dynamics.ergodic.measure_preserving ⟷ Mathlib.Dynamics.Ergodic.MeasurePreserving

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import MeasureTheory.Measure.AeMeasurable
+import MeasureTheory.Measure.AEMeasurable
 
 #align_import dynamics.ergodic.measure_preserving from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
 
@@ -195,7 +195,7 @@ theorem exists_mem_iterate_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f
 #align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_iterate_mem_of_volume_lt_mul_volume
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (m «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (m «expr ≠ » 0) -/
 #print MeasureTheory.MeasurePreserving.exists_mem_iterate_mem /-
 /-- A self-map preserving a finite measure is conservative: if `μ s ≠ 0`, then at least one point
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`

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

@@ -189,7 +189,7 @@ theorem exists_mem_iterate_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f
     ⟨i, hi, j, hj, hij, x, hxi, hxj⟩
   wlog hlt : i < j generalizing i j
   · exact this j hj i hi hij.symm hxj hxi (hij.lt_or_lt.resolve_left hlt)
-  simp only [Set.mem_preimage, Finset.mem_range] at hi hj hxi hxj 
+  simp only [Set.mem_preimage, Finset.mem_range] at hi hj hxi hxj
   refine' ⟨(f^[i]) x, hxi, j - i, ⟨tsub_pos_of_lt hlt, lt_of_le_of_lt (j.sub_le i) hj⟩, _⟩
   rwa [← iterate_add_apply, tsub_add_cancel_of_le hlt.le]
 #align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_iterate_mem_of_volume_lt_mul_volume

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

@@ -174,10 +174,10 @@ protected theorem iterate {f : α → α} (hf : MeasurePreserving f μa μa) :
 
 variable {μ : Measure α} {f : α → α} {s : Set α}
 
-#print MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume /-
+#print MeasureTheory.MeasurePreserving.exists_mem_iterate_mem_of_volume_lt_mul_volume /-
 /-- If `μ univ < n * μ s` and `f` is a map preserving measure `μ`,
 then for some `x ∈ s` and `0 < m < n`, `f^[m] x ∈ s`. -/
-theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f μ μ)
+theorem exists_mem_iterate_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f μ μ)
     (hs : MeasurableSet s) {n : ℕ} (hvol : μ (univ : Set α) < n * μ s) :
     ∃ x ∈ s, ∃ m ∈ Ioo 0 n, (f^[m]) x ∈ s :=
   by
@@ -192,22 +192,22 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
   simp only [Set.mem_preimage, Finset.mem_range] at hi hj hxi hxj 
   refine' ⟨(f^[i]) x, hxi, j - i, ⟨tsub_pos_of_lt hlt, lt_of_le_of_lt (j.sub_le i) hj⟩, _⟩
   rwa [← iterate_add_apply, tsub_add_cancel_of_le hlt.le]
-#align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
+#align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_iterate_mem_of_volume_lt_mul_volume
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (m «expr ≠ » 0) -/
-#print MeasureTheory.MeasurePreserving.exists_mem_image_mem /-
+#print MeasureTheory.MeasurePreserving.exists_mem_iterate_mem /-
 /-- A self-map preserving a finite measure is conservative: if `μ s ≠ 0`, then at least one point
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`
 infinitely many times, see `measure_theory.measure_preserving.conservative` and theorems about
 `measure_theory.conservative`. -/
-theorem exists_mem_image_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
+theorem exists_mem_iterate_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
     (hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), (f^[m]) x ∈ s :=
   by
   rcases ENNReal.exists_nat_mul_gt hs' (measure_ne_top μ (univ : Set α)) with ⟨N, hN⟩
   rcases hf.exists_mem_image_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩
   exact ⟨x, hx, m, hm.1.ne', hmx⟩
-#align measure_theory.measure_preserving.exists_mem_image_mem MeasureTheory.MeasurePreserving.exists_mem_image_mem
+#align measure_theory.measure_preserving.exists_mem_image_mem MeasureTheory.MeasurePreserving.exists_mem_iterate_mem
 -/
 
 end MeasurePreserving

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.MeasureTheory.Measure.AeMeasurable
+import MeasureTheory.Measure.AeMeasurable
 
 #align_import dynamics.ergodic.measure_preserving from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
 
@@ -195,7 +195,7 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
 #align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (m «expr ≠ » 0) -/
 #print MeasureTheory.MeasurePreserving.exists_mem_image_mem /-
 /-- A self-map preserving a finite measure is conservative: if `μ s ≠ 0`, then at least one point
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module dynamics.ergodic.measure_preserving
-! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Measure.AeMeasurable
 
+#align_import dynamics.ergodic.measure_preserving from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
+
 /-!
 # Measure preserving maps
 
@@ -198,7 +195,7 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
 #align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (m «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m «expr ≠ » 0) -/
 #print MeasureTheory.MeasurePreserving.exists_mem_image_mem /-
 /-- A self-map preserving a finite measure is conservative: if `μ s ≠ 0`, then at least one point
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`

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

@@ -55,10 +55,12 @@ structure MeasurePreserving (f : α → β)
 #align measure_theory.measure_preserving MeasureTheory.MeasurePreserving
 -/
 
+#print Measurable.measurePreserving /-
 protected theorem Measurable.measurePreserving {f : α → β} (h : Measurable f) (μa : Measure α) :
     MeasurePreserving f μa (map f μa) :=
   ⟨h, rfl⟩
 #align measurable.measure_preserving Measurable.measurePreserving
+-/
 
 namespace MeasurePreserving
 
@@ -68,47 +70,64 @@ protected theorem id (μ : Measure α) : MeasurePreserving id μ μ :=
 #align measure_theory.measure_preserving.id MeasureTheory.MeasurePreserving.id
 -/
 
+#print MeasureTheory.MeasurePreserving.aemeasurable /-
 protected theorem aemeasurable {f : α → β} (hf : MeasurePreserving f μa μb) : AEMeasurable f μa :=
   hf.1.AEMeasurable
 #align measure_theory.measure_preserving.ae_measurable MeasureTheory.MeasurePreserving.aemeasurable
+-/
 
+#print MeasureTheory.MeasurePreserving.symm /-
 theorem symm (e : α ≃ᵐ β) {μa : Measure α} {μb : Measure β} (h : MeasurePreserving e μa μb) :
     MeasurePreserving e.symm μb μa :=
   ⟨e.symm.Measurable, by
     rw [← h.map_eq, map_map e.symm.measurable e.measurable, e.symm_comp_self, map_id]⟩
 #align measure_theory.measure_preserving.symm MeasureTheory.MeasurePreserving.symm
+-/
 
+#print MeasureTheory.MeasurePreserving.restrict_preimage /-
 theorem restrict_preimage {f : α → β} (hf : MeasurePreserving f μa μb) {s : Set β}
     (hs : MeasurableSet s) : MeasurePreserving f (μa.restrict (f ⁻¹' s)) (μb.restrict s) :=
   ⟨hf.Measurable, by rw [← hf.map_eq, restrict_map hf.measurable hs]⟩
 #align measure_theory.measure_preserving.restrict_preimage MeasureTheory.MeasurePreserving.restrict_preimage
+-/
 
+#print MeasureTheory.MeasurePreserving.restrict_preimage_emb /-
 theorem restrict_preimage_emb {f : α → β} (hf : MeasurePreserving f μa μb)
     (h₂ : MeasurableEmbedding f) (s : Set β) :
     MeasurePreserving f (μa.restrict (f ⁻¹' s)) (μb.restrict s) :=
   ⟨hf.Measurable, by rw [← hf.map_eq, h₂.restrict_map]⟩
 #align measure_theory.measure_preserving.restrict_preimage_emb MeasureTheory.MeasurePreserving.restrict_preimage_emb
+-/
 
+#print MeasureTheory.MeasurePreserving.restrict_image_emb /-
 theorem restrict_image_emb {f : α → β} (hf : MeasurePreserving f μa μb) (h₂ : MeasurableEmbedding f)
     (s : Set α) : MeasurePreserving f (μa.restrict s) (μb.restrict (f '' s)) := by
   simpa only [preimage_image_eq _ h₂.injective] using hf.restrict_preimage_emb h₂ (f '' s)
 #align measure_theory.measure_preserving.restrict_image_emb MeasureTheory.MeasurePreserving.restrict_image_emb
+-/
 
+#print MeasureTheory.MeasurePreserving.aemeasurable_comp_iff /-
 theorem aemeasurable_comp_iff {f : α → β} (hf : MeasurePreserving f μa μb)
     (h₂ : MeasurableEmbedding f) {g : β → γ} : AEMeasurable (g ∘ f) μa ↔ AEMeasurable g μb := by
   rw [← hf.map_eq, h₂.ae_measurable_map_iff]
 #align measure_theory.measure_preserving.ae_measurable_comp_iff MeasureTheory.MeasurePreserving.aemeasurable_comp_iff
+-/
 
+#print MeasureTheory.MeasurePreserving.quasiMeasurePreserving /-
 protected theorem quasiMeasurePreserving {f : α → β} (hf : MeasurePreserving f μa μb) :
     QuasiMeasurePreserving f μa μb :=
   ⟨hf.1, hf.2.AbsolutelyContinuous⟩
 #align measure_theory.measure_preserving.quasi_measure_preserving MeasureTheory.MeasurePreserving.quasiMeasurePreserving
+-/
 
+#print MeasureTheory.MeasurePreserving.comp /-
 protected theorem comp {g : β → γ} {f : α → β} (hg : MeasurePreserving g μb μc)
     (hf : MeasurePreserving f μa μb) : MeasurePreserving (g ∘ f) μa μc :=
   ⟨hg.1.comp hf.1, by rw [← map_map hg.1 hf.1, hf.2, hg.2]⟩
 #align measure_theory.measure_preserving.comp MeasureTheory.MeasurePreserving.comp
+-/
 
+#print MeasureTheory.MeasurePreserving.comp_left_iff /-
 protected theorem comp_left_iff {g : α → β} {e : β ≃ᵐ γ} (h : MeasurePreserving e μb μc) :
     MeasurePreserving (e ∘ g) μa μc ↔ MeasurePreserving g μa μb :=
   by
@@ -116,7 +135,9 @@ protected theorem comp_left_iff {g : α → β} {e : β ≃ᵐ γ} (h : MeasureP
   convert (measure_preserving.symm e h).comp hg
   simp [← Function.comp.assoc e.symm e g]
 #align measure_theory.measure_preserving.comp_left_iff MeasureTheory.MeasurePreserving.comp_left_iff
+-/
 
