dynamics.ergodic.conservative ⟷ Mathlib.Dynamics.Ergodic.Conservative

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

@@ -54,7 +54,7 @@ namespace MeasureTheory
 open Measure
 
 #print MeasureTheory.Conservative /-
-/- ./././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) -/
 /-- We say that a non-singular (`measure_theory.quasi_measure_preserving`) self-map is
 *conservative* if for any measurable set `s` of positive measure there exists `x ∈ s` such that `x`
 returns back to `s` under some iteration of `f`. -/

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

@@ -93,11 +93,11 @@ after `m` iterations of `f`. -/
 theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : MeasurableSet s)
     (h0 : μ s ≠ 0) : ∃ᶠ m in atTop, μ (s ∩ f^[m] ⁻¹' s) ≠ 0 :=
   by
-  by_contra H; simp only [not_frequently, eventually_at_top, Ne.def, Classical.not_not] at H 
+  by_contra H; simp only [not_frequently, eventually_at_top, Ne.def, Classical.not_not] at H
   rcases H with ⟨N, hN⟩
   induction' N with N ihN
   · apply h0; simpa using hN 0 le_rfl
-  rw [imp_false] at ihN ; push_neg at ihN 
+  rw [imp_false] at ihN; push_neg at ihN
   rcases ihN with ⟨n, hn, hμn⟩
   set T := s ∩ ⋃ n ≥ N + 1, f^[n] ⁻¹' s
   have hT : MeasurableSet T :=
@@ -111,7 +111,7 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
     ⟨x, ⟨⟨hxs, hxn⟩, hxT⟩, m, hm0, ⟨hxms, hxm⟩, hxx⟩
   refine' hxT ⟨hxs, mem_Union₂.2 ⟨n + m, _, _⟩⟩
   · exact add_le_add hn (Nat.one_le_of_lt <| pos_iff_ne_zero.2 hm0)
-  · rwa [Set.mem_preimage, ← iterate_add_apply] at hxm 
+  · rwa [Set.mem_preimage, ← iterate_add_apply] at hxm
 #align measure_theory.conservative.frequently_measure_inter_ne_zero MeasureTheory.Conservative.frequently_measure_inter_ne_zero
 -/
 
@@ -224,7 +224,7 @@ protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative (f^[
   /- We take a point `x ∈ s` such that `f^[k] x ∈ s` for infinitely many values of `k`,
     then we choose two of these values `k < l` such that `k ≡ l [MOD (n + 1)]`.
     Then `f^[k] x ∈ s` and `(f^[n + 1])^[(l - k) / (n + 1)] (f^[k] x) = f^[l] x ∈ s`. -/
-  rw [Nat.frequently_atTop_iff_infinite] at hx 
+  rw [Nat.frequently_atTop_iff_infinite] at hx
   rcases Nat.exists_lt_modEq_of_infinite hx n.succ_pos with ⟨k, hk, l, hl, hkl, hn⟩
   set m := (l - k) / (n + 1)
   have : (n + 1) * m = l - k := by
@@ -232,7 +232,7 @@ protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative (f^[
     exact (Nat.modEq_iff_dvd' hkl.le).1 hn
   refine' ⟨(f^[k]) x, hk, m, _, _⟩
   · intro hm
-    rw [hm, MulZeroClass.mul_zero, eq_comm, tsub_eq_zero_iff_le] at this 
+    rw [hm, MulZeroClass.mul_zero, eq_comm, tsub_eq_zero_iff_le] at this
     exact this.not_lt hkl
   · rwa [← iterate_mul, this, ← iterate_add_apply, tsub_add_cancel_of_le]
     exact hkl.le

