫ x in g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ := tsum_congr fun g =>
-      (measurePreserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
+      (measurePreserving_smul g⁻¹ μ).setIntegral_image_emb (measurableEmbedding_const_smul _) _ _
 #align measure_theory.is_fundamental_domain.integral_eq_tsum' MeasureTheory.IsFundamentalDomain.integral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum'
 
@@ -454,42 +454,54 @@ theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
   (integral_eq_tsum' h f hf).trans ((Equiv.inv G).tsum_eq (fun g ↦ ∫ (x : α) in s, f (g • x) ∂μ))
 
 @[to_additive]
-theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
+theorem setIntegral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
     (hf : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ :=
   calc
     ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in g • s, f x ∂μ.restrict t :=
       h.integral_eq_tsum_of_ac restrict_le_self.absolutelyContinuous f hf
     _ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := by
       simp only [h.restrict_restrict, measure_smul, inter_comm]
-#align measure_theory.is_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum
-#align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsAddFundamentalDomain.set_integral_eq_tsum
+#align measure_theory.is_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsFundamentalDomain.setIntegral_eq_tsum
+#align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum MeasureTheory.IsAddFundamentalDomain.setIntegral_eq_tsum
+
+@[deprecated]
+alias set_integral_eq_tsum :=
+  setIntegral_eq_tsum -- deprecated on 2024-04-17
 
 @[to_additive]
-theorem set_integral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
+theorem setIntegral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
     (hf : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
   calc
-    ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := h.set_integral_eq_tsum hf
+    ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := h.setIntegral_eq_tsum hf
     _ = ∑' g : G, ∫ x in t ∩ g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫ x in g⁻¹ • (g • t ∩ s), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
     _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
       tsum_congr fun g =>
-        (measurePreserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
-#align measure_theory.is_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsFundamentalDomain.set_integral_eq_tsum'
-#align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.set_integral_eq_tsum'
+        (measurePreserving_smul g⁻¹ μ).setIntegral_image_emb (measurableEmbedding_const_smul _) _ _
+#align measure_theory.is_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsFundamentalDomain.setIntegral_eq_tsum'
+#align measure_theory.is_add_fundamental_domain.set_integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.setIntegral_eq_tsum'
+
+@[deprecated]
+alias set_integral_eq_tsum' :=
+  setIntegral_eq_tsum' -- deprecated on 2024-04-17
 
 @[to_additive]
-protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
+protected theorem setIntegral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
     {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) : ∫ x in s, f x ∂μ = ∫ x in t, f x ∂μ := by
   by_cases hfs : IntegrableOn f s μ
   · have hft : IntegrableOn f t μ := by rwa [ht.integrableOn_iff hs hf]
     calc
-      ∫ x in s, f x ∂μ = ∑' g : G, ∫ x in s ∩ g • t, f x ∂μ := ht.set_integral_eq_tsum hfs
+      ∫ x in s, f x ∂μ = ∑' g : G, ∫ x in s ∩ g • t, f x ∂μ := ht.setIntegral_eq_tsum hfs
       _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := by simp only [hf, inter_comm]
-      _ = ∫ x in t, f x ∂μ := (hs.set_integral_eq_tsum' hft).symm
+      _ = ∫ x in t, f x ∂μ := (hs.setIntegral_eq_tsum' hft).symm
   · rw [integral_undef hfs, integral_undef]
     rwa [hs.integrableOn_iff ht hf] at hfs
-#align measure_theory.is_fundamental_domain.set_integral_eq MeasureTheory.IsFundamentalDomain.set_integral_eq
-#align measure_theory.is_add_fundamental_domain.set_integral_eq MeasureTheory.IsAddFundamentalDomain.set_integral_eq
+#align measure_theory.is_fundamental_domain.set_integral_eq MeasureTheory.IsFundamentalDomain.setIntegral_eq
+#align measure_theory.is_add_fundamental_domain.set_integral_eq MeasureTheory.IsAddFundamentalDomain.setIntegral_eq
+
+@[deprecated]
+alias set_integral_eq :=
+  MeasureTheory.IsFundamentalDomain.setIntegral_eq -- deprecated on 2024-04-17
 
 /-- If the action of a countable group `G` admits an invariant measure `μ` with a fundamental domain
 `s`, then every null-measurable set `t` such that the sets `g • t ∩ s` are pairwise a.e.-disjoint

doc: fix many more mathlib3 names in doc comments (#11987)

A mix of various changes; generated with a script and manually tweaked.

2098023c

Diff

@@ -531,7 +531,7 @@ theorem exists_ne_one_smul_eq (hs : IsFundamentalDomain G s μ) (htm : NullMeasu
   measure with a fundamental domain `s`, then the `essSup` of `f` restricted to `s` is the same as
   that of `f` on all of its domain. -/
 @[to_additive "If `f` is invariant under the action of a countable additive group `G`, and `μ` is a
-  `G`-invariant measure with a fundamental domain `s`, then the `ess_sup` of `f` restricted to `s`
+  `G`-invariant measure with a fundamental domain `s`, then the `essSup` of `f` restricted to `s`
   is the same as that of `f` on all of its domain."]
 theorem essSup_measure_restrict (hs : IsFundamentalDomain G s μ) {f : α → ℝ≥0∞}
     (hf : ∀ γ : G, ∀ x : α, f (γ • x) = f x) : essSup f (μ.restrict s) = essSup f μ := by

refactor: typeclasses for measures on quotient spaces and groups (#7506)

We introduce a new typeclass QuotientMeasureEqMeasurePreimage which expresses a relationship between a measure on a space and a measure on its quotient under a discrete group action. Namely, the volume of a measurable set in the quotient is equal to the volume of its preimage, intersected with any fundamental domain.

Our main application is in the context of a discrete normal subgroup of a topological group acting on the group itself, so as to compare Haar measures on a group and its quotient. Before this typeclass, you could have Haar measure upstairs and downstairs and you would have ugly scaling factors if you wanted to compare the two. This typeclass more accurately reflects what is needed in order to have a clear relationship between the upstairs and downstairs measures.

Two big theorems (proved under various technical assumptions, like finiteness of the volume - which shouldn't be necessary):

(1) if you're Haar upstairs and satisfy QuotientMeasureEqMeasurePreimage, then you're Haar downstairs.

And conversely (2): if you're Haar upstairs and downstairs, and scale correctly on a single measurable set, then you satisfy QuotientMeasureEqMeasurePreimage.

Contains the forward-port of https://github.com/leanprover-community/mathlib/pull/18863

Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com>

fea58cd7

Diff

@@ -1,10 +1,11 @@
 /-
 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
+Authors: Yury G. Kudryashov, Alex Kontorovich, Heather Macbeth
 -/
 import Mathlib.MeasureTheory.Group.Action
 import Mathlib.MeasureTheory.Integral.SetIntegral
+import Mathlib.MeasureTheory.Group.Pointwise
 
 #align_import measure_theory.group.fundamental_domain from "leanprover-community/mathlib"@"3b52265189f3fb43aa631edffce5d060fafaf82f"
 
@@ -27,6 +28,14 @@ two fundamental domains are equal to each other.
 
 We also generate additive versions of all theorems in this file using the `to_additive` attribute.
 