+#print MeasureTheory.MeasurePreserving.comp_right_iff /-
 protected theorem comp_right_iff {g : α → β} {e : γ ≃ᵐ α} (h : MeasurePreserving e μc μa) :
     MeasurePreserving (g ∘ e) μc μb ↔ MeasurePreserving g μa μb :=
   by
@@ -124,20 +145,27 @@ protected theorem comp_right_iff {g : α → β} {e : γ ≃ᵐ α} (h : Measure
   convert hg.comp (measure_preserving.symm e h)
   simp [Function.comp.assoc g e e.symm]
 #align measure_theory.measure_preserving.comp_right_iff MeasureTheory.MeasurePreserving.comp_right_iff
+-/
 
+#print MeasureTheory.MeasurePreserving.sigmaFinite /-
 protected theorem sigmaFinite {f : α → β} (hf : MeasurePreserving f μa μb) [SigmaFinite μb] :
     SigmaFinite μa :=
   SigmaFinite.of_map μa hf.AEMeasurable (by rwa [hf.map_eq])
 #align measure_theory.measure_preserving.sigma_finite MeasureTheory.MeasurePreserving.sigmaFinite
+-/
 
+#print MeasureTheory.MeasurePreserving.measure_preimage /-
 theorem measure_preimage {f : α → β} (hf : MeasurePreserving f μa μb) {s : Set β}
     (hs : MeasurableSet s) : μa (f ⁻¹' s) = μb s := by rw [← hf.map_eq, map_apply hf.1 hs]
 #align measure_theory.measure_preserving.measure_preimage MeasureTheory.MeasurePreserving.measure_preimage
+-/
 
+#print MeasureTheory.MeasurePreserving.measure_preimage_emb /-
 theorem measure_preimage_emb {f : α → β} (hf : MeasurePreserving f μa μb)
     (hfe : MeasurableEmbedding f) (s : Set β) : μa (f ⁻¹' s) = μb s := by
   rw [← hf.map_eq, hfe.map_apply]
 #align measure_theory.measure_preserving.measure_preimage_emb MeasureTheory.MeasurePreserving.measure_preimage_emb
+-/
 
 #print MeasureTheory.MeasurePreserving.iterate /-
 protected theorem iterate {f : α → α} (hf : MeasurePreserving f μa μa) :
@@ -149,6 +177,7 @@ protected theorem iterate {f : α → α} (hf : MeasurePreserving f μa μa) :
 
 variable {μ : Measure α} {f : α → α} {s : Set α}
 
+#print MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume /-
 /-- If `μ univ < n * μ s` and `f` is a map preserving measure `μ`,
 then for some `x ∈ s` and `0 < m < n`, `f^[m] x ∈ s`. -/
 theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f μ μ)
@@ -167,8 +196,10 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
   refine' ⟨(f^[i]) x, hxi, j - i, ⟨tsub_pos_of_lt hlt, lt_of_le_of_lt (j.sub_le i) hj⟩, _⟩
   rwa [← iterate_add_apply, tsub_add_cancel_of_le hlt.le]
 #align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (m «expr ≠ » 0) -/
+#print MeasureTheory.MeasurePreserving.exists_mem_image_mem /-
 /-- A self-map preserving a finite measure is conservative: if `μ s ≠ 0`, then at least one point
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`
 infinitely many times, see `measure_theory.measure_preserving.conservative` and theorems about
@@ -180,15 +211,18 @@ theorem exists_mem_image_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ 
   rcases hf.exists_mem_image_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩
   exact ⟨x, hx, m, hm.1.ne', hmx⟩
 #align measure_theory.measure_preserving.exists_mem_image_mem MeasureTheory.MeasurePreserving.exists_mem_image_mem
+-/
 
 end MeasurePreserving
 
 namespace MeasurableEquiv
 
+#print MeasureTheory.MeasurableEquiv.measurePreserving_symm /-
 theorem measurePreserving_symm (μ : Measure α) (e : α ≃ᵐ β) :
     MeasurePreserving e.symm (map e μ) μ :=
   (e.Measurable.MeasurePreserving μ).symm _
 #align measure_theory.measurable_equiv.measure_preserving_symm MeasureTheory.MeasurableEquiv.measurePreserving_symm
+-/
 
 end MeasurableEquiv
 

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

@@ -168,7 +168,7 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
   rwa [← iterate_add_apply, tsub_add_cancel_of_le hlt.le]
 #align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (m «expr ≠ » 0) -/
 /-- A self-map preserving a finite measure is conservative: if `μ s ≠ 0`, then at least one point
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`
 infinitely many times, see `measure_theory.measure_preserving.conservative` and theorems about

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

@@ -113,7 +113,7 @@ protected theorem comp_left_iff {g : α → β} {e : β ≃ᵐ γ} (h : MeasureP
     MeasurePreserving (e ∘ g) μa μc ↔ MeasurePreserving g μa μb :=
   by
   refine' ⟨fun hg => _, fun hg => h.comp hg⟩
-  convert(measure_preserving.symm e h).comp hg
+  convert (measure_preserving.symm e h).comp hg
   simp [← Function.comp.assoc e.symm e g]
 #align measure_theory.measure_preserving.comp_left_iff MeasureTheory.MeasurePreserving.comp_left_iff
 
@@ -173,8 +173,8 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`
 infinitely many times, see `measure_theory.measure_preserving.conservative` and theorems about
 `measure_theory.conservative`. -/
-theorem exists_mem_image_mem [FiniteMeasure μ] (hf : MeasurePreserving f μ μ) (hs : MeasurableSet s)
-    (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), (f^[m]) x ∈ s :=
+theorem exists_mem_image_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
+    (hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), (f^[m]) x ∈ s :=
   by
   rcases ENNReal.exists_nat_mul_gt hs' (measure_ne_top μ (univ : Set α)) with ⟨N, hN⟩
   rcases hf.exists_mem_image_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩

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

@@ -48,8 +48,8 @@ variable {μa : Measure α} {μb : Measure β} {μc : Measure γ} {μd : Measure
 and `map f μa = μb`. -/
 @[protect_proj]
 structure MeasurePreserving (f : α → β)
-  (μa : Measure α := by exact MeasureTheory.MeasureSpace.volume)
-  (μb : Measure β := by exact MeasureTheory.MeasureSpace.volume) : Prop where
+    (μa : Measure α := by exact MeasureTheory.MeasureSpace.volume)
+    (μb : Measure β := by exact MeasureTheory.MeasureSpace.volume) : Prop where
   Measurable : Measurable f
   map_eq : map f μa = μb
 #align measure_theory.measure_preserving MeasureTheory.MeasurePreserving
@@ -163,7 +163,7 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
     ⟨i, hi, j, hj, hij, x, hxi, hxj⟩
   wlog hlt : i < j generalizing i j
   · exact this j hj i hi hij.symm hxj hxi (hij.lt_or_lt.resolve_left hlt)
-  simp only [Set.mem_preimage, Finset.mem_range] at hi hj hxi hxj
+  simp only [Set.mem_preimage, Finset.mem_range] at hi hj hxi hxj 
   refine' ⟨(f^[i]) x, hxi, j - i, ⟨tsub_pos_of_lt hlt, lt_of_le_of_lt (j.sub_le i) hj⟩, _⟩
   rwa [← iterate_add_apply, tsub_add_cancel_of_le hlt.le]
 #align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
@@ -174,7 +174,7 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
 infinitely many times, see `measure_theory.measure_preserving.conservative` and theorems about
 `measure_theory.conservative`. -/
 theorem exists_mem_image_mem [FiniteMeasure μ] (hf : MeasurePreserving f μ μ) (hs : MeasurableSet s)
-    (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _)(_ : m ≠ 0), (f^[m]) x ∈ s :=
+    (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), (f^[m]) x ∈ s :=
   by
   rcases ENNReal.exists_nat_mul_gt hs' (measure_ne_top μ (univ : Set α)) with ⟨N, hN⟩
   rcases hf.exists_mem_image_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩

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

@@ -55,12 +55,6 @@ structure MeasurePreserving (f : α → β)
 #align measure_theory.measure_preserving MeasureTheory.MeasurePreserving
 -/
 
-/- warning: measurable.measure_preserving -> Measurable.measurePreserving is a dubious translation:
-lean 3 declaration is
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 protected theorem Measurable.measurePreserving {f : α → β} (h : Measurable f) (μa : Measure α) :
     MeasurePreserving f μa (map f μa) :=
   ⟨h, rfl⟩
@@ -74,101 +68,47 @@ protected theorem id (μ : Measure α) : MeasurePreserving id μ μ :=
 #align measure_theory.measure_preserving.id MeasureTheory.MeasurePreserving.id
 -/
 
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 protected theorem aemeasurable {f : α → β} (hf : MeasurePreserving f μa μb) : AEMeasurable f μa :=
   hf.1.AEMeasurable
 #align measure_theory.measure_preserving.ae_measurable MeasureTheory.MeasurePreserving.aemeasurable
 
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 theorem symm (e : α ≃ᵐ β) {μa : Measure α} {μb : Measure β} (h : MeasurePreserving e μa μb) :
     MeasurePreserving e.symm μb μa :=
   ⟨e.symm.Measurable, by
     rw [← h.map_eq, map_map e.symm.measurable e.measurable, e.symm_comp_self, map_id]⟩
 #align measure_theory.measure_preserving.symm MeasureTheory.MeasurePreserving.symm
 
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 theorem restrict_preimage {f : α → β} (hf : MeasurePreserving f μa μb) {s : Set β}
     (hs : MeasurableSet s) : MeasurePreserving f (μa.restrict (f ⁻¹' s)) (μb.restrict s) :=
   ⟨hf.Measurable, by rw [← hf.map_eq, restrict_map hf.measurable hs]⟩
 #align measure_theory.measure_preserving.restrict_preimage MeasureTheory.MeasurePreserving.restrict_preimage
 
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 theorem restrict_preimage_emb {f : α → β} (hf : MeasurePreserving f μa μb)
     (h₂ : MeasurableEmbedding f) (s : Set β) :
     MeasurePreserving f (μa.restrict (f ⁻¹' s)) (μb.restrict s) :=
   ⟨hf.Measurable, by rw [← hf.map_eq, h₂.restrict_map]⟩
 #align measure_theory.measure_preserving.restrict_preimage_emb MeasureTheory.MeasurePreserving.restrict_preimage_emb
 
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 theorem restrict_image_emb {f : α → β} (hf : MeasurePreserving f μa μb) (h₂ : MeasurableEmbedding f)
     (s : Set α) : MeasurePreserving f (μa.restrict s) (μb.restrict (f '' s)) := by
   simpa only [preimage_image_eq _ h₂.injective] using hf.restrict_preimage_emb h₂ (f '' s)
 #align measure_theory.measure_preserving.restrict_image_emb MeasureTheory.MeasurePreserving.restrict_image_emb
 