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

@@ -61,7 +61,7 @@ returns back to `s` under some iteration of `f`. -/
 structure Conservative (f : α → α)
     (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) extends
     QuasiMeasurePreserving f μ μ : Prop where
-  exists_mem_image_mem :
+  exists_mem_iterate_mem :
     ∀ ⦃s⦄, MeasurableSet s → μ s ≠ 0 → ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), (f^[m]) x ∈ s
 #align measure_theory.conservative MeasureTheory.Conservative
 -/
@@ -70,7 +70,7 @@ structure Conservative (f : α → α)
 /-- A self-map preserving a finite measure is conservative. -/
 protected theorem MeasurePreserving.conservative [IsFiniteMeasure μ] (h : MeasurePreserving f μ μ) :
     Conservative f μ :=
-  ⟨h.QuasiMeasurePreserving, fun s hsm h0 => h.exists_mem_image_mem hsm h0⟩
+  ⟨h.QuasiMeasurePreserving, fun s hsm h0 => h.exists_mem_iterate_mem hsm h0⟩
 #align measure_theory.measure_preserving.conservative MeasureTheory.MeasurePreserving.conservative
 -/
 
@@ -80,7 +80,7 @@ namespace Conservative
 /-- The identity map is conservative w.r.t. any measure. -/
 protected theorem id (μ : Measure α) : Conservative id μ :=
   { to_quasiMeasurePreserving := QuasiMeasurePreserving.id μ
-    exists_mem_image_mem := fun s hs h0 =>
+    exists_mem_iterate_mem := fun s hs h0 =>
       let ⟨x, hx⟩ := nonempty_of_measure_ne_zero h0
       ⟨x, hx, 1, one_ne_zero, hx⟩ }
 #align measure_theory.conservative.id MeasureTheory.Conservative.id

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

@@ -3,9 +3,9 @@ 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.Constructions.BorelSpace.Basic
-import Mathbin.Dynamics.Ergodic.MeasurePreserving
-import Mathbin.Combinatorics.Pigeonhole
+import MeasureTheory.Constructions.BorelSpace.Basic
+import Dynamics.Ergodic.MeasurePreserving
+import Combinatorics.Pigeonhole
 
 #align_import dynamics.ergodic.conservative from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 
@@ -54,7 +54,7 @@ namespace MeasureTheory
 open Measure
 
 #print MeasureTheory.Conservative /-
-/- ./././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) -/
 /-- We say that a non-singular (`measure_theory.quasi_measure_preserving`) self-map is
 *conservative* if for any measurable set `s` of positive measure there exists `x ∈ s` such that `x`
 returns back to `s` under some iteration of `f`. -/

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

@@ -2,16 +2,13 @@
 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.conservative
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
 import Mathbin.Dynamics.Ergodic.MeasurePreserving
 import Mathbin.Combinatorics.Pigeonhole
 
+#align_import dynamics.ergodic.conservative from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # Conservative systems
 
@@ -57,7 +54,7 @@ namespace MeasureTheory
 open Measure
 
 #print MeasureTheory.Conservative /-
-/- ./././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) -/
 /-- We say that a non-singular (`measure_theory.quasi_measure_preserving`) self-map is
 *conservative* if for any measurable set `s` of positive measure there exists `x ∈ s` such that `x`
 returns back to `s` under some iteration of `f`. -/

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

@@ -89,6 +89,7 @@ protected theorem id (μ : Measure α) : Conservative id μ :=
 #align measure_theory.conservative.id MeasureTheory.Conservative.id
 -/
 
+#print MeasureTheory.Conservative.frequently_measure_inter_ne_zero /-
 /-- If `f` is a conservative map and `s` is a measurable set of nonzero measure, then
 for infinitely many values of `m` a positive measure of points `x ∈ s` returns back to `s`
 after `m` iterations of `f`. -/
@@ -115,7 +116,9 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
   · exact add_le_add hn (Nat.one_le_of_lt <| pos_iff_ne_zero.2 hm0)
   · rwa [Set.mem_preimage, ← iterate_add_apply] at hxm 
 #align measure_theory.conservative.frequently_measure_inter_ne_zero MeasureTheory.Conservative.frequently_measure_inter_ne_zero
+-/
 