+* We define the `HasFundamentalDomain` typeclass, in particular to be able to define the `covolume`
+of a quotient of `α` by a group `G`, which under reasonable conditions does not depend on the choice
+of fundamental domain.
+
+* We define the `QuotientMeasureEqMeasurePreimage` typeclass to describe a situation in which a
+measure `μ` on `α ⧸ G` can be computed by taking a measure `ν` on `α` of the intersection of the
+pullback with a fundamental domain.
+
 ## Main declarations
 
 * `MeasureTheory.IsFundamentalDomain`: Predicate for a set to be a fundamental domain of the
@@ -718,4 +727,289 @@ protected theorem fundamentalInterior : IsFundamentalDomain G (fundamentalInteri
 
 end IsFundamentalDomain
 
+section FundamentalDomainMeasure
+
+variable (G) [Group G] [MulAction G α] [MeasurableSpace α]
+  (μ : Measure α)
+
+local notation "α_mod_G" => MulAction.orbitRel G α
+
+local notation "π" => @Quotient.mk _ α_mod_G
+
+variable {G}
+
+@[to_additive addMeasure_map_restrict_apply]
+lemma measure_map_restrict_apply (s : Set α) {U : Set (Quotient α_mod_G)}
+    (meas_U : MeasurableSet U) :
+    (μ.restrict s).map π U = μ ((π ⁻¹' U) ∩ s) := by
+  rw [map_apply (f := π) (fun V hV ↦ measurableSet_quotient.mp hV) meas_U,
+    Measure.restrict_apply (t := (Quotient.mk α_mod_G ⁻¹' U)) (measurableSet_quotient.mp meas_U)]
+
+@[to_additive]
+lemma IsFundamentalDomain.quotientMeasure_eq [Countable G] [MeasurableSpace G] {s t : Set α}
+    [SMulInvariantMeasure G α μ] [MeasurableSMul G α] (fund_dom_s : IsFundamentalDomain G s μ)
+    (fund_dom_t : IsFundamentalDomain G t μ) :
+    (μ.restrict s).map π = (μ.restrict t).map π := by
+  ext U meas_U
+  rw [measure_map_restrict_apply (meas_U := meas_U), measure_map_restrict_apply (meas_U := meas_U)]
+  apply MeasureTheory.IsFundamentalDomain.measure_set_eq fund_dom_s fund_dom_t
+  · exact measurableSet_quotient.mp meas_U
+  · intro g
+    ext x
+    have : Quotient.mk α_mod_G (g • x) = Quotient.mk α_mod_G x := by
+      apply Quotient.sound
+      use g
+    simp only [mem_preimage, this]
+
+end FundamentalDomainMeasure
+
+/-! ## `HasFundamentalDomain` typeclass
+
+We define `HasFundamentalDomain` in order to be able to define the `covolume` of a quotient of `α`
+by a group `G`, which under reasonable conditions does not depend on the choice of fundamental
+domain. Even though any "sensible" action should have a fundamental domain, this is a rather
+delicate question which was recently addressed by Misha Kapovich: https://arxiv.org/abs/2301.05325
+
+TODO: Formalize the existence of a Dirichlet domain as in Kapovich's paper.
+
+-/
+
+section HasFundamentalDomain
+
+/-- We say a quotient of `α` by `G` `HasAddFundamentalDomain` if there is a measurable set
+  `s` for which `IsAddFundamentalDomain G s` holds. -/
+class HasAddFundamentalDomain (G α : Type*) [Zero G] [VAdd G α] [MeasurableSpace α]
+    (ν : Measure α := by volume_tac) : Prop where
+  ExistsIsAddFundamentalDomain : ∃ s : Set α, IsAddFundamentalDomain G s ν
+
+/-- We say a quotient of `α` by `G` `HasFundamentalDomain` if there is a measurable set `s` for
+  which `IsFundamentalDomain G s` holds. -/
+class HasFundamentalDomain (G : Type*) (α : Type*) [One G] [SMul G α] [MeasurableSpace α]
+    (ν : Measure α := by volume_tac) : Prop where
+  ExistsIsFundamentalDomain : ∃ (s : Set α), IsFundamentalDomain G s ν
+
+attribute [to_additive existing] MeasureTheory.HasFundamentalDomain
+
+open Classical in
+/-- The `covolume` of an action of `G` on `α` the volume of some fundamental domain, or `0` if
+none exists. -/
+@[to_additive addCovolume "The `addCovolume` of an action of `G` on `α` is the volume of some
+fundamental domain, or `0` if none exists."]
+noncomputable def covolume (G α : Type*) [One G] [SMul G α] [MeasurableSpace α]
+    (ν : Measure α := by volume_tac) : ℝ≥0∞ :=
+  if funDom : HasFundamentalDomain G α ν then ν funDom.ExistsIsFundamentalDomain.choose else 0
+
+variable [Group G] [MulAction G α] [MeasurableSpace G] [MeasurableSpace α]
+
+/-- If there is a fundamental domain `s`, then `HasFundamentalDomain` holds. -/
+@[to_additive]
+lemma IsFundamentalDomain.hasFundamentalDomain (ν : Measure α) {s : Set α}
+    (fund_dom_s : IsFundamentalDomain G s ν) :
+    HasFundamentalDomain G α ν := ⟨⟨s, fund_dom_s⟩⟩
+
+/-- The `covolume` can be computed by taking the `volume` of any given fundamental domain `s`. -/
+@[to_additive]
+lemma IsFundamentalDomain.covolume_eq_volume (ν : Measure α) [Countable G]
+    [MeasurableSMul G α] [SMulInvariantMeasure G α ν] {s : Set α}
+    (fund_dom_s : IsFundamentalDomain G s ν) : covolume G α ν = ν s := by
+  dsimp [covolume]
+  simp only [(fund_dom_s.hasFundamentalDomain ν), ↓reduceDite]
+  rw [fund_dom_s.measure_eq]
+  exact (fund_dom_s.hasFundamentalDomain ν).ExistsIsFundamentalDomain.choose_spec
+
+end HasFundamentalDomain
+
+/-! ## `QuotientMeasureEqMeasurePreimage` typeclass
+
+This typeclass describes a situation in which a measure `μ` on `α ⧸ G` can be computed by
+taking a measure `ν` on `α` of the intersection of the pullback with a fundamental domain.
+
+It's curious that in measure theory, measures can be pushed forward, while in geometry, volumes can
+be pulled back. And yet here, we are describing a situation involving measures in a geometric way.
+
+Another viewpoint is that if a set is small enough to fit in a single fundamental domain, then its
+`ν` measure in `α` is the same as the `μ` measure of its pushforward in `α ⧸ G`.
+
+-/
+
+section QuotientMeasureEqMeasurePreimage
+
+section additive
+
+variable [AddGroup G] [AddAction G α] [MeasurableSpace α]
+
+local notation "α_mod_G" => AddAction.orbitRel G α
+
+local notation "π" => @Quotient.mk _ α_mod_G
+
+/-- A measure `μ` on the `AddQuotient` of `α` mod `G` satisfies
+  `AddQuotientMeasureEqMeasurePreimage` if: for any fundamental domain `t`, and any measurable
+  subset `U` of the quotient, `μ U = volume ((π ⁻¹' U) ∩ t)`. -/
+class AddQuotientMeasureEqMeasurePreimage (ν : Measure α := by volume_tac)
+    (μ : Measure (Quotient α_mod_G)) : Prop where
+  addProjection_respects_measure' : ∀ (t : Set α) (_ : IsAddFundamentalDomain G t ν),
+    μ = (ν.restrict t).map π
+
+end additive
+
+variable [Group G] [MulAction G α] [MeasurableSpace α]
+
+local notation "α_mod_G" => MulAction.orbitRel G α
+
+local notation "π" => @Quotient.mk _ α_mod_G
+
+/-- Measures `ν` on `α` and `μ` on the `Quotient` of `α` mod `G` satisfy
+  `QuotientMeasureEqMeasurePreimage` if: for any fundamental domain `t`, and any measurable subset
+  `U` of the quotient, `μ U = ν ((π ⁻¹' U) ∩ t)`. -/
+class QuotientMeasureEqMeasurePreimage (ν : Measure α := by volume_tac)
+    (μ : Measure (Quotient α_mod_G)) : Prop where
+  projection_respects_measure' : ∀ (t : Set α) (_ : IsFundamentalDomain G t ν),
+    μ = (ν.restrict t).map π
+
+attribute [to_additive]
+  MeasureTheory.QuotientMeasureEqMeasurePreimage
+
+@[to_additive addProjection_respects_measure]
+lemma IsFundamentalDomain.projection_respects_measure {ν : Measure α}