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 theorem aemeasurable_comp_iff {f : α → β} (hf : MeasurePreserving f μa μb)
     (h₂ : MeasurableEmbedding f) {g : β → γ} : AEMeasurable (g ∘ f) μa ↔ AEMeasurable g μb := by
   rw [← hf.map_eq, h₂.ae_measurable_map_iff]
 #align measure_theory.measure_preserving.ae_measurable_comp_iff MeasureTheory.MeasurePreserving.aemeasurable_comp_iff
 
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 protected theorem quasiMeasurePreserving {f : α → β} (hf : MeasurePreserving f μa μb) :
     QuasiMeasurePreserving f μa μb :=
   ⟨hf.1, hf.2.AbsolutelyContinuous⟩
 #align measure_theory.measure_preserving.quasi_measure_preserving MeasureTheory.MeasurePreserving.quasiMeasurePreserving
 
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 protected theorem comp {g : β → γ} {f : α → β} (hg : MeasurePreserving g μb μc)
     (hf : MeasurePreserving f μa μb) : MeasurePreserving (g ∘ f) μa μc :=
   ⟨hg.1.comp hf.1, by rw [← map_map hg.1 hf.1, hf.2, hg.2]⟩
 #align measure_theory.measure_preserving.comp MeasureTheory.MeasurePreserving.comp
 
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 protected theorem comp_left_iff {g : α → β} {e : β ≃ᵐ γ} (h : MeasurePreserving e μb μc) :
     MeasurePreserving (e ∘ g) μa μc ↔ MeasurePreserving g μa μb :=
   by
@@ -177,12 +117,6 @@ protected theorem comp_left_iff {g : α → β} {e : β ≃ᵐ γ} (h : MeasureP
   simp [← Function.comp.assoc e.symm e g]
 #align measure_theory.measure_preserving.comp_left_iff MeasureTheory.MeasurePreserving.comp_left_iff
 
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 protected theorem comp_right_iff {g : α → β} {e : γ ≃ᵐ α} (h : MeasurePreserving e μc μa) :
     MeasurePreserving (g ∘ e) μc μb ↔ MeasurePreserving g μa μb :=
   by
@@ -191,33 +125,15 @@ protected theorem comp_right_iff {g : α → β} {e : γ ≃ᵐ α} (h : Measure
   simp [Function.comp.assoc g e e.symm]
 #align measure_theory.measure_preserving.comp_right_iff MeasureTheory.MeasurePreserving.comp_right_iff
 
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 protected theorem sigmaFinite {f : α → β} (hf : MeasurePreserving f μa μb) [SigmaFinite μb] :
     SigmaFinite μa :=
   SigmaFinite.of_map μa hf.AEMeasurable (by rwa [hf.map_eq])
 #align measure_theory.measure_preserving.sigma_finite MeasureTheory.MeasurePreserving.sigmaFinite
 
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 theorem measure_preimage {f : α → β} (hf : MeasurePreserving f μa μb) {s : Set β}
     (hs : MeasurableSet s) : μa (f ⁻¹' s) = μb s := by rw [← hf.map_eq, map_apply hf.1 hs]
 #align measure_theory.measure_preserving.measure_preimage MeasureTheory.MeasurePreserving.measure_preimage
 
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 theorem measure_preimage_emb {f : α → β} (hf : MeasurePreserving f μa μb)
     (hfe : MeasurableEmbedding f) (s : Set β) : μa (f ⁻¹' s) = μb s := by
   rw [← hf.map_eq, hfe.map_apply]
@@ -233,12 +149,6 @@ protected theorem iterate {f : α → α} (hf : MeasurePreserving f μa μa) :
 
 variable {μ : Measure α} {f : α → α} {s : Set α}
 
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 /-- If `μ univ < n * μ s` and `f` is a map preserving measure `μ`,
 then for some `x ∈ s` and `0 < m < n`, `f^[m] x ∈ s`. -/
 theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f μ μ)
@@ -258,12 +168,6 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
   rwa [← iterate_add_apply, tsub_add_cancel_of_le hlt.le]
 #align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.exists_mem_image_mem MeasureTheory.MeasurePreserving.exists_mem_image_memₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m «expr ≠ » 0) -/
 /-- A self-map preserving a finite measure is conservative: if `μ s ≠ 0`, then at least one point
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`
@@ -281,12 +185,6 @@ end MeasurePreserving
 
 namespace MeasurableEquiv
 
-/- warning: measure_theory.measurable_equiv.measure_preserving_symm -> MeasureTheory.MeasurableEquiv.measurePreserving_symm is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : MeasurableSpace.{u2} β] (μ : MeasureTheory.Measure.{u1} α _inst_1) (e : MeasurableEquiv.{u1, u2} α β _inst_1 _inst_2), MeasureTheory.MeasurePreserving.{u2, u1} β α _inst_2 _inst_1 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (MeasurableEquiv.{u2, u1} β α _inst_2 _inst_1) (fun (_x : MeasurableEquiv.{u2, u1} β α _inst_2 _inst_1) => β -> α) (MeasurableEquiv.hasCoeToFun.{u2, u1} β α _inst_2 _inst_1) (MeasurableEquiv.symm.{u1, u2} α β _inst_1 _inst_2 e)) (MeasureTheory.Measure.map.{u1, u2} α β _inst_2 _inst_1 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MeasurableEquiv.{u1, u2} α β _inst_1 _inst_2) (fun (_x : MeasurableEquiv.{u1, u2} α β _inst_1 _inst_2) => α -> β) (MeasurableEquiv.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) e) μ) μ
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : MeasurableSpace.{u1} β] (μ : MeasureTheory.Measure.{u2} α _inst_1) (e : MeasurableEquiv.{u2, u1} α β _inst_1 _inst_2), MeasureTheory.MeasurePreserving.{u1, u2} β α _inst_2 _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MeasurableEquiv.{u1, u2} β α _inst_2 _inst_1) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u2} (MeasurableEquiv.{u1, u2} β α _inst_2 _inst_1) β α (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u2} (MeasurableEquiv.{u1, u2} β α _inst_2 _inst_1) β α (MeasurableEquiv.instEquivLike.{u1, u2} β α _inst_2 _inst_1))) (MeasurableEquiv.symm.{u2, u1} α β _inst_1 _inst_2 e)) (MeasureTheory.Measure.map.{u2, u1} α β _inst_2 _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MeasurableEquiv.{u2, u1} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (MeasurableEquiv.{u2, u1} α β _inst_1 _inst_2) α β (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u2, succ u1} (MeasurableEquiv.{u2, u1} α β _inst_1 _inst_2) α β (MeasurableEquiv.instEquivLike.{u2, u1} α β _inst_1 _inst_2))) e) μ) μ
-Case conversion may be inaccurate. Consider using '#align measure_theory.measurable_equiv.measure_preserving_symm MeasureTheory.MeasurableEquiv.measurePreserving_symmₓ'. -/
 theorem measurePreserving_symm (μ : Measure α) (e : α ≃ᵐ β) :
     MeasurePreserving e.symm (map e μ) μ :=
   (e.Measurable.MeasurePreserving μ).symm _

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

@@ -235,7 +235,7 @@ variable {μ : Measure α} {f : α → α} {s : Set α}
 
 /- warning: measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume -> MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {f : α -> α} {s : Set.{u1} α}, (MeasureTheory.MeasurePreserving.{u1, u1} α α _inst_1 _inst_1 f μ μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (forall {n : Nat}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) μ (Set.univ.{u1} α)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat ENNReal (HasLiftT.mk.{1, 1} Nat ENNReal (CoeTCₓ.coe.{1, 1} Nat ENNReal (Nat.castCoe.{0} ENNReal (AddMonoidWithOne.toNatCast.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) n) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) μ s))) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) m (Set.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (fun (H : Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) m (Set.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Nat.iterate.{succ u1} α f m x) s))))))
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {f : α -> α} {s : Set.{u1} α}, (MeasureTheory.MeasurePreserving.{u1, u1} α α _inst_1 _inst_1 f μ μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (forall {n : Nat}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) μ (Set.univ.{u1} α)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat ENNReal (HasLiftT.mk.{1, 1} Nat ENNReal (CoeTCₓ.coe.{1, 1} Nat ENNReal (Nat.castCoe.{0} ENNReal (AddMonoidWithOne.toNatCast.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) n) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) μ s))) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) m (Set.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (fun (H : Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) m (Set.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Nat.iterate.{succ u1} α f m x) s))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {f : α -> α} {s : Set.{u1} α}, (MeasureTheory.MeasurePreserving.{u1, u1} α α _inst_1 _inst_1 f μ μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (forall {n : Nat}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) (Set.univ.{u1} α)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (Nat.cast.{0} ENNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) n) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) s))) -> (Exists.{succ u1} α (fun (x : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (Exists.{1} Nat (fun (m : Nat) => And (Membership.mem.{0, 0} Nat (Set.{0} Nat) (Set.instMembershipSet.{0} Nat) m (Set.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Nat.iterate.{succ u1} α f m x) s))))))
 Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volumeₓ'. -/

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module dynamics.ergodic.measure_preserving
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
+! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.MeasureTheory.Measure.AeMeasurable
 /-!
 # Measure preserving maps
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We say that `f : α → β` is a measure preserving map w.r.t. measures `μ : measure α` and
 `ν : measure β` if `f` is measurable and `map f μ = ν`. In this file we define the predicate
 `measure_theory.measure_preserving` and prove its basic properties.

mathlib commit https://github.com/leanprover-community/mathlib/commit/28b2a92f2996d28e580450863c130955de0ed398

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module dynamics.ergodic.measure_preserving
-! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
+! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,9 +13,6 @@ import Mathbin.MeasureTheory.Measure.AeMeasurable
 /-!
 # Measure preserving maps
 
-> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
-> Any changes to this file require a corresponding PR to mathlib4.
-
 We say that `f : α → β` is a measure preserving map w.r.t. measures `μ : measure α` and
 `ν : measure β` if `f` is measurable and `map f μ = ν`. In this file we define the predicate
 `measure_theory.measure_preserving` and prove its basic properties.

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module dynamics.ergodic.measure_preserving
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
+! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.MeasureTheory.Measure.AeMeasurable
 /-!
 # Measure preserving maps
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 We say that `f : α → β` is a measure preserving map w.r.t. measures `μ : measure α` and
 `ν : measure β` if `f` is measurable and `map f μ = ν`. In this file we define the predicate
 `measure_theory.measure_preserving` and prove its basic properties.