+#print MeasureTheory.Conservative.exists_gt_measure_inter_ne_zero /-
 /-- If `f` is a conservative map and `s` is a measurable set of nonzero measure, then
 for an arbitrarily large `m` a positive measure of points `x ∈ s` returns back to `s`
 after `m` iterations of `f`. -/
@@ -125,7 +128,9 @@ theorem exists_gt_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurabl
     ((hf.frequently_measure_inter_ne_zero hs h0).and_eventually (eventually_gt_atTop N)).exists
   ⟨m, hmN, hm⟩
 #align measure_theory.conservative.exists_gt_measure_inter_ne_zero MeasureTheory.Conservative.exists_gt_measure_inter_ne_zero
+-/
 
+#print MeasureTheory.Conservative.measure_mem_forall_ge_image_not_mem_eq_zero /-
 /-- Poincaré recurrence theorem: given a conservative map `f` and a measurable set `s`, the set
 of points `x ∈ s` such that `x` does not return to `s` after `≥ n` iterations has measure zero. -/
 theorem measure_mem_forall_ge_image_not_mem_eq_zero (hf : Conservative f μ) (hs : MeasurableSet s)
@@ -141,6 +146,7 @@ theorem measure_mem_forall_ge_image_not_mem_eq_zero (hf : Conservative f μ) (hs
   rcases nonempty_of_measure_ne_zero hm with ⟨x, ⟨hxs, hxn⟩, hxm, -⟩
   exact hxn m hmn.lt.le hxm
 #align measure_theory.conservative.measure_mem_forall_ge_image_not_mem_eq_zero MeasureTheory.Conservative.measure_mem_forall_ge_image_not_mem_eq_zero
+-/
 
 #print MeasureTheory.Conservative.ae_mem_imp_frequently_image_mem /-
 /-- Poincaré recurrence theorem: given a conservative map `f` and a measurable set `s`,
@@ -155,15 +161,19 @@ theorem ae_mem_imp_frequently_image_mem (hf : Conservative f μ) (hs : Measurabl
 #align measure_theory.conservative.ae_mem_imp_frequently_image_mem MeasureTheory.Conservative.ae_mem_imp_frequently_image_mem
 -/
 
+#print MeasureTheory.Conservative.inter_frequently_image_mem_ae_eq /-
 theorem inter_frequently_image_mem_ae_eq (hf : Conservative f μ) (hs : MeasurableSet s) :
     (s ∩ {x | ∃ᶠ n in atTop, (f^[n]) x ∈ s} : Set α) =ᵐ[μ] s :=
   inter_eventuallyEq_left.2 <| hf.ae_mem_imp_frequently_image_mem hs
 #align measure_theory.conservative.inter_frequently_image_mem_ae_eq MeasureTheory.Conservative.inter_frequently_image_mem_ae_eq
+-/
 
+#print MeasureTheory.Conservative.measure_inter_frequently_image_mem_eq /-
 theorem measure_inter_frequently_image_mem_eq (hf : Conservative f μ) (hs : MeasurableSet s) :
     μ (s ∩ {x | ∃ᶠ n in atTop, (f^[n]) x ∈ s}) = μ s :=
   measure_congr (hf.inter_frequently_image_mem_ae_eq hs)
 #align measure_theory.conservative.measure_inter_frequently_image_mem_eq MeasureTheory.Conservative.measure_inter_frequently_image_mem_eq
+-/
 
 #print MeasureTheory.Conservative.ae_forall_image_mem_imp_frequently_image_mem /-
 /-- Poincaré recurrence theorem: if `f` is a conservative dynamical system and `s` is a measurable
@@ -180,6 +190,7 @@ theorem ae_forall_image_mem_imp_frequently_image_mem (hf : Conservative f μ)
 #align measure_theory.conservative.ae_forall_image_mem_imp_frequently_image_mem MeasureTheory.Conservative.ae_forall_image_mem_imp_frequently_image_mem
 -/
 