+    (μ : Measure (Quotient α_mod_G)) [i : QuotientMeasureEqMeasurePreimage ν μ] {t : Set α}
+    (fund_dom_t : IsFundamentalDomain G t ν) : μ = (ν.restrict t).map π :=
+  i.projection_respects_measure' t fund_dom_t
+
+@[to_additive addProjection_respects_measure_apply]
+lemma IsFundamentalDomain.projection_respects_measure_apply {ν : Measure α}
+    (μ : Measure (Quotient α_mod_G)) [i : QuotientMeasureEqMeasurePreimage ν μ] {t : Set α}
+    (fund_dom_t : IsFundamentalDomain G t ν) {U : Set (Quotient α_mod_G)}
+    (meas_U : MeasurableSet U) : μ U = ν (π ⁻¹' U ∩ t) := by
+  rw [fund_dom_t.projection_respects_measure (μ := μ), measure_map_restrict_apply ν t meas_U]
+
+variable {ν : Measure α} [Countable G] [MeasurableSpace G]
+  [SMulInvariantMeasure G α ν] [MeasurableSMul G α]
+
+/-- Given a measure upstairs (i.e., on `α`), and a choice `s` of fundamental domain, there's always
+an artificial way to generate a measure downstairs such that the pair satisfies the
+`QuotientMeasureEqMeasurePreimage` typeclass. -/
+@[to_additive]
+lemma IsFundamentalDomain.quotientMeasureEqMeasurePreimage_quotientMeasure
+    {s : Set α} (fund_dom_s : IsFundamentalDomain G s ν) :
+    QuotientMeasureEqMeasurePreimage ν ((ν.restrict s).map π) where
+  projection_respects_measure' := by
+    intro t fund_dom_t
+    rw [fund_dom_s.quotientMeasure_eq _ fund_dom_t]
+
+/-- One can prove `QuotientMeasureEqMeasurePreimage` by checking behavior with respect to a single
+fundamental domain. -/
+@[to_additive]
+lemma IsFundamentalDomain.quotientMeasureEqMeasurePreimage {μ : Measure (Quotient α_mod_G)}
+    {s : Set α} (fund_dom_s : IsFundamentalDomain G s ν) (h : μ = (ν.restrict s).map π) :
+    QuotientMeasureEqMeasurePreimage ν μ := by
+  simpa [h] using fund_dom_s.quotientMeasureEqMeasurePreimage_quotientMeasure
+
+/-- Any two measures satisfying `QuotientMeasureEqMeasurePreimage` are equal. -/
+@[to_additive]
+lemma QuotientMeasureEqMeasurePreimage.unique
+    [hasFun : HasFundamentalDomain G α ν] (μ μ' : Measure (Quotient α_mod_G))
+    [QuotientMeasureEqMeasurePreimage ν μ] [QuotientMeasureEqMeasurePreimage ν μ'] :
+    μ = μ' := by
+  obtain ⟨𝓕, h𝓕⟩ := hasFun.ExistsIsFundamentalDomain
+  rw [h𝓕.projection_respects_measure (μ := μ), h𝓕.projection_respects_measure (μ := μ')]
+
+/-- The quotient map to `α ⧸ G` is measure-preserving between the restriction of `volume` to a
+  fundamental domain in `α` and a related measure satisfying `QuotientMeasureEqMeasurePreimage`. -/
+@[to_additive IsAddFundamentalDomain.measurePreserving_add_quotient_mk]
+theorem IsFundamentalDomain.measurePreserving_quotient_mk
+    {𝓕 : Set α} (h𝓕 : IsFundamentalDomain G 𝓕 ν)
+    (μ : Measure (Quotient α_mod_G)) [QuotientMeasureEqMeasurePreimage ν μ] :
+    MeasurePreserving π (ν.restrict 𝓕) μ where
+  measurable := measurable_quotient_mk' (s := α_mod_G)
+  map_eq := by
+    haveI : HasFundamentalDomain G α ν := ⟨𝓕, h𝓕⟩
+    rw [h𝓕.projection_respects_measure (μ := μ)]
+
+/-- If a fundamental domain has volume 0, then `QuotientMeasureEqMeasurePreimage` holds. -/
+@[to_additive]
+theorem IsFundamentalDomain.quotientMeasureEqMeasurePreimage_of_zero
+    {s : Set α} (fund_dom_s : IsFundamentalDomain G s ν)
+    (vol_s : ν s = 0) :
+    QuotientMeasureEqMeasurePreimage ν (0 : Measure (Quotient α_mod_G)) := by
+  apply fund_dom_s.quotientMeasureEqMeasurePreimage
+  ext U meas_U
+  simp only [zero_toOuterMeasure, OuterMeasure.coe_zero, Pi.zero_apply]
+  convert (measure_inter_null_of_null_right (h := vol_s) (Quotient.mk α_mod_G ⁻¹' U)).symm
+  rw [measure_map_restrict_apply (meas_U := meas_U)]
+
+/-- If a measure `μ` on a quotient satisfies `QuotientMeasureEqMeasurePreimage` with respect to a
+sigma-finite measure `ν`, then it is itself `SigmaFinite`. -/
+@[to_additive]
+lemma QuotientMeasureEqMeasurePreimage.sigmaFiniteQuotient
+    [i : SigmaFinite ν] [i' : HasFundamentalDomain G α ν]
+    (μ : Measure (Quotient α_mod_G)) [QuotientMeasureEqMeasurePreimage ν μ] :
+    SigmaFinite μ := by
+  rw [sigmaFinite_iff]
+  obtain ⟨A, hA_meas, hA, hA'⟩ := Measure.toFiniteSpanningSetsIn (h := i)
+  simp only [mem_setOf_eq] at hA_meas
+  refine ⟨⟨fun n ↦ π '' (A n), by simp, fun n ↦ ?_, ?_⟩⟩
+  · obtain ⟨s, fund_dom_s⟩ := i'
+    have : π ⁻¹' (π '' (A n)) = _ := MulAction.quotient_preimage_image_eq_union_mul (A n) (G := G)
+    have measπAn : MeasurableSet (π '' A n) := by
+      let _ : Setoid α := α_mod_G
+      rw [measurableSet_quotient, Quotient.mk''_eq_mk, this]
+      apply MeasurableSet.iUnion
+      exact fun g ↦ MeasurableSet.const_smul (hA_meas n) g
+    rw [fund_dom_s.projection_respects_measure_apply (μ := μ) measπAn, this, iUnion_inter]
+    refine lt_of_le_of_lt ?_ (hA n)
+    rw [fund_dom_s.measure_eq_tsum (A n)]
+    exact measure_iUnion_le _
+  · rw [← image_iUnion, hA']
+    refine image_univ_of_surjective (by convert surjective_quotient_mk' α)
+
+/-- A measure `μ` on `α ⧸ G` satisfying `QuotientMeasureEqMeasurePreimage` and having finite
+covolume is a finite measure. -/
+@[to_additive]
+theorem QuotientMeasureEqMeasurePreimage.isFiniteMeasure_quotient
+    (μ : Measure (Quotient α_mod_G)) [QuotientMeasureEqMeasurePreimage ν μ]
+    [hasFun : HasFundamentalDomain G α ν] (h : covolume G α ν ≠ ∞) :
+    IsFiniteMeasure μ := by
+  obtain ⟨𝓕, h𝓕⟩ := hasFun.ExistsIsFundamentalDomain
+  rw [h𝓕.projection_respects_measure (μ := μ)]
+  have : Fact (ν 𝓕 < ∞) := by
+    apply Fact.mk
+    convert Ne.lt_top h
+    exact (h𝓕.covolume_eq_volume ν).symm
+  infer_instance
+
+/-- A finite measure `μ` on `α ⧸ G` satisfying `QuotientMeasureEqMeasurePreimage` has finite
+covolume. -/
+@[to_additive]
+theorem QuotientMeasureEqMeasurePreimage.covolume_ne_top
+    (μ : Measure (Quotient α_mod_G)) [QuotientMeasureEqMeasurePreimage ν μ] [IsFiniteMeasure μ] :
+    covolume G α ν < ∞ := by
+  by_cases hasFun : HasFundamentalDomain G α ν
+  · obtain ⟨𝓕, h𝓕⟩ := hasFun.ExistsIsFundamentalDomain
+    have H : μ univ < ∞ := IsFiniteMeasure.measure_univ_lt_top
+    rw [h𝓕.projection_respects_measure_apply (μ := μ) MeasurableSet.univ] at H
+    simpa [h𝓕.covolume_eq_volume ν] using H
+  · simp [covolume, hasFun]
+
+end QuotientMeasureEqMeasurePreimage
+
+section QuotientMeasureEqMeasurePreimage
+
+
+variable [Group G] [MulAction G α] [MeasureSpace α] [Countable G] [MeasurableSpace G]
+  [SMulInvariantMeasure G α volume] [MeasurableSMul G α]
+
+local notation "α_mod_G" => MulAction.orbitRel G α
+
+local notation "π" => @Quotient.mk _ α_mod_G
+
+/-- If a measure `μ` on a quotient satisfies `QuotientVolumeEqVolumePreimage` with respect to a
+sigma-finite measure, then it is itself `SigmaFinite`. -/
+@[to_additive MeasureTheory.instSigmaFiniteAddQuotientOrbitRelInstMeasurableSpaceToMeasurableSpace]
+instance [SigmaFinite (volume : Measure α)] [HasFundamentalDomain G α]
+    (μ : Measure (Quotient α_mod_G)) [QuotientMeasureEqMeasurePreimage volume μ] :
+    SigmaFinite μ := by
+  exact QuotientMeasureEqMeasurePreimage.sigmaFiniteQuotient (ν := (volume : Measure α)) (μ := μ)
+
+end QuotientMeasureEqMeasurePreimage
+
 end MeasureTheory