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

@@ -40,6 +40,7 @@ open Measure Function Set
 
 variable {μa : Measure α} {μb : Measure β} {μc : Measure γ} {μd : Measure δ}
 
+#print MeasureTheory.MeasurePreserving /-
 /-- `f` is a measure preserving map w.r.t. measures `μa` and `μb` if `f` is measurable
 and `map f μa = μb`. -/
 @[protect_proj]
@@ -49,7 +50,14 @@ structure MeasurePreserving (f : α → β)
   Measurable : Measurable f
   map_eq : map f μa = μb
 #align measure_theory.measure_preserving MeasureTheory.MeasurePreserving
+-/
 
+/- warning: measurable.measure_preserving -> Measurable.measurePreserving is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : MeasurableSpace.{u2} β] {f : α -> β}, (Measurable.{u1, u2} α β _inst_1 _inst_2 f) -> (forall (μa : MeasureTheory.Measure.{u1} α _inst_1), MeasureTheory.MeasurePreserving.{u1, u2} α β _inst_1 _inst_2 f μa (MeasureTheory.Measure.map.{u1, u2} α β _inst_2 _inst_1 f μa))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : MeasurableSpace.{u1} β] {f : α -> β}, (Measurable.{u2, u1} α β _inst_1 _inst_2 f) -> (forall (μa : MeasureTheory.Measure.{u2} α _inst_1), MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f μa (MeasureTheory.Measure.map.{u2, u1} α β _inst_2 _inst_1 f μa))
+Case conversion may be inaccurate. Consider using '#align measurable.measure_preserving Measurable.measurePreservingₓ'. -/
 protected theorem Measurable.measurePreserving {f : α → β} (h : Measurable f) (μa : Measure α) :
     MeasurePreserving f μa (map f μa) :=
   ⟨h, rfl⟩
@@ -57,51 +65,107 @@ protected theorem Measurable.measurePreserving {f : α → β} (h : Measurable f
 
 namespace MeasurePreserving
 
+#print MeasureTheory.MeasurePreserving.id /-
 protected theorem id (μ : Measure α) : MeasurePreserving id μ μ :=
   ⟨measurable_id, map_id⟩
 #align measure_theory.measure_preserving.id MeasureTheory.MeasurePreserving.id
+-/
 
-protected theorem aEMeasurable {f : α → β} (hf : MeasurePreserving f μa μb) : AEMeasurable f μa :=
+/- warning: measure_theory.measure_preserving.ae_measurable -> MeasureTheory.MeasurePreserving.aemeasurable is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : MeasurableSpace.{u2} β] {μa : MeasureTheory.Measure.{u1} α _inst_1} {μb : MeasureTheory.Measure.{u2} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u1, u2} α β _inst_1 _inst_2 f μa μb) -> (AEMeasurable.{u1, u2} α β _inst_2 _inst_1 f μa)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : MeasurableSpace.{u1} β] {μa : MeasureTheory.Measure.{u2} α _inst_1} {μb : MeasureTheory.Measure.{u1} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f μa μb) -> (AEMeasurable.{u2, u1} α β _inst_2 _inst_1 f μa)
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.ae_measurable MeasureTheory.MeasurePreserving.aemeasurableₓ'. -/
+protected theorem aemeasurable {f : α → β} (hf : MeasurePreserving f μa μb) : AEMeasurable f μa :=
   hf.1.AEMeasurable
-#align measure_theory.measure_preserving.ae_measurable MeasureTheory.MeasurePreserving.aEMeasurable
-
+#align measure_theory.measure_preserving.ae_measurable MeasureTheory.MeasurePreserving.aemeasurable
+
+/- warning: measure_theory.measure_preserving.symm -> MeasureTheory.MeasurePreserving.symm is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : MeasurableSpace.{u2} β] (e : MeasurableEquiv.{u1, u2} α β _inst_1 _inst_2) {μa : MeasureTheory.Measure.{u1} α _inst_1} {μb : MeasureTheory.Measure.{u2} β _inst_2}, (MeasureTheory.MeasurePreserving.{u1, u2} α β _inst_1 _inst_2 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MeasurableEquiv.{u1, u2} α β _inst_1 _inst_2) (fun (_x : MeasurableEquiv.{u1, u2} α β _inst_1 _inst_2) => α -> β) (MeasurableEquiv.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) e) μa μb) -> (MeasureTheory.MeasurePreserving.{u2, u1} β α _inst_2 _inst_1 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (MeasurableEquiv.{u2, u1} β α _inst_2 _inst_1) (fun (_x : MeasurableEquiv.{u2, u1} β α _inst_2 _inst_1) => β -> α) (MeasurableEquiv.hasCoeToFun.{u2, u1} β α _inst_2 _inst_1) (MeasurableEquiv.symm.{u1, u2} α β _inst_1 _inst_2 e)) μb μa)
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.symm MeasureTheory.MeasurePreserving.symmₓ'. -/
 theorem symm (e : α ≃ᵐ β) {μa : Measure α} {μb : Measure β} (h : MeasurePreserving e μa μb) :
     MeasurePreserving e.symm μb μa :=
   ⟨e.symm.Measurable, by
     rw [← h.map_eq, map_map e.symm.measurable e.measurable, e.symm_comp_self, map_id]⟩
 #align measure_theory.measure_preserving.symm MeasureTheory.MeasurePreserving.symm
 
+/- warning: measure_theory.measure_preserving.restrict_preimage -> MeasureTheory.MeasurePreserving.restrict_preimage is a dubious translation:
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+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : MeasurableSpace.{u1} β] {μa : MeasureTheory.Measure.{u2} α _inst_1} {μb : MeasureTheory.Measure.{u1} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f μa μb) -> (forall {s : Set.{u1} β}, (MeasurableSet.{u1} β _inst_2 s) -> (MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f (MeasureTheory.Measure.restrict.{u2} α _inst_1 μa (Set.preimage.{u2, u1} α β f s)) (MeasureTheory.Measure.restrict.{u1} β _inst_2 μb s)))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.restrict_preimage MeasureTheory.MeasurePreserving.restrict_preimageₓ'. -/
 theorem restrict_preimage {f : α → β} (hf : MeasurePreserving f μa μb) {s : Set β}
     (hs : MeasurableSet s) : MeasurePreserving f (μa.restrict (f ⁻¹' s)) (μb.restrict s) :=
   ⟨hf.Measurable, by rw [← hf.map_eq, restrict_map hf.measurable hs]⟩
 #align measure_theory.measure_preserving.restrict_preimage MeasureTheory.MeasurePreserving.restrict_preimage
 
+/- warning: measure_theory.measure_preserving.restrict_preimage_emb -> MeasureTheory.MeasurePreserving.restrict_preimage_emb is a dubious translation:
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+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : MeasurableSpace.{u1} β] {μa : MeasureTheory.Measure.{u2} α _inst_1} {μb : MeasureTheory.Measure.{u1} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f μa μb) -> (MeasurableEmbedding.{u2, u1} α β _inst_1 _inst_2 f) -> (forall (s : Set.{u1} β), MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f (MeasureTheory.Measure.restrict.{u2} α _inst_1 μa (Set.preimage.{u2, u1} α β f s)) (MeasureTheory.Measure.restrict.{u1} β _inst_2 μb s))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.restrict_preimage_emb MeasureTheory.MeasurePreserving.restrict_preimage_embₓ'. -/
 theorem restrict_preimage_emb {f : α → β} (hf : MeasurePreserving f μa μb)
     (h₂ : MeasurableEmbedding f) (s : Set β) :
     MeasurePreserving f (μa.restrict (f ⁻¹' s)) (μb.restrict s) :=
   ⟨hf.Measurable, by rw [← hf.map_eq, h₂.restrict_map]⟩
 #align measure_theory.measure_preserving.restrict_preimage_emb MeasureTheory.MeasurePreserving.restrict_preimage_emb
 
+/- warning: measure_theory.measure_preserving.restrict_image_emb -> MeasureTheory.MeasurePreserving.restrict_image_emb is a dubious translation:
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+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : MeasurableSpace.{u1} β] {μa : MeasureTheory.Measure.{u2} α _inst_1} {μb : MeasureTheory.Measure.{u1} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f μa μb) -> (MeasurableEmbedding.{u2, u1} α β _inst_1 _inst_2 f) -> (forall (s : Set.{u2} α), MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f (MeasureTheory.Measure.restrict.{u2} α _inst_1 μa s) (MeasureTheory.Measure.restrict.{u1} β _inst_2 μb (Set.image.{u2, u1} α β f s)))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.restrict_image_emb MeasureTheory.MeasurePreserving.restrict_image_embₓ'. -/
 theorem restrict_image_emb {f : α → β} (hf : MeasurePreserving f μa μb) (h₂ : MeasurableEmbedding f)
     (s : Set α) : MeasurePreserving f (μa.restrict s) (μb.restrict (f '' s)) := by
   simpa only [preimage_image_eq _ h₂.injective] using hf.restrict_preimage_emb h₂ (f '' s)
 #align measure_theory.measure_preserving.restrict_image_emb MeasureTheory.MeasurePreserving.restrict_image_emb
 