+#print MeasureTheory.Conservative.frequently_ae_mem_and_frequently_image_mem /-
 /-- If `f` is a conservative self-map and `s` is a measurable set of positive measure, then
 `μ.ae`-frequently we have `x ∈ s` and `s` returns to `s` under infinitely many iterations of `f`. -/
 theorem frequently_ae_mem_and_frequently_image_mem (hf : Conservative f μ) (hs : MeasurableSet s)
@@ -187,6 +198,7 @@ theorem frequently_ae_mem_and_frequently_image_mem (hf : Conservative f μ) (hs
   ((frequently_ae_mem_iff.2 h0).and_eventually (hf.ae_mem_imp_frequently_image_mem hs)).mono
     fun x hx => ⟨hx.1, hx.2 hx.1⟩
 #align measure_theory.conservative.frequently_ae_mem_and_frequently_image_mem MeasureTheory.Conservative.frequently_ae_mem_and_frequently_image_mem
+-/
 
 #print MeasureTheory.Conservative.ae_frequently_mem_of_mem_nhds /-
 /-- Poincaré recurrence theorem. Let `f : α → α` be a conservative dynamical system on a topological

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

@@ -57,7 +57,7 @@ namespace MeasureTheory
 open Measure
 
 #print MeasureTheory.Conservative /-
-/- ./././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) -/
 /-- We say that a non-singular (`measure_theory.quasi_measure_preserving`) self-map is
 *conservative* if for any measurable set `s` of positive measure there exists `x ∈ s` such that `x`
 returns back to `s` under some iteration of `f`. -/

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

@@ -71,7 +71,7 @@ structure Conservative (f : α → α)
 
 #print MeasureTheory.MeasurePreserving.conservative /-
 /-- A self-map preserving a finite measure is conservative. -/
-protected theorem MeasurePreserving.conservative [FiniteMeasure μ] (h : MeasurePreserving f μ μ) :
+protected theorem MeasurePreserving.conservative [IsFiniteMeasure μ] (h : MeasurePreserving f μ μ) :
     Conservative f μ :=
   ⟨h.QuasiMeasurePreserving, fun s hsm h0 => h.exists_mem_image_mem hsm h0⟩
 #align measure_theory.measure_preserving.conservative MeasureTheory.MeasurePreserving.conservative
@@ -99,14 +99,14 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
   rcases H with ⟨N, hN⟩
   induction' N with N ihN
   · apply h0; simpa using hN 0 le_rfl
-  rw [imp_false] at ihN ; push_neg  at ihN 
+  rw [imp_false] at ihN ; push_neg at ihN 
   rcases ihN with ⟨n, hn, hμn⟩
   set T := s ∩ ⋃ n ≥ N + 1, f^[n] ⁻¹' s
   have hT : MeasurableSet T :=
     hs.inter (MeasurableSet.biUnion (to_countable _) fun _ _ => hf.measurable.iterate _ hs)
   have hμT : μ T = 0 :=
     by
-    convert(measure_bUnion_null_iff <| to_countable _).2 hN
+    convert (measure_bUnion_null_iff <| to_countable _).2 hN
     rw [← inter_Union₂]; rfl
   have : μ ((s ∩ f^[n] ⁻¹' s) \ T) ≠ 0 := by rwa [measure_diff_null hμT]
   rcases hf.exists_mem_image_mem ((hs.inter (hf.measurable.iterate n hs)).diffₓ hT) this with
@@ -129,10 +129,10 @@ theorem exists_gt_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurabl
 /-- Poincaré recurrence theorem: given a conservative map `f` and a measurable set `s`, the set
 of points `x ∈ s` such that `x` does not return to `s` after `≥ n` iterations has measure zero. -/
 theorem measure_mem_forall_ge_image_not_mem_eq_zero (hf : Conservative f μ) (hs : MeasurableSet s)
-    (n : ℕ) : μ ({ x ∈ s | ∀ m ≥ n, (f^[m]) x ∉ s }) = 0 :=
+    (n : ℕ) : μ ({x ∈ s | ∀ m ≥ n, (f^[m]) x ∉ s}) = 0 :=
   by
   by_contra H
-  have : MeasurableSet (s ∩ { x | ∀ m ≥ n, (f^[m]) x ∉ s }) :=
+  have : MeasurableSet (s ∩ {x | ∀ m ≥ n, (f^[m]) x ∉ s}) :=
     by
     simp only [set_of_forall, ← compl_set_of]
     exact
@@ -156,12 +156,12 @@ theorem ae_mem_imp_frequently_image_mem (hf : Conservative f μ) (hs : Measurabl
 -/
 