chore: avoid Ne.def (adaptation for nightly-2024-03-27) (#11813)

08686b25

Diff

@@ -648,7 +648,7 @@ theorem pairwise_disjoint_fundamentalInterior :
   rintro _ ⟨x, hx, rfl⟩ ⟨y, hy, hxy⟩
   rw [mem_fundamentalInterior] at hx hy
   refine' hx.2 (a⁻¹ * b) _ _
-  rwa [Ne.def, inv_mul_eq_iff_eq_mul, mul_one, eq_comm]
+  rwa [Ne, inv_mul_eq_iff_eq_mul, mul_one, eq_comm]
   simpa [mul_smul, ← hxy, mem_inv_smul_set_iff] using hy.1
 #align measure_theory.pairwise_disjoint_fundamental_interior MeasureTheory.pairwise_disjoint_fundamentalInterior
 #align measure_theory.pairwise_disjoint_add_fundamental_interior MeasureTheory.pairwise_disjoint_addFundamentalInterior

style: homogenise porting notes (#11145)

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

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

8be0b69c

Diff

@@ -613,7 +613,7 @@ theorem fundamentalFrontier_union_fundamentalInterior :
     fundamentalFrontier G s ∪ fundamentalInterior G s = s :=
   inter_union_diff _ _
 #align measure_theory.fundamental_frontier_union_fundamental_interior MeasureTheory.fundamentalFrontier_union_fundamentalInterior
--- porting note: there is a typo in `to_additive` in mathlib3, so there is no additive version
+-- Porting note: there is a typo in `to_additive` in mathlib3, so there is no additive version
 
 @[to_additive (attr := simp) MeasureTheory.sdiff_addFundamentalInterior]
 theorem sdiff_fundamentalInterior : s \ fundamentalInterior G s = fundamentalFrontier G s :=

feat(MeasureTheory): generalize some theorem to Sort* (#9769)

Generalize some theorems from {β : Type*} [Countable β] (f : β → α) to {ι : Sort*} [Countable ι] (f : ι → α). This way they automatically work for f : (p : Prop) → α.

Generalize MeasureTheory.OuterMeasure.iUnion_null, MeasureTheory.OuterMeasure.iUnion_null_iff, MeasureTheory.measure_iUnion_null, and MeasureTheory.measure_iUnion_null_iff.
Deprecate MeasureTheory.OuterMeasure.iUnion_null_iff' and MeasureTheory.measure_iUnion_null_iff'.
Generalize MeasureTheory.exists_measurable_superset_forall_eq and MeasureTheory.exists_measure_pos_of_not_measure_iUnion_null.
Reorder implicit arguments in some theorems (move ι around).