-theorem aEMeasurable_comp_iff {f : α → β} (hf : MeasurePreserving f μa μb)
+/- warning: measure_theory.measure_preserving.ae_measurable_comp_iff -> MeasureTheory.MeasurePreserving.aemeasurable_comp_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : MeasurableSpace.{u2} β] [_inst_3 : MeasurableSpace.{u3} γ] {μa : MeasureTheory.Measure.{u1} α _inst_1} {μb : MeasureTheory.Measure.{u2} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u1, u2} α β _inst_1 _inst_2 f μa μb) -> (MeasurableEmbedding.{u1, u2} α β _inst_1 _inst_2 f) -> (forall {g : β -> γ}, Iff (AEMeasurable.{u1, u3} α γ _inst_3 _inst_1 (Function.comp.{succ u1, succ u2, succ u3} α β γ g f) μa) (AEMeasurable.{u2, u3} β γ _inst_3 _inst_2 g μb))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : MeasurableSpace.{u3} α] [_inst_2 : MeasurableSpace.{u2} β] [_inst_3 : MeasurableSpace.{u1} γ] {μa : MeasureTheory.Measure.{u3} α _inst_1} {μb : MeasureTheory.Measure.{u2} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u3, u2} α β _inst_1 _inst_2 f μa μb) -> (MeasurableEmbedding.{u3, u2} α β _inst_1 _inst_2 f) -> (forall {g : β -> γ}, Iff (AEMeasurable.{u3, u1} α γ _inst_3 _inst_1 (Function.comp.{succ u3, succ u2, succ u1} α β γ g f) μa) (AEMeasurable.{u2, u1} β γ _inst_3 _inst_2 g μb))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.ae_measurable_comp_iff MeasureTheory.MeasurePreserving.aemeasurable_comp_iffₓ'. -/
+theorem aemeasurable_comp_iff {f : α → β} (hf : MeasurePreserving f μa μb)
     (h₂ : MeasurableEmbedding f) {g : β → γ} : AEMeasurable (g ∘ f) μa ↔ AEMeasurable g μb := by
   rw [← hf.map_eq, h₂.ae_measurable_map_iff]
-#align measure_theory.measure_preserving.ae_measurable_comp_iff MeasureTheory.MeasurePreserving.aEMeasurable_comp_iff
-
+#align measure_theory.measure_preserving.ae_measurable_comp_iff MeasureTheory.MeasurePreserving.aemeasurable_comp_iff
+
+/- warning: measure_theory.measure_preserving.quasi_measure_preserving -> MeasureTheory.MeasurePreserving.quasiMeasurePreserving is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : MeasurableSpace.{u2} β] {μa : MeasureTheory.Measure.{u1} α _inst_1} {μb : MeasureTheory.Measure.{u2} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u1, u2} α β _inst_1 _inst_2 f μa μb) -> (MeasureTheory.Measure.QuasiMeasurePreserving.{u1, u2} α β _inst_2 _inst_1 f μa μb)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : MeasurableSpace.{u1} β] {μa : MeasureTheory.Measure.{u2} α _inst_1} {μb : MeasureTheory.Measure.{u1} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f μa μb) -> (MeasureTheory.Measure.QuasiMeasurePreserving.{u2, u1} α β _inst_2 _inst_1 f μa μb)
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.quasi_measure_preserving MeasureTheory.MeasurePreserving.quasiMeasurePreservingₓ'. -/
 protected theorem quasiMeasurePreserving {f : α → β} (hf : MeasurePreserving f μa μb) :
     QuasiMeasurePreserving f μa μb :=
   ⟨hf.1, hf.2.AbsolutelyContinuous⟩
 #align measure_theory.measure_preserving.quasi_measure_preserving MeasureTheory.MeasurePreserving.quasiMeasurePreserving
 
+/- warning: measure_theory.measure_preserving.comp -> MeasureTheory.MeasurePreserving.comp is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : MeasurableSpace.{u2} β] [_inst_3 : MeasurableSpace.{u3} γ] {μa : MeasureTheory.Measure.{u1} α _inst_1} {μb : MeasureTheory.Measure.{u2} β _inst_2} {μc : MeasureTheory.Measure.{u3} γ _inst_3} {g : β -> γ} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u2, u3} β γ _inst_2 _inst_3 g μb μc) -> (MeasureTheory.MeasurePreserving.{u1, u2} α β _inst_1 _inst_2 f μa μb) -> (MeasureTheory.MeasurePreserving.{u1, u3} α γ _inst_1 _inst_3 (Function.comp.{succ u1, succ u2, succ u3} α β γ g f) μa μc)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u3}} {γ : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : MeasurableSpace.{u3} β] [_inst_3 : MeasurableSpace.{u2} γ] {μa : MeasureTheory.Measure.{u1} α _inst_1} {μb : MeasureTheory.Measure.{u3} β _inst_2} {μc : MeasureTheory.Measure.{u2} γ _inst_3} {g : β -> γ} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u3, u2} β γ _inst_2 _inst_3 g μb μc) -> (MeasureTheory.MeasurePreserving.{u1, u3} α β _inst_1 _inst_2 f μa μb) -> (MeasureTheory.MeasurePreserving.{u1, u2} α γ _inst_1 _inst_3 (Function.comp.{succ u1, succ u3, succ u2} α β γ g f) μa μc)
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.comp MeasureTheory.MeasurePreserving.compₓ'. -/
 protected theorem comp {g : β → γ} {f : α → β} (hg : MeasurePreserving g μb μc)
     (hf : MeasurePreserving f μa μb) : MeasurePreserving (g ∘ f) μa μc :=
   ⟨hg.1.comp hf.1, by rw [← map_map hg.1 hf.1, hf.2, hg.2]⟩
 #align measure_theory.measure_preserving.comp MeasureTheory.MeasurePreserving.comp
 
+/- warning: measure_theory.measure_preserving.comp_left_iff -> MeasureTheory.MeasurePreserving.comp_left_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.comp_left_iff MeasureTheory.MeasurePreserving.comp_left_iffₓ'. -/
 protected theorem comp_left_iff {g : α → β} {e : β ≃ᵐ γ} (h : MeasurePreserving e μb μc) :
     MeasurePreserving (e ∘ g) μa μc ↔ MeasurePreserving g μa μb :=
   by
@@ -110,6 +174,12 @@ protected theorem comp_left_iff {g : α → β} {e : β ≃ᵐ γ} (h : MeasureP
   simp [← Function.comp.assoc e.symm e g]
 #align measure_theory.measure_preserving.comp_left_iff MeasureTheory.MeasurePreserving.comp_left_iff
 
+/- warning: measure_theory.measure_preserving.comp_right_iff -> MeasureTheory.MeasurePreserving.comp_right_iff is a dubious translation:
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+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.comp_right_iff MeasureTheory.MeasurePreserving.comp_right_iffₓ'. -/
 protected theorem comp_right_iff {g : α → β} {e : γ ≃ᵐ α} (h : MeasurePreserving e μc μa) :
     MeasurePreserving (g ∘ e) μc μb ↔ MeasurePreserving g μa μb :=
   by
@@ -118,28 +188,54 @@ protected theorem comp_right_iff {g : α → β} {e : γ ≃ᵐ α} (h : Measure
   simp [Function.comp.assoc g e e.symm]
 #align measure_theory.measure_preserving.comp_right_iff MeasureTheory.MeasurePreserving.comp_right_iff
 
+/- warning: measure_theory.measure_preserving.sigma_finite -> MeasureTheory.MeasurePreserving.sigmaFinite is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : MeasurableSpace.{u2} β] {μa : MeasureTheory.Measure.{u1} α _inst_1} {μb : MeasureTheory.Measure.{u2} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u1, u2} α β _inst_1 _inst_2 f μa μb) -> (forall [_inst_5 : MeasureTheory.SigmaFinite.{u2} β _inst_2 μb], MeasureTheory.SigmaFinite.{u1} α _inst_1 μa)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : MeasurableSpace.{u1} β] {μa : MeasureTheory.Measure.{u2} α _inst_1} {μb : MeasureTheory.Measure.{u1} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f μa μb) -> (forall [_inst_5 : MeasureTheory.SigmaFinite.{u1} β _inst_2 μb], MeasureTheory.SigmaFinite.{u2} α _inst_1 μa)
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.sigma_finite MeasureTheory.MeasurePreserving.sigmaFiniteₓ'. -/
 protected theorem sigmaFinite {f : α → β} (hf : MeasurePreserving f μa μb) [SigmaFinite μb] :
     SigmaFinite μa :=
   SigmaFinite.of_map μa hf.AEMeasurable (by rwa [hf.map_eq])
 #align measure_theory.measure_preserving.sigma_finite MeasureTheory.MeasurePreserving.sigmaFinite
 
+/- warning: measure_theory.measure_preserving.measure_preimage -> MeasureTheory.MeasurePreserving.measure_preimage is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : MeasurableSpace.{u2} β] {μa : MeasureTheory.Measure.{u1} α _inst_1} {μb : MeasureTheory.Measure.{u2} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u1, u2} α β _inst_1 _inst_2 f μa μb) -> (forall {s : Set.{u2} β}, (MeasurableSet.{u2} β _inst_2 s) -> (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) μa (Set.preimage.{u1, u2} α β f s)) (coeFn.{succ u2, succ u2} (MeasureTheory.Measure.{u2} β _inst_2) (fun (_x : MeasureTheory.Measure.{u2} β _inst_2) => (Set.{u2} β) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u2} β _inst_2) μb s)))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : MeasurableSpace.{u1} β] {μa : MeasureTheory.Measure.{u2} α _inst_1} {μb : MeasureTheory.Measure.{u1} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f μa μb) -> (forall {s : Set.{u1} β}, (MeasurableSet.{u1} β _inst_2 s) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α _inst_1 μa) (Set.preimage.{u2, u1} α β f s)) (MeasureTheory.OuterMeasure.measureOf.{u1} β (MeasureTheory.Measure.toOuterMeasure.{u1} β _inst_2 μb) s)))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.measure_preimage MeasureTheory.MeasurePreserving.measure_preimageₓ'. -/
 theorem measure_preimage {f : α → β} (hf : MeasurePreserving f μa μb) {s : Set β}
     (hs : MeasurableSet s) : μa (f ⁻¹' s) = μb s := by rw [← hf.map_eq, map_apply hf.1 hs]
 #align measure_theory.measure_preserving.measure_preimage MeasureTheory.MeasurePreserving.measure_preimage
 
+/- warning: measure_theory.measure_preserving.measure_preimage_emb -> MeasureTheory.MeasurePreserving.measure_preimage_emb is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : MeasurableSpace.{u1} β] {μa : MeasureTheory.Measure.{u2} α _inst_1} {μb : MeasureTheory.Measure.{u1} β _inst_2} {f : α -> β}, (MeasureTheory.MeasurePreserving.{u2, u1} α β _inst_1 _inst_2 f μa μb) -> (MeasurableEmbedding.{u2, u1} α β _inst_1 _inst_2 f) -> (forall (s : Set.{u1} β), Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α _inst_1 μa) (Set.preimage.{u2, u1} α β f s)) (MeasureTheory.OuterMeasure.measureOf.{u1} β (MeasureTheory.Measure.toOuterMeasure.{u1} β _inst_2 μb) s))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.measure_preimage_emb MeasureTheory.MeasurePreserving.measure_preimage_embₓ'. -/
 theorem measure_preimage_emb {f : α → β} (hf : MeasurePreserving f μa μb)
     (hfe : MeasurableEmbedding f) (s : Set β) : μa (f ⁻¹' s) = μb s := by
   rw [← hf.map_eq, hfe.map_apply]
 #align measure_theory.measure_preserving.measure_preimage_emb MeasureTheory.MeasurePreserving.measure_preimage_emb
 