25e096f2

Diff

@@ -681,9 +681,8 @@ variable [Countable G] [Group G] [MulAction G α] [MeasurableSpace α] {μ : Mea
 
 @[to_additive MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalFrontier]
 theorem measure_fundamentalFrontier : μ (fundamentalFrontier G s) = 0 := by
-  simpa only [fundamentalFrontier, iUnion₂_inter, measure_iUnion_null_iff', one_smul,
-    measure_iUnion_null_iff, inter_comm s, Function.onFun] using fun g (hg : g ≠ 1) =>
-    hs.aedisjoint hg
+  simpa only [fundamentalFrontier, iUnion₂_inter, one_smul, measure_iUnion_null_iff, inter_comm s,
+    Function.onFun] using fun g (hg : g ≠ 1) => hs.aedisjoint hg
 #align measure_theory.is_fundamental_domain.measure_fundamental_frontier MeasureTheory.IsFundamentalDomain.measure_fundamentalFrontier
 #align measure_theory.is_add_fundamental_domain.measure_add_fundamental_frontier MeasureTheory.IsAddFundamentalDomain.measure_addFundamentalFrontier

chore(*): use ∃ x ∈ s, _ instead of ∃ (x) (_ : x ∈ s), _ (#9215)

Follow-up #9184

ef974f86

Diff

@@ -110,7 +110,7 @@ sufficiently large. -/
   to check that its translates `g +ᵥ s` are (almost) disjoint and that the sum `∑' g, μ (g +ᵥ s)` is
   sufficiently large."]
 theorem mk_of_measure_univ_le [IsFiniteMeasure μ] [Countable G] (h_meas : NullMeasurableSet s μ)
-    (h_ae_disjoint : ∀ (g) (_ : g ≠ (1 : G)), AEDisjoint μ (g • s) s)
+    (h_ae_disjoint : ∀ g ≠ (1 : G), AEDisjoint μ (g • s) s)
     (h_qmp : ∀ g : G, QuasiMeasurePreserving (g • · : α → α) μ μ)
     (h_measure_univ_le : μ (univ : Set α) ≤ ∑' g : G, μ (g • s)) : IsFundamentalDomain G s μ :=
   have aedisjoint : Pairwise (AEDisjoint μ on fun g : G => g • s) :=

chore: Replace (· op ·) a by (a op ·) (#8843)

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

d14658b4

Diff

@@ -111,7 +111,7 @@ sufficiently large. -/
   sufficiently large."]
 theorem mk_of_measure_univ_le [IsFiniteMeasure μ] [Countable G] (h_meas : NullMeasurableSet s μ)
     (h_ae_disjoint : ∀ (g) (_ : g ≠ (1 : G)), AEDisjoint μ (g • s) s)
-    (h_qmp : ∀ g : G, QuasiMeasurePreserving ((· • ·) g : α → α) μ μ)
+    (h_qmp : ∀ g : G, QuasiMeasurePreserving (g • · : α → α) μ μ)
     (h_measure_univ_le : μ (univ : Set α) ≤ ∑' g : G, μ (g • s)) : IsFundamentalDomain G s μ :=
   have aedisjoint : Pairwise (AEDisjoint μ on fun g : G => g • s) :=
     pairwise_aedisjoint_of_aedisjoint_forall_ne_one h_ae_disjoint h_qmp
@@ -384,7 +384,7 @@ protected theorem aEStronglyMeasurable_on_iff {β : Type*} [TopologicalSpace β]
     _ ↔ ∀ g : G, AEStronglyMeasurable f (μ.restrict (g⁻¹ • (g • s ∩ t))) := by simp only [inv_inv]
     _ ↔ ∀ g : G, AEStronglyMeasurable f (μ.restrict (g • s ∩ t)) := by
       refine' forall_congr' fun g => _
-      have he : MeasurableEmbedding ((· • ·) g⁻¹ : α → α) := measurableEmbedding_const_smul _
+      have he : MeasurableEmbedding (g⁻¹ • · : α → α) := measurableEmbedding_const_smul _
       rw [← image_smul, ← ((measurePreserving_smul g⁻¹ μ).restrict_image_emb he
         _).aestronglyMeasurable_comp_iff he]
       simp only [(· ∘ ·), hf]

feat: Prove that a fundamental domain has nonzero volume (#8287)

b9c3765b

Diff

@@ -136,6 +136,16 @@ theorem iUnion_smul_ae_eq (h : IsFundamentalDomain G s μ) : ⋃ g : G, g • s
 #align measure_theory.is_fundamental_domain.Union_smul_ae_eq MeasureTheory.IsFundamentalDomain.iUnion_smul_ae_eq
 #align measure_theory.is_add_fundamental_domain.Union_vadd_ae_eq MeasureTheory.IsAddFundamentalDomain.iUnion_vadd_ae_eq
 
+@[to_additive]
+theorem measure_ne_zero [MeasurableSpace G] [Countable G] [MeasurableSMul G α]
+    [SMulInvariantMeasure G α μ] (hμ : μ ≠ 0) (h : IsFundamentalDomain G s μ) :
+    μ s ≠ 0 := by
+  have hc := measure_univ_pos.mpr hμ
+  contrapose! hc
+  rw [← measure_congr h.iUnion_smul_ae_eq]
+  refine le_trans (measure_iUnion_le _) ?_
+  simp_rw [measure_smul, hc, tsum_zero, le_refl]
+
 @[to_additive]
 theorem mono (h : IsFundamentalDomain G s μ) {ν : Measure α} (hle : ν ≪ μ) :
     IsFundamentalDomain G s ν :=

chore: clean up names with iUnion instead of Union (#7550)

c151d070

Diff

@@ -620,14 +620,14 @@ theorem sdiff_fundamentalFrontier : s \ fundamentalFrontier G s = fundamentalInt
 @[to_additive (attr := simp) MeasureTheory.addFundamentalFrontier_vadd]
 theorem fundamentalFrontier_smul [Group H] [MulAction H α] [SMulCommClass H G α] (g : H) :
     fundamentalFrontier G (g • s) = g • fundamentalFrontier G s := by
-  simp_rw [fundamentalFrontier, smul_set_inter, smul_set_Union, smul_comm g (_ : G) (_ : Set α)]
+  simp_rw [fundamentalFrontier, smul_set_inter, smul_set_iUnion, smul_comm g (_ : G) (_ : Set α)]
 #align measure_theory.fundamental_frontier_smul MeasureTheory.fundamentalFrontier_smul
 #align measure_theory.add_fundamental_frontier_vadd MeasureTheory.addFundamentalFrontier_vadd
 
 @[to_additive (attr := simp) MeasureTheory.addFundamentalInterior_vadd]
 theorem fundamentalInterior_smul [Group H] [MulAction H α] [SMulCommClass H G α] (g : H) :
     fundamentalInterior G (g • s) = g • fundamentalInterior G s := by
-  simp_rw [fundamentalInterior, smul_set_sdiff, smul_set_Union, smul_comm g (_ : G) (_ : Set α)]
+  simp_rw [fundamentalInterior, smul_set_sdiff, smul_set_iUnion, smul_comm g (_ : G) (_ : Set α)]
 #align measure_theory.fundamental_interior_smul MeasureTheory.fundamentalInterior_smul
 #align measure_theory.add_fundamental_interior_vadd MeasureTheory.addFundamentalInterior_vadd

feat: the Unfolding Trick (#6223)

This PR is a forward port of mathlib3 PR 3#18863

Co-authored-by: Heather Macbeth <25316162+hrmacbeth@users.noreply.github.com>

Co-authored-by: Matthew Ballard <matt@mrb.email>

95aba723

Diff

@@ -6,7 +6,7 @@ Authors: Yury G. Kudryashov
 import Mathlib.MeasureTheory.Group.Action
 import Mathlib.MeasureTheory.Integral.SetIntegral
 
-#align_import measure_theory.group.fundamental_domain from "leanprover-community/mathlib"@"eb810cf549db839dadf13353dbe69bac55acdbbc"
+#align_import measure_theory.group.fundamental_domain from "leanprover-community/mathlib"@"3b52265189f3fb43aa631edffce5d060fafaf82f"
 
 /-!
 # Fundamental domain of a group action
@@ -253,6 +253,10 @@ theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0
 #align measure_theory.is_fundamental_domain.lintegral_eq_tsum' MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum'
 
+@[to_additive] lemma lintegral_eq_tsum'' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) :
+    ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in s, f (g • x) ∂μ :=
+  (lintegral_eq_tsum' h f).trans ((Equiv.inv G).tsum_eq (fun g ↦ ∫⁻ (x : α) in s, f (g • x) ∂μ))
+
 @[to_additive]
 theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
     ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ :=
@@ -426,6 +430,10 @@ theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
 #align measure_theory.is_fundamental_domain.integral_eq_tsum' MeasureTheory.IsFundamentalDomain.integral_eq_tsum'
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum' MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum'
 
+@[to_additive] lemma integral_eq_tsum'' (h : IsFundamentalDomain G s μ)
+    (f : α → E) (hf : Integrable f μ) : ∫ x, f x ∂μ = ∑' g : G, ∫ x in s, f (g • x) ∂μ :=
+  (integral_eq_tsum' h f hf).trans ((Equiv.inv G).tsum_eq (fun g ↦ ∫ (x : α) in s, f (g • x) ∂μ))
+
 @[to_additive]
 theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
     (hf : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ :=

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -47,7 +47,7 @@ namespace MeasureTheory
 /-- A measurable set `s` is a *fundamental domain* for an additive action of an additive group `G`
 on a measurable space `α` with respect to a measure `α` if the sets `g +ᵥ s`, `g : G`, are pairwise
 a.e. disjoint and cover the whole space. -/
-structure IsAddFundamentalDomain (G : Type _) {α : Type _} [Zero G] [VAdd G α] [MeasurableSpace α]
+structure IsAddFundamentalDomain (G : Type*) {α : Type*} [Zero G] [VAdd G α] [MeasurableSpace α]
     (s : Set α) (μ : Measure α := by volume_tac) : Prop where
   protected nullMeasurableSet : NullMeasurableSet s μ
   protected ae_covers : ∀ᵐ x ∂μ, ∃ g : G, g +ᵥ x ∈ s
@@ -58,14 +58,14 @@ structure IsAddFundamentalDomain (G : Type _) {α : Type _} [Zero G] [VAdd G α]
 space `α` with respect to a measure `α` if the sets `g • s`, `g : G`, are pairwise a.e. disjoint and
 cover the whole space. -/
 @[to_additive IsAddFundamentalDomain]
-structure IsFundamentalDomain (G : Type _) {α : Type _} [One G] [SMul G α] [MeasurableSpace α]
+structure IsFundamentalDomain (G : Type*) {α : Type*} [One G] [SMul G α] [MeasurableSpace α]
     (s : Set α) (μ : Measure α := by volume_tac) : Prop where
   protected nullMeasurableSet : NullMeasurableSet s μ
   protected ae_covers : ∀ᵐ x ∂μ, ∃ g : G, g • x ∈ s
   protected aedisjoint : Pairwise <| (AEDisjoint μ on fun g : G => g • s)
 #align measure_theory.is_fundamental_domain MeasureTheory.IsFundamentalDomain
 
-variable {G H α β E : Type _}
+variable {G H α β E : Type*}
 
 namespace IsFundamentalDomain
 
@@ -178,7 +178,7 @@ theorem pairwise_aedisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : 
 #align measure_theory.is_add_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsAddFundamentalDomain.pairwise_aedisjoint_of_ac
 
 @[to_additive]
-theorem smul_of_comm {G' : Type _} [Group G'] [MulAction G' α] [MeasurableSpace G']
+theorem smul_of_comm {G' : Type*} [Group G'] [MulAction G' α] [MeasurableSpace G']
     [MeasurableSMul G' α] [SMulInvariantMeasure G' α μ] [SMulCommClass G' G α]
     (h : IsFundamentalDomain G s μ) (g : G') : IsFundamentalDomain G (g • s) μ :=
   h.image_of_equiv (MulAction.toPerm g) (measurePreserving_smul _ _).quasiMeasurePreserving
@@ -354,7 +354,7 @@ protected theorem measure_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundament
 #align measure_theory.is_add_fundamental_domain.measure_eq MeasureTheory.IsAddFundamentalDomain.measure_eq
 
 @[to_additive]
-protected theorem aEStronglyMeasurable_on_iff {β : Type _} [TopologicalSpace β]
+protected theorem aEStronglyMeasurable_on_iff {β : Type*} [TopologicalSpace β]
     [PseudoMetrizableSpace β] (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
     {f : α → β} (hf : ∀ (g : G) (x), f (g • x) = f x) :
     AEStronglyMeasurable f (μ.restrict s) ↔ AEStronglyMeasurable f (μ.restrict t) :=

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,15 +2,12 @@
 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.fundamental_domain
-! leanprover-community/mathlib commit eb810cf549db839dadf13353dbe69bac55acdbbc
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Group.Action
 import Mathlib.MeasureTheory.Integral.SetIntegral
 
+#align_import measure_theory.group.fundamental_domain from "leanprover-community/mathlib"@"eb810cf549db839dadf13353dbe69bac55acdbbc"
+
 /-!
 # Fundamental domain of a group action

fix: precedences of ⨆⋃⋂⨅ (#5614)

e3c8f983

Diff

@@ -133,7 +133,7 @@ theorem mk_of_measure_univ_le [IsFiniteMeasure μ] [Countable G] (h_meas : NullM
 #align measure_theory.is_add_fundamental_domain.mk_of_measure_univ_le MeasureTheory.IsAddFundamentalDomain.mk_of_measure_univ_le
 
 @[to_additive]
-theorem iUnion_smul_ae_eq (h : IsFundamentalDomain G s μ) : (⋃ g : G, g • s) =ᵐ[μ] univ :=
+theorem iUnion_smul_ae_eq (h : IsFundamentalDomain G s μ) : ⋃ g : G, g • s =ᵐ[μ] univ :=
   eventuallyEq_univ.2 <| h.ae_covers.mono fun _ ⟨g, hg⟩ =>
     mem_iUnion.2 ⟨g⁻¹, _, hg, inv_smul_smul _ _⟩
 #align measure_theory.is_fundamental_domain.Union_smul_ae_eq MeasureTheory.IsFundamentalDomain.iUnion_smul_ae_eq

chore: remove superfluous parentheses around integrals (#5591)

5d442693

Diff

@@ -227,7 +227,7 @@ theorem sum_restrict_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
 
 @[to_additive]
 theorem lintegral_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) (f : α → ℝ≥0∞) :
-    (∫⁻ x, f x ∂ν) = ∑' g : G, ∫⁻ x in g • s, f x ∂ν := by
+    ∫⁻ x, f x ∂ν = ∑' g : G, ∫⁻ x in g • s, f x ∂ν := by
   rw [← lintegral_sum_measure, h.sum_restrict_of_ac hν]
 #align measure_theory.is_fundamental_domain.lintegral_eq_tsum_of_ac MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum_of_ac
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum_of_ac MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum_of_ac
@@ -240,16 +240,16 @@ theorem sum_restrict (h : IsFundamentalDomain G s μ) : (sum fun g : G => μ.res
 