+#print MeasureTheory.MeasurePreserving.iterate /-
 protected theorem iterate {f : α → α} (hf : MeasurePreserving f μa μa) :
     ∀ n, MeasurePreserving (f^[n]) μa μa
   | 0 => MeasurePreserving.id μa
   | n + 1 => (iterate n).comp hf
 #align measure_theory.measure_preserving.iterate MeasureTheory.MeasurePreserving.iterate
+-/
 
 variable {μ : Measure α} {f : α → α} {s : Set α}
 
+/- warning: measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume -> MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {f : α -> α} {s : Set.{u1} α}, (MeasureTheory.MeasurePreserving.{u1, u1} α α _inst_1 _inst_1 f μ μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (forall {n : Nat}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) μ (Set.univ.{u1} α)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat ENNReal (HasLiftT.mk.{1, 1} Nat ENNReal (CoeTCₓ.coe.{1, 1} Nat ENNReal (Nat.castCoe.{0} ENNReal (AddMonoidWithOne.toNatCast.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) n) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) μ s))) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => Exists.{1} Nat (fun (m : Nat) => Exists.{0} (Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) m (Set.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) (fun (H : Membership.Mem.{0, 0} Nat (Set.{0} Nat) (Set.hasMem.{0} Nat) m (Set.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero))) n)) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Nat.iterate.{succ u1} α f m x) s))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {f : α -> α} {s : Set.{u1} α}, (MeasureTheory.MeasurePreserving.{u1, u1} α α _inst_1 _inst_1 f μ μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (forall {n : Nat}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) (Set.univ.{u1} α)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (Nat.cast.{0} ENNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) n) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) s))) -> (Exists.{succ u1} α (fun (x : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (Exists.{1} Nat (fun (m : Nat) => And (Membership.mem.{0, 0} Nat (Set.{0} Nat) (Set.instMembershipSet.{0} Nat) m (Set.Ioo.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)) n)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Nat.iterate.{succ u1} α f m x) s))))))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volumeₓ'. -/
 /-- If `μ univ < n * μ s` and `f` is a map preserving measure `μ`,
 then for some `x ∈ s` and `0 < m < n`, `f^[m] x ∈ s`. -/
 theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f μ μ)
@@ -159,6 +255,12 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
   rwa [← iterate_add_apply, tsub_add_cancel_of_le hlt.le]
 #align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
 
+/- warning: measure_theory.measure_preserving.exists_mem_image_mem -> MeasureTheory.MeasurePreserving.exists_mem_image_mem is a dubious translation:
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+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {f : α -> α} {s : Set.{u1} α} [_inst_5 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 μ], (MeasureTheory.MeasurePreserving.{u1, u1} α α _inst_1 _inst_1 f μ μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (Ne.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} α (fun (x : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (Exists.{1} Nat (fun (m : Nat) => Exists.{0} (Ne.{1} Nat m (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (fun (x._@.Mathlib.Dynamics.Ergodic.MeasurePreserving._hyg.1885 : Ne.{1} Nat m (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Nat.iterate.{succ u1} α f m x) s)))))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure_preserving.exists_mem_image_mem MeasureTheory.MeasurePreserving.exists_mem_image_memₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m «expr ≠ » 0) -/
 /-- A self-map preserving a finite measure is conservative: if `μ s ≠ 0`, then at least one point
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`
@@ -176,6 +278,12 @@ end MeasurePreserving
 
 namespace MeasurableEquiv
 
+/- warning: measure_theory.measurable_equiv.measure_preserving_symm -> MeasureTheory.MeasurableEquiv.measurePreserving_symm is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : MeasurableSpace.{u1} α] [_inst_2 : MeasurableSpace.{u2} β] (μ : MeasureTheory.Measure.{u1} α _inst_1) (e : MeasurableEquiv.{u1, u2} α β _inst_1 _inst_2), MeasureTheory.MeasurePreserving.{u2, u1} β α _inst_2 _inst_1 (coeFn.{max (succ u2) (succ u1), max (succ u2) (succ u1)} (MeasurableEquiv.{u2, u1} β α _inst_2 _inst_1) (fun (_x : MeasurableEquiv.{u2, u1} β α _inst_2 _inst_1) => β -> α) (MeasurableEquiv.hasCoeToFun.{u2, u1} β α _inst_2 _inst_1) (MeasurableEquiv.symm.{u1, u2} α β _inst_1 _inst_2 e)) (MeasureTheory.Measure.map.{u1, u2} α β _inst_2 _inst_1 (coeFn.{max (succ u1) (succ u2), max (succ u1) (succ u2)} (MeasurableEquiv.{u1, u2} α β _inst_1 _inst_2) (fun (_x : MeasurableEquiv.{u1, u2} α β _inst_1 _inst_2) => α -> β) (MeasurableEquiv.hasCoeToFun.{u1, u2} α β _inst_1 _inst_2) e) μ) μ
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : MeasurableSpace.{u2} α] [_inst_2 : MeasurableSpace.{u1} β] (μ : MeasureTheory.Measure.{u2} α _inst_1) (e : MeasurableEquiv.{u2, u1} α β _inst_1 _inst_2), MeasureTheory.MeasurePreserving.{u1, u2} β α _inst_2 _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (MeasurableEquiv.{u1, u2} β α _inst_2 _inst_1) β (fun (_x : β) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : β) => α) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u1, succ u2} (MeasurableEquiv.{u1, u2} β α _inst_2 _inst_1) β α (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u1, succ u2} (MeasurableEquiv.{u1, u2} β α _inst_2 _inst_1) β α (MeasurableEquiv.instEquivLike.{u1, u2} β α _inst_2 _inst_1))) (MeasurableEquiv.symm.{u2, u1} α β _inst_1 _inst_2 e)) (MeasureTheory.Measure.map.{u2, u1} α β _inst_2 _inst_1 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (MeasurableEquiv.{u2, u1} α β _inst_1 _inst_2) α (fun (_x : α) => (fun (x._@.Mathlib.Data.FunLike.Embedding._hyg.19 : α) => β) _x) (EmbeddingLike.toFunLike.{max (succ u2) (succ u1), succ u2, succ u1} (MeasurableEquiv.{u2, u1} α β _inst_1 _inst_2) α β (EquivLike.toEmbeddingLike.{max (succ u2) (succ u1), succ u2, succ u1} (MeasurableEquiv.{u2, u1} α β _inst_1 _inst_2) α β (MeasurableEquiv.instEquivLike.{u2, u1} α β _inst_1 _inst_2))) e) μ) μ
+Case conversion may be inaccurate. Consider using '#align measure_theory.measurable_equiv.measure_preserving_symm MeasureTheory.MeasurableEquiv.measurePreserving_symmₓ'. -/
 theorem measurePreserving_symm (μ : Measure α) (e : α ≃ᵐ β) :
     MeasurePreserving e.symm (map e μ) μ :=
   (e.Measurable.MeasurePreserving μ).symm _

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

@@ -164,8 +164,8 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`
 infinitely many times, see `measure_theory.measure_preserving.conservative` and theorems about
 `measure_theory.conservative`. -/
-theorem exists_mem_image_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
-    (hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _)(_ : m ≠ 0), (f^[m]) x ∈ s :=
+theorem exists_mem_image_mem [FiniteMeasure μ] (hf : MeasurePreserving f μ μ) (hs : MeasurableSet s)
+    (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _)(_ : m ≠ 0), (f^[m]) x ∈ s :=
   by
   rcases ENNReal.exists_nat_mul_gt hs' (measure_ne_top μ (univ : Set α)) with ⟨N, hN⟩
   rcases hf.exists_mem_image_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩

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

@@ -61,9 +61,9 @@ protected theorem id (μ : Measure α) : MeasurePreserving id μ μ :=
   ⟨measurable_id, map_id⟩
 #align measure_theory.measure_preserving.id MeasureTheory.MeasurePreserving.id
 
-protected theorem aeMeasurable {f : α → β} (hf : MeasurePreserving f μa μb) : AeMeasurable f μa :=
-  hf.1.AeMeasurable
-#align measure_theory.measure_preserving.ae_measurable MeasureTheory.MeasurePreserving.aeMeasurable
+protected theorem aEMeasurable {f : α → β} (hf : MeasurePreserving f μa μb) : AEMeasurable f μa :=
+  hf.1.AEMeasurable
+#align measure_theory.measure_preserving.ae_measurable MeasureTheory.MeasurePreserving.aEMeasurable
 
 theorem symm (e : α ≃ᵐ β) {μa : Measure α} {μb : Measure β} (h : MeasurePreserving e μa μb) :
     MeasurePreserving e.symm μb μa :=
@@ -71,26 +71,26 @@ theorem symm (e : α ≃ᵐ β) {μa : Measure α} {μb : Measure β} (h : Measu
     rw [← h.map_eq, map_map e.symm.measurable e.measurable, e.symm_comp_self, map_id]⟩
 #align measure_theory.measure_preserving.symm MeasureTheory.MeasurePreserving.symm
 
-theorem restrictPreimage {f : α → β} (hf : MeasurePreserving f μa μb) {s : Set β}
+theorem restrict_preimage {f : α → β} (hf : MeasurePreserving f μa μb) {s : Set β}
     (hs : MeasurableSet s) : MeasurePreserving f (μa.restrict (f ⁻¹' s)) (μb.restrict s) :=
   ⟨hf.Measurable, by rw [← hf.map_eq, restrict_map hf.measurable hs]⟩
-#align measure_theory.measure_preserving.restrict_preimage MeasureTheory.MeasurePreserving.restrictPreimage
+#align measure_theory.measure_preserving.restrict_preimage MeasureTheory.MeasurePreserving.restrict_preimage
 
-theorem restrictPreimageEmb {f : α → β} (hf : MeasurePreserving f μa μb)
+theorem restrict_preimage_emb {f : α → β} (hf : MeasurePreserving f μa μb)
     (h₂ : MeasurableEmbedding f) (s : Set β) :
     MeasurePreserving f (μa.restrict (f ⁻¹' s)) (μb.restrict s) :=
   ⟨hf.Measurable, by rw [← hf.map_eq, h₂.restrict_map]⟩
-#align measure_theory.measure_preserving.restrict_preimage_emb MeasureTheory.MeasurePreserving.restrictPreimageEmb
+#align measure_theory.measure_preserving.restrict_preimage_emb MeasureTheory.MeasurePreserving.restrict_preimage_emb
 