 @[to_additive]
 theorem lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) :
-    (∫⁻ x, f x ∂μ) = ∑' g : G, ∫⁻ x in g • s, f x ∂μ :=
+    ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in g • s, f x ∂μ :=
   h.lintegral_eq_tsum_of_ac (refl _) f
 #align measure_theory.is_fundamental_domain.lintegral_eq_tsum MeasureTheory.IsFundamentalDomain.lintegral_eq_tsum
 #align measure_theory.is_add_fundamental_domain.lintegral_eq_tsum MeasureTheory.IsAddFundamentalDomain.lintegral_eq_tsum
 
 @[to_additive]
 theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) :
-    (∫⁻ x, f x ∂μ) = ∑' g : G, ∫⁻ x in s, f (g⁻¹ • x) ∂μ :=
+    ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in s, f (g⁻¹ • x) ∂μ :=
   calc
-    (∫⁻ x, f x ∂μ) = ∑' g : G, ∫⁻ x in g • s, f x ∂μ := h.lintegral_eq_tsum f
+    ∫⁻ x, f x ∂μ = ∑' g : G, ∫⁻ x in g • s, f x ∂μ := h.lintegral_eq_tsum f
     _ = ∑' g : G, ∫⁻ x in g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫⁻ x in s, f (g⁻¹ • x) ∂μ := tsum_congr fun g => Eq.symm <|
       (measurePreserving_smul g⁻¹ μ).set_lintegral_comp_emb (measurableEmbedding_const_smul _) _ _
@@ -258,9 +258,9 @@ theorem lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0
 
 @[to_additive]
 theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
-    (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ :=
+    ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ :=
   calc
-    (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in g • s, f x ∂μ.restrict t :=
+    ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in g • s, f x ∂μ.restrict t :=
       h.lintegral_eq_tsum_of_ac restrict_le_self.absolutelyContinuous _
     _ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ := by simp only [h.restrict_restrict, inter_comm]
 #align measure_theory.is_fundamental_domain.set_lintegral_eq_tsum MeasureTheory.IsFundamentalDomain.set_lintegral_eq_tsum
@@ -268,9 +268,9 @@ theorem set_lintegral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → ℝ
 
 @[to_additive]
 theorem set_lintegral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → ℝ≥0∞) (t : Set α) :
-    (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
+    ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
   calc
-    (∫⁻ x in t, f x ∂μ) = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ := h.set_lintegral_eq_tsum f t
+    ∫⁻ x in t, f x ∂μ = ∑' g : G, ∫⁻ x in t ∩ g • s, f x ∂μ := h.set_lintegral_eq_tsum f t
     _ = ∑' g : G, ∫⁻ x in t ∩ g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫⁻ x in g⁻¹ • (g • t ∩ s), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
     _ = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := tsum_congr fun g => Eq.symm <|
@@ -328,9 +328,9 @@ theorem measure_eq_card_smul_of_smul_ae_eq_self [Finite G] (h : IsFundamentalDom
 @[to_additive]
 protected theorem set_lintegral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
     (f : α → ℝ≥0∞) (hf : ∀ (g : G) (x), f (g • x) = f x) :
-    (∫⁻ x in s, f x ∂μ) = ∫⁻ x in t, f x ∂μ :=
+    ∫⁻ x in s, f x ∂μ = ∫⁻ x in t, f x ∂μ :=
   calc
-    (∫⁻ x in s, f x ∂μ) = ∑' g : G, ∫⁻ x in s ∩ g • t, f x ∂μ := ht.set_lintegral_eq_tsum _ _
+    ∫⁻ x in s, f x ∂μ = ∑' g : G, ∫⁻ x in s ∩ g • t, f x ∂μ := ht.set_lintegral_eq_tsum _ _
     _ = ∑' g : G, ∫⁻ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := by simp only [hf, inter_comm]
     _ = ∫⁻ x in t, f x ∂μ := (hs.set_lintegral_eq_tsum' _ _).symm
 #align measure_theory.is_fundamental_domain.set_lintegral_eq MeasureTheory.IsFundamentalDomain.set_lintegral_eq
@@ -339,7 +339,7 @@ protected theorem set_lintegral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFun
 @[to_additive]
 theorem measure_set_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ) {A : Set α}
     (hA₀ : MeasurableSet A) (hA : ∀ g : G, (fun x => g • x) ⁻¹' A = A) : μ (A ∩ s) = μ (A ∩ t) := by
-  have : (∫⁻ x in s, A.indicator 1 x ∂μ) = ∫⁻ x in t, A.indicator 1 x ∂μ := by
+  have : ∫⁻ x in s, A.indicator 1 x ∂μ = ∫⁻ x in t, A.indicator 1 x ∂μ := by
     refine hs.set_lintegral_eq ht (Set.indicator A fun _ => 1) fun g x ↦ ?_
     convert (Set.indicator_comp_right (g • · : α → α) (g := fun _ ↦ (1 : ℝ≥0∞))).symm
     rw [hA g]
@@ -404,7 +404,7 @@ variable [NormedSpace ℝ E] [CompleteSpace E]
 
 @[to_additive]
 theorem integral_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) (f : α → E)
-    (hf : Integrable f ν) : (∫ x, f x ∂ν) = ∑' g : G, ∫ x in g • s, f x ∂ν := by
+    (hf : Integrable f ν) : ∫ x, f x ∂ν = ∑' g : G, ∫ x in g • s, f x ∂ν := by
   rw [← MeasureTheory.integral_sum_measure, h.sum_restrict_of_ac hν]
   rw [h.sum_restrict_of_ac hν]
   exact hf
@@ -413,16 +413,16 @@ theorem integral_eq_tsum_of_ac (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ
 
 @[to_additive]
 theorem integral_eq_tsum (h : IsFundamentalDomain G s μ) (f : α → E) (hf : Integrable f μ) :
-    (∫ x, f x ∂μ) = ∑' g : G, ∫ x in g • s, f x ∂μ :=
+    ∫ x, f x ∂μ = ∑' g : G, ∫ x in g • s, f x ∂μ :=
   integral_eq_tsum_of_ac h (by rfl) f hf
 #align measure_theory.is_fundamental_domain.integral_eq_tsum MeasureTheory.IsFundamentalDomain.integral_eq_tsum
 #align measure_theory.is_add_fundamental_domain.integral_eq_tsum MeasureTheory.IsAddFundamentalDomain.integral_eq_tsum
 
 @[to_additive]
 theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf : Integrable f μ) :
-    (∫ x, f x ∂μ) = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ :=
+    ∫ x, f x ∂μ = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ :=
   calc
-    (∫ x, f x ∂μ) = ∑' g : G, ∫ x in g • s, f x ∂μ := h.integral_eq_tsum f hf
+    ∫ x, f x ∂μ = ∑' g : G, ∫ x in g • s, f x ∂μ := h.integral_eq_tsum f hf
     _ = ∑' g : G, ∫ x in g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫ x in s, f (g⁻¹ • x) ∂μ := tsum_congr fun g =>
       (measurePreserving_smul g⁻¹ μ).set_integral_image_emb (measurableEmbedding_const_smul _) _ _
@@ -431,9 +431,9 @@ theorem integral_eq_tsum' (h : IsFundamentalDomain G s μ) (f : α → E) (hf :
 