-theorem restrictImageEmb {f : α → β} (hf : MeasurePreserving f μa μb) (h₂ : MeasurableEmbedding f)
+theorem restrict_image_emb {f : α → β} (hf : MeasurePreserving f μa μb) (h₂ : MeasurableEmbedding f)
     (s : Set α) : MeasurePreserving f (μa.restrict s) (μb.restrict (f '' s)) := by
   simpa only [preimage_image_eq _ h₂.injective] using hf.restrict_preimage_emb h₂ (f '' s)
-#align measure_theory.measure_preserving.restrict_image_emb MeasureTheory.MeasurePreserving.restrictImageEmb
+#align measure_theory.measure_preserving.restrict_image_emb MeasureTheory.MeasurePreserving.restrict_image_emb
 
-theorem aeMeasurable_comp_iff {f : α → β} (hf : MeasurePreserving f μa μb)
-    (h₂ : MeasurableEmbedding f) {g : β → γ} : AeMeasurable (g ∘ f) μa ↔ AeMeasurable g μb := by
+theorem aEMeasurable_comp_iff {f : α → β} (hf : MeasurePreserving f μa μb)
+    (h₂ : MeasurableEmbedding f) {g : β → γ} : AEMeasurable (g ∘ f) μa ↔ AEMeasurable g μb := by
   rw [← hf.map_eq, h₂.ae_measurable_map_iff]
-#align measure_theory.measure_preserving.ae_measurable_comp_iff MeasureTheory.MeasurePreserving.aeMeasurable_comp_iff
+#align measure_theory.measure_preserving.ae_measurable_comp_iff MeasureTheory.MeasurePreserving.aEMeasurable_comp_iff
 
 protected theorem quasiMeasurePreserving {f : α → β} (hf : MeasurePreserving f μa μb) :
     QuasiMeasurePreserving f μa μb :=
@@ -120,7 +120,7 @@ protected theorem comp_right_iff {g : α → β} {e : γ ≃ᵐ α} (h : Measure
 
 protected theorem sigmaFinite {f : α → β} (hf : MeasurePreserving f μa μb) [SigmaFinite μb] :
     SigmaFinite μa :=
-  SigmaFinite.ofMap μa hf.AeMeasurable (by rwa [hf.map_eq])
+  SigmaFinite.of_map μa hf.AEMeasurable (by rwa [hf.map_eq])
 #align measure_theory.measure_preserving.sigma_finite MeasureTheory.MeasurePreserving.sigmaFinite
 
 theorem measure_preimage {f : α → β} (hf : MeasurePreserving f μa μb) {s : Set β}
@@ -176,9 +176,10 @@ end MeasurePreserving
 
 namespace MeasurableEquiv
 
-theorem measurePreservingSymm (μ : Measure α) (e : α ≃ᵐ β) : MeasurePreserving e.symm (map e μ) μ :=
+theorem measurePreserving_symm (μ : Measure α) (e : α ≃ᵐ β) :
+    MeasurePreserving e.symm (map e μ) μ :=
   (e.Measurable.MeasurePreserving μ).symm _
-#align measure_theory.measurable_equiv.measure_preserving_symm MeasureTheory.MeasurableEquiv.measurePreservingSymm
+#align measure_theory.measurable_equiv.measure_preserving_symm MeasureTheory.MeasurableEquiv.measurePreserving_symm
 
 end MeasurableEquiv
 

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

@@ -106,7 +106,7 @@ protected theorem comp_left_iff {g : α → β} {e : β ≃ᵐ γ} (h : MeasureP
     MeasurePreserving (e ∘ g) μa μc ↔ MeasurePreserving g μa μb :=
   by
   refine' ⟨fun hg => _, fun hg => h.comp hg⟩
-  convert (measure_preserving.symm e h).comp hg
+  convert(measure_preserving.symm e h).comp hg
   simp [← Function.comp.assoc e.symm e g]
 #align measure_theory.measure_preserving.comp_left_iff MeasureTheory.MeasurePreserving.comp_left_iff
 

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

@@ -159,7 +159,7 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
   rwa [← iterate_add_apply, tsub_add_cancel_of_le hlt.le]
 #align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (m «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m «expr ≠ » 0) -/
 /-- A self-map preserving a finite measure is conservative: if `μ s ≠ 0`, then at least one point
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`
 infinitely many times, see `measure_theory.measure_preserving.conservative` and theorems about

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

@@ -167,7 +167,7 @@ infinitely many times, see `measure_theory.measure_preserving.conservative` and
 theorem exists_mem_image_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
     (hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _)(_ : m ≠ 0), (f^[m]) x ∈ s :=
   by
-  rcases Ennreal.exists_nat_mul_gt hs' (measure_ne_top μ (univ : Set α)) with ⟨N, hN⟩
+  rcases ENNReal.exists_nat_mul_gt hs' (measure_ne_top μ (univ : Set α)) with ⟨N, hN⟩
   rcases hf.exists_mem_image_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩
   exact ⟨x, hx, m, hm.1.ne', hmx⟩
 #align measure_theory.measure_preserving.exists_mem_image_mem MeasureTheory.MeasurePreserving.exists_mem_image_mem

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

A PR accompanying #12339.

Zulip discussion

@@ -153,7 +153,7 @@ open scoped symmDiff in
 lemma measure_symmDiff_preimage_iterate_le
     (hf : MeasurePreserving f μ μ) (hs : MeasurableSet s) (n : ℕ) :
     μ (s ∆ (f^[n] ⁻¹' s)) ≤ n • μ (s ∆ (f ⁻¹' s)) := by
-  induction' n with n ih; simp
+  induction' n with n ih; · simp
   simp only [add_smul, one_smul, ← n.add_one]
   refine' le_trans (measure_symmDiff_le s (f^[n] ⁻¹' s) (f^[n+1] ⁻¹' s)) (add_le_add ih _)
   replace hs : MeasurableSet (s ∆ (f ⁻¹' s)) := hs.symmDiff <| hf.measurable hs

@@ -181,7 +181,7 @@ theorem exists_mem_iterate_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f
 infinitely many times, see `MeasureTheory.MeasurePreserving.conservative` and theorems about
 `MeasureTheory.Conservative`. -/
 theorem exists_mem_iterate_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
-    (hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ m, m ≠ 0 ∧ f^[m] x ∈ s := by
+    (hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ m ≠ 0, f^[m] x ∈ s := by
   rcases ENNReal.exists_nat_mul_gt hs' (measure_ne_top μ (Set.univ : Set α)) with ⟨N, hN⟩
   rcases hf.exists_mem_iterate_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩
   exact ⟨x, hx, m, hm.1.ne', hmx⟩

Those notations are not scoped whereas the file is very low in the import hierarchy.

@@ -149,6 +149,7 @@ protected theorem iterate {f : α → α} (hf : MeasurePreserving f μa μa) :
 
 variable {μ : Measure α} {f : α → α} {s : Set α}
 
+open scoped symmDiff in
 lemma measure_symmDiff_preimage_iterate_le
     (hf : MeasurePreserving f μ μ) (hs : MeasurableSet s) (n : ℕ) :
     μ (s ∆ (f^[n] ⁻¹' s)) ≤ n • μ (s ∆ (f ⁻¹' s)) := by

See Zulip thread for the discussion.

@@ -155,7 +155,7 @@ lemma measure_symmDiff_preimage_iterate_le
   induction' n with n ih; simp
   simp only [add_smul, one_smul, ← n.add_one]
   refine' le_trans (measure_symmDiff_le s (f^[n] ⁻¹' s) (f^[n+1] ⁻¹' s)) (add_le_add ih _)
-  replace hs : MeasurableSet (s ∆ (f ⁻¹' s)) := hs.symmDiff $ hf.measurable hs
+  replace hs : MeasurableSet (s ∆ (f ⁻¹' s)) := hs.symmDiff <| hf.measurable hs
   rw [iterate_succ', preimage_comp, ← preimage_symmDiff, (hf.iterate n).measure_preimage hs]
 
 /-- If `μ univ < n * μ s` and `f` is a map preserving measure `μ`,

• rename exists_mem_image_mem* to exists_mem_iterate_mem* because there is no Set.image in the statement.
• Add type annotations to a proof. I made these changes to improve readability for a conference talk, so why not make them in the library?

@@ -34,6 +34,7 @@ variable {α β γ δ : Type*} [MeasurableSpace α] [MeasurableSpace β] [Measur
 namespace MeasureTheory
 
 open Measure Function Set
+open scoped BigOperators
 
 variable {μa : Measure α} {μb : Measure β} {μc : Measure γ} {μd : Measure δ}
 
@@ -159,32 +160,31 @@ lemma measure_symmDiff_preimage_iterate_le
 
 /-- If `μ univ < n * μ s` and `f` is a map preserving measure `μ`,
 then for some `x ∈ s` and `0 < m < n`, `f^[m] x ∈ s`. -/
-theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f μ μ)
+theorem exists_mem_iterate_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f μ μ)
     (hs : MeasurableSet s) {n : ℕ} (hvol : μ (Set.univ : Set α) < n * μ s) :
     ∃ x ∈ s, ∃ m ∈ Set.Ioo 0 n, f^[m] x ∈ s := by
-  have A : ∀ m, MeasurableSet (f^[m] ⁻¹' s) := fun m => (hf.iterate m).measurable hs
-  have B : ∀ m, μ (f^[m] ⁻¹' s) = μ s := fun m => (hf.iterate m).measure_preimage hs
-  have : μ (Set.univ : Set α) < (Finset.range n).sum fun m => μ (f^[m] ⁻¹' s) := by
-    simpa only [B, nsmul_eq_mul, Finset.sum_const, Finset.card_range]
-  rcases exists_nonempty_inter_of_measure_univ_lt_sum_measure μ (fun m _ => A m) this with
-    ⟨i, hi, j, hj, hij, x, hxi, hxj⟩
+  have A : ∀ m, MeasurableSet (f^[m] ⁻¹' s) := fun m ↦ (hf.iterate m).measurable hs
+  have B : ∀ m, μ (f^[m] ⁻¹' s) = μ s := fun m ↦ (hf.iterate m).measure_preimage hs
+  have : μ (univ : Set α) < ∑ m in Finset.range n, μ (f^[m] ⁻¹' s) := by simpa [B]
+  obtain ⟨i, hi, j, hj, hij, x, hxi : f^[i] x ∈ s, hxj : f^[j] x ∈ s⟩ :
+      ∃ i < n, ∃ j < n, i ≠ j ∧ (f^[i] ⁻¹' s ∩ f^[j] ⁻¹' s).Nonempty := by
+    simpa using exists_nonempty_inter_of_measure_univ_lt_sum_measure μ (fun m _ ↦ A m) this
   wlog hlt : i < j generalizing i j
   · exact this j hj i hi hij.symm hxj hxi (hij.lt_or_lt.resolve_left hlt)
-  simp only [Set.mem_preimage, Finset.mem_range] at hi hj hxi hxj
-  refine' ⟨f^[i] x, hxi, j - i, ⟨tsub_pos_of_lt hlt, lt_of_le_of_lt (j.sub_le i) hj⟩, _⟩
+  refine ⟨f^[i] x, hxi, j - i, ⟨tsub_pos_of_lt hlt, lt_of_le_of_lt (j.sub_le i) hj⟩, ?_⟩
   rwa [← iterate_add_apply, tsub_add_cancel_of_le hlt.le]
-#align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
+#align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_iterate_mem_of_volume_lt_mul_volume
 