 @[to_additive]
 theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
-    (hf : IntegrableOn f t μ) : (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ :=
+    (hf : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ :=
   calc
-    (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in g • s, f x ∂μ.restrict t :=
+    ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in g • s, f x ∂μ.restrict t :=
       h.integral_eq_tsum_of_ac restrict_le_self.absolutelyContinuous f hf
     _ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := by
       simp only [h.restrict_restrict, measure_smul, inter_comm]
@@ -442,9 +442,9 @@ theorem set_integral_eq_tsum (h : IsFundamentalDomain G s μ) {f : α → E} {t
 
 @[to_additive]
 theorem set_integral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t : Set α}
-    (hf : IntegrableOn f t μ) : (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
+    (hf : IntegrableOn f t μ) : ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
   calc
-    (∫ x in t, f x ∂μ) = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := h.set_integral_eq_tsum hf
+    ∫ x in t, f x ∂μ = ∑' g : G, ∫ x in t ∩ g • s, f x ∂μ := h.set_integral_eq_tsum hf
     _ = ∑' g : G, ∫ x in t ∩ g⁻¹ • s, f x ∂μ := ((Equiv.inv G).tsum_eq _).symm
     _ = ∑' g : G, ∫ x in g⁻¹ • (g • t ∩ s), f x ∂μ := by simp only [smul_set_inter, inv_smul_smul]
     _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ :=
@@ -455,11 +455,11 @@ theorem set_integral_eq_tsum' (h : IsFundamentalDomain G s μ) {f : α → E} {t
 
 @[to_additive]
 protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFundamentalDomain G t μ)
-    {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) : (∫ x in s, f x ∂μ) = ∫ x in t, f x ∂μ := by
+    {f : α → E} (hf : ∀ (g : G) (x), f (g • x) = f x) : ∫ x in s, f x ∂μ = ∫ x in t, f x ∂μ := by
   by_cases hfs : IntegrableOn f s μ
   · have hft : IntegrableOn f t μ := by rwa [ht.integrableOn_iff hs hf]
     calc
-      (∫ x in s, f x ∂μ) = ∑' g : G, ∫ x in s ∩ g • t, f x ∂μ := ht.set_integral_eq_tsum hfs
+      ∫ x in s, f x ∂μ = ∑' g : G, ∫ x in s ∩ g • t, f x ∂μ := ht.set_integral_eq_tsum hfs
       _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := by simp only [hf, inter_comm]
       _ = ∫ x in t, f x ∂μ := (hs.set_integral_eq_tsum' hft).symm
   · rw [integral_undef hfs, integral_undef]

chore: tidy various files (#5233)

697ac1d3

Diff

@@ -84,7 +84,7 @@ theorem mk' (h_meas : NullMeasurableSet s μ) (h_exists : ∀ x : α, ∃! g : G
   nullMeasurableSet := h_meas
   ae_covers := eventually_of_forall fun x => (h_exists x).exists
   aedisjoint a b hab := Disjoint.aedisjoint <| disjoint_left.2 fun x hxa hxb => by
-    rw [mem_smul_set_iff_inv_smul_mem] at hxa hxb 
+    rw [mem_smul_set_iff_inv_smul_mem] at hxa hxb
     exact hab (inv_injective <| (h_exists x).unique hxa hxb)
 #align measure_theory.is_fundamental_domain.mk' MeasureTheory.IsFundamentalDomain.mk'
 #align measure_theory.is_add_fundamental_domain.mk' MeasureTheory.IsAddFundamentalDomain.mk'
@@ -174,11 +174,11 @@ theorem image_of_equiv {ν : Measure β} (h : IsFundamentalDomain G s μ) (f : 
 #align measure_theory.is_add_fundamental_domain.image_of_equiv MeasureTheory.IsAddFundamentalDomain.image_of_equiv
 
 @[to_additive]
-theorem pairwise_aEDisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
+theorem pairwise_aedisjoint_of_ac {ν} (h : IsFundamentalDomain G s μ) (hν : ν ≪ μ) :
     Pairwise fun g₁ g₂ : G => AEDisjoint ν (g₁ • s) (g₂ • s) :=
   h.aedisjoint.mono fun _ _ H => hν H
-#align measure_theory.is_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsFundamentalDomain.pairwise_aEDisjoint_of_ac
-#align measure_theory.is_add_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsAddFundamentalDomain.pairwise_aEDisjoint_of_ac
+#align measure_theory.is_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsFundamentalDomain.pairwise_aedisjoint_of_ac
+#align measure_theory.is_add_fundamental_domain.pairwise_ae_disjoint_of_ac MeasureTheory.IsAddFundamentalDomain.pairwise_aedisjoint_of_ac
 
 @[to_additive]
 theorem smul_of_comm {G' : Type _} [Group G'] [MulAction G' α] [MeasurableSpace G']
@@ -463,7 +463,7 @@ protected theorem set_integral_eq (hs : IsFundamentalDomain G s μ) (ht : IsFund
       _ = ∑' g : G, ∫ x in g • t ∩ s, f (g⁻¹ • x) ∂μ := by simp only [hf, inter_comm]
       _ = ∫ x in t, f x ∂μ := (hs.set_integral_eq_tsum' hft).symm
   · rw [integral_undef hfs, integral_undef]
-    rwa [hs.integrableOn_iff ht hf] at hfs 
+    rwa [hs.integrableOn_iff ht hf] at hfs
 #align measure_theory.is_fundamental_domain.set_integral_eq MeasureTheory.IsFundamentalDomain.set_integral_eq
 #align measure_theory.is_add_fundamental_domain.set_integral_eq MeasureTheory.IsAddFundamentalDomain.set_integral_eq
 
@@ -515,7 +515,7 @@ theorem essSup_measure_restrict (hs : IsFundamentalDomain G s μ) {f : α → 
   rw [essSup_eq_sInf (μ.restrict s) f, essSup_eq_sInf μ f]
   refine' sInf_le_sInf _
   rintro a (ha : (μ.restrict s) {x : α | a < f x} = 0)
-  rw [Measure.restrict_apply₀' hs.nullMeasurableSet] at ha 
+  rw [Measure.restrict_apply₀' hs.nullMeasurableSet] at ha
   refine' measure_zero_of_invariant hs _ _ ha
   intro γ
   ext x
@@ -631,7 +631,7 @@ theorem pairwise_disjoint_fundamentalInterior :
     Pairwise (Disjoint on fun g : G => g • fundamentalInterior G s) := by
   refine' fun a b hab => disjoint_left.2 _
   rintro _ ⟨x, hx, rfl⟩ ⟨y, hy, hxy⟩
-  rw [mem_fundamentalInterior] at hx hy 
+  rw [mem_fundamentalInterior] at hx hy
   refine' hx.2 (a⁻¹ * b) _ _
   rwa [Ne.def, inv_mul_eq_iff_eq_mul, mul_one, eq_comm]
   simpa [mul_smul, ← hxy, mem_inv_smul_set_iff] using hy.1
@@ -705,4 +705,3 @@ protected theorem fundamentalInterior : IsFundamentalDomain G (fundamentalInteri
 end IsFundamentalDomain
 
 end MeasureTheory
-