 /-- A self-map preserving a finite measure is conservative: if `μ s ≠ 0`, then at least one point
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`
 infinitely many times, see `MeasureTheory.MeasurePreserving.conservative` and theorems about
 `MeasureTheory.Conservative`. -/
-theorem exists_mem_image_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
-    (hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), f^[m] x ∈ s := by
+theorem exists_mem_iterate_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
+    (hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ m, m ≠ 0 ∧ f^[m] x ∈ s := by
   rcases ENNReal.exists_nat_mul_gt hs' (measure_ne_top μ (Set.univ : Set α)) with ⟨N, hN⟩
-  rcases hf.exists_mem_image_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩
+  rcases hf.exists_mem_iterate_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩
   exact ⟨x, hx, m, hm.1.ne', hmx⟩
-#align measure_theory.measure_preserving.exists_mem_image_mem MeasureTheory.MeasurePreserving.exists_mem_image_mem
+#align measure_theory.measure_preserving.exists_mem_image_mem MeasureTheory.MeasurePreserving.exists_mem_iterate_mem
 
 end MeasurePreserving
 

We prove the formula for the area of a disc

theorem volume_ball (x : EuclideanSpace ℝ (Fin 2)) (r : ℝ) :
    volume (Metric.ball x r) = NNReal.pi * (ENNReal.ofReal r) ^ 2 

and deduce from this, the volume of complex balls

theorem volume_ball (a : ℂ) (r : ℝ) :  
    volume (Metric.ball a r) = NNReal.pi * (ENNReal.ofReal r) ^ 2

Co-authored-by: James Arthur Co-authored-by: Benjamin Davidson Co-authored-by: Andrew Souther

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

@@ -104,6 +104,14 @@ protected theorem comp {g : β → γ} {f : α → β} (hg : MeasurePreserving g
   ⟨hg.1.comp hf.1, by rw [← map_map hg.1 hf.1, hf.2, hg.2]⟩
 #align measure_theory.measure_preserving.comp MeasureTheory.MeasurePreserving.comp
 
+/-- An alias of `MeasureTheory.MeasurePreserving.comp` with a convenient defeq and argument order
+for `MeasurableEquiv` -/
+protected theorem trans {e : α ≃ᵐ β} {e' : β ≃ᵐ γ}
+    {μa : Measure α} {μb : Measure β} {μc : Measure γ}
+    (h : MeasurePreserving e μa μb) (h' : MeasurePreserving e' μb μc) :
+    MeasurePreserving (e.trans e') μa μc :=
+  h'.comp h
+
 protected theorem comp_left_iff {g : α → β} {e : β ≃ᵐ γ} (h : MeasurePreserving e μb μc) :
     MeasurePreserving (e ∘ g) μa μc ↔ MeasurePreserving g μa μb := by
   refine' ⟨fun hg => _, fun hg => h.comp hg⟩

@@ -62,6 +62,11 @@ protected theorem aemeasurable {f : α → β} (hf : MeasurePreserving f μa μb
   hf.1.aemeasurable
 #align measure_theory.measure_preserving.ae_measurable MeasureTheory.MeasurePreserving.aemeasurable
 
+@[nontriviality]
+theorem of_isEmpty [IsEmpty β] (f : α → β) (μa : Measure α) (μb : Measure β) :
+    MeasurePreserving f μa μb :=
+  ⟨measurable_of_subsingleton_codomain _, Subsingleton.elim _ _⟩
+
 theorem symm (e : α ≃ᵐ β) {μa : Measure α} {μb : Measure β} (h : MeasurePreserving e μa μb) :
     MeasurePreserving e.symm μb μa :=
   ⟨e.symm.measurable, by

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

This has nice performance benefits.

@@ -28,7 +28,7 @@ measure preserving map, measure
 -/
 
 
-variable {α β γ δ : Type _} [MeasurableSpace α] [MeasurableSpace β] [MeasurableSpace γ]
+variable {α β γ δ : Type*} [MeasurableSpace α] [MeasurableSpace β] [MeasurableSpace γ]
   [MeasurableSpace δ]
 
 namespace MeasureTheory

Also some minor loosely-related other changes.

@@ -135,6 +135,15 @@ protected theorem iterate {f : α → α} (hf : MeasurePreserving f μa μa) :
 
 variable {μ : Measure α} {f : α → α} {s : Set α}
 
+lemma measure_symmDiff_preimage_iterate_le
+    (hf : MeasurePreserving f μ μ) (hs : MeasurableSet s) (n : ℕ) :
+    μ (s ∆ (f^[n] ⁻¹' s)) ≤ n • μ (s ∆ (f ⁻¹' s)) := by
+  induction' n with n ih; simp
+  simp only [add_smul, one_smul, ← n.add_one]
+  refine' le_trans (measure_symmDiff_le s (f^[n] ⁻¹' s) (f^[n+1] ⁻¹' s)) (add_le_add ih _)
+  replace hs : MeasurableSet (s ∆ (f ⁻¹' s)) := hs.symmDiff $ hf.measurable hs
+  rw [iterate_succ', preimage_comp, ← preimage_symmDiff, (hf.iterate n).measure_preimage hs]
+
 /-- If `μ univ < n * μ s` and `f` is a map preserving measure `μ`,
 then for some `x ∈ s` and `0 < m < n`, `f^[m] x ∈ s`. -/
 theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f μ μ)

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module dynamics.ergodic.measure_preserving
-! leanprover-community/mathlib commit 92ca63f0fb391a9ca5f22d2409a6080e786d99f7
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Measure.AEMeasurable
 
+#align_import dynamics.ergodic.measure_preserving from "leanprover-community/mathlib"@"92ca63f0fb391a9ca5f22d2409a6080e786d99f7"
+
 /-!
 # Measure preserving maps
 

@@ -131,7 +131,7 @@ theorem measure_preimage_emb {f : α → β} (hf : MeasurePreserving f μa μb)
 #align measure_theory.measure_preserving.measure_preimage_emb MeasureTheory.MeasurePreserving.measure_preimage_emb
 
 protected theorem iterate {f : α → α} (hf : MeasurePreserving f μa μa) :
-    ∀ n, MeasurePreserving (f^[n]) μa μa
+    ∀ n, MeasurePreserving f^[n] μa μa
   | 0 => MeasurePreserving.id μa
   | n + 1 => (MeasurePreserving.iterate hf n).comp hf
 #align measure_theory.measure_preserving.iterate MeasureTheory.MeasurePreserving.iterate
@@ -142,7 +142,7 @@ variable {μ : Measure α} {f : α → α} {s : Set α}
 then for some `x ∈ s` and `0 < m < n`, `f^[m] x ∈ s`. -/
 theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f μ μ)
     (hs : MeasurableSet s) {n : ℕ} (hvol : μ (Set.univ : Set α) < n * μ s) :
-    ∃ x ∈ s, ∃ m ∈ Set.Ioo 0 n, (f^[m]) x ∈ s := by
+    ∃ x ∈ s, ∃ m ∈ Set.Ioo 0 n, f^[m] x ∈ s := by
   have A : ∀ m, MeasurableSet (f^[m] ⁻¹' s) := fun m => (hf.iterate m).measurable hs
   have B : ∀ m, μ (f^[m] ⁻¹' s) = μ s := fun m => (hf.iterate m).measure_preimage hs
   have : μ (Set.univ : Set α) < (Finset.range n).sum fun m => μ (f^[m] ⁻¹' s) := by
@@ -152,7 +152,7 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
   wlog hlt : i < j generalizing i j
   · exact this j hj i hi hij.symm hxj hxi (hij.lt_or_lt.resolve_left hlt)
   simp only [Set.mem_preimage, Finset.mem_range] at hi hj hxi hxj
-  refine' ⟨(f^[i]) x, hxi, j - i, ⟨tsub_pos_of_lt hlt, lt_of_le_of_lt (j.sub_le i) hj⟩, _⟩
+  refine' ⟨f^[i] x, hxi, j - i, ⟨tsub_pos_of_lt hlt, lt_of_le_of_lt (j.sub_le i) hj⟩, _⟩
   rwa [← iterate_add_apply, tsub_add_cancel_of_le hlt.le]
 #align measure_theory.measure_preserving.exists_mem_image_mem_of_volume_lt_mul_volume MeasureTheory.MeasurePreserving.exists_mem_image_mem_of_volume_lt_mul_volume
 
@@ -161,7 +161,7 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
 infinitely many times, see `MeasureTheory.MeasurePreserving.conservative` and theorems about
 `MeasureTheory.Conservative`. -/
 theorem exists_mem_image_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
-    (hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), (f^[m]) x ∈ s := by
+    (hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), f^[m] x ∈ s := by
   rcases ENNReal.exists_nat_mul_gt hs' (measure_ne_top μ (Set.univ : Set α)) with ⟨N, hN⟩
   rcases hf.exists_mem_image_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩
   exact ⟨x, hx, m, hm.1.ne', hmx⟩

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

@@ -160,7 +160,7 @@ theorem exists_mem_image_mem_of_volume_lt_mul_volume (hf : MeasurePreserving f 
 `x ∈ s` comes back to `s` under iterations of `f`. Actually, a.e. point of `s` comes back to `s`
 infinitely many times, see `MeasureTheory.MeasurePreserving.conservative` and theorems about
 `MeasureTheory.Conservative`. -/
-theorem exists_mem_image_mem [FiniteMeasure μ] (hf : MeasurePreserving f μ μ)
+theorem exists_mem_image_mem [IsFiniteMeasure μ] (hf : MeasurePreserving f μ μ)
     (hs : MeasurableSet s) (hs' : μ s ≠ 0) : ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), (f^[m]) x ∈ s := by
   rcases ENNReal.exists_nat_mul_gt hs' (measure_ne_top μ (Set.univ : Set α)) with ⟨N, hN⟩
   rcases hf.exists_mem_image_mem_of_volume_lt_mul_volume hs hN with ⟨x, hx, m, hm, hmx⟩

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: MonadMaverick <MonadMaverick@pm.me>