 theorem inter_frequently_image_mem_ae_eq (hf : Conservative f μ) (hs : MeasurableSet s) :
-    (s ∩ { x | ∃ᶠ n in atTop, (f^[n]) x ∈ s } : Set α) =ᵐ[μ] s :=
+    (s ∩ {x | ∃ᶠ n in atTop, (f^[n]) x ∈ s} : Set α) =ᵐ[μ] s :=
   inter_eventuallyEq_left.2 <| hf.ae_mem_imp_frequently_image_mem hs
 #align measure_theory.conservative.inter_frequently_image_mem_ae_eq MeasureTheory.Conservative.inter_frequently_image_mem_ae_eq
 
 theorem measure_inter_frequently_image_mem_eq (hf : Conservative f μ) (hs : MeasurableSet s) :
-    μ (s ∩ { x | ∃ᶠ n in atTop, (f^[n]) x ∈ s }) = μ s :=
+    μ (s ∩ {x | ∃ᶠ n in atTop, (f^[n]) x ∈ s}) = μ s :=
   measure_congr (hf.inter_frequently_image_mem_ae_eq hs)
 #align measure_theory.conservative.measure_inter_frequently_image_mem_eq MeasureTheory.Conservative.measure_inter_frequently_image_mem_eq
 

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

@@ -62,10 +62,10 @@ open Measure
 *conservative* if for any measurable set `s` of positive measure there exists `x ∈ s` such that `x`
 returns back to `s` under some iteration of `f`. -/
 structure Conservative (f : α → α)
-  (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) extends
-  QuasiMeasurePreserving f μ μ : Prop where
+    (μ : Measure α := by exact MeasureTheory.MeasureSpace.volume) extends
+    QuasiMeasurePreserving f μ μ : Prop where
   exists_mem_image_mem :
-    ∀ ⦃s⦄, MeasurableSet s → μ s ≠ 0 → ∃ x ∈ s, ∃ (m : _)(_ : m ≠ 0), (f^[m]) x ∈ s
+    ∀ ⦃s⦄, MeasurableSet s → μ s ≠ 0 → ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), (f^[m]) x ∈ s
 #align measure_theory.conservative MeasureTheory.Conservative
 -/
 
@@ -95,11 +95,11 @@ after `m` iterations of `f`. -/
 theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : MeasurableSet s)
     (h0 : μ s ≠ 0) : ∃ᶠ m in atTop, μ (s ∩ f^[m] ⁻¹' s) ≠ 0 :=
   by
-  by_contra H; simp only [not_frequently, eventually_at_top, Ne.def, Classical.not_not] at H
+  by_contra H; simp only [not_frequently, eventually_at_top, Ne.def, Classical.not_not] at H 
   rcases H with ⟨N, hN⟩
   induction' N with N ihN
   · apply h0; simpa using hN 0 le_rfl
-  rw [imp_false] at ihN; push_neg  at ihN
+  rw [imp_false] at ihN ; push_neg  at ihN 
   rcases ihN with ⟨n, hn, hμn⟩
   set T := s ∩ ⋃ n ≥ N + 1, f^[n] ⁻¹' s
   have hT : MeasurableSet T :=
@@ -113,7 +113,7 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
     ⟨x, ⟨⟨hxs, hxn⟩, hxT⟩, m, hm0, ⟨hxms, hxm⟩, hxx⟩
   refine' hxT ⟨hxs, mem_Union₂.2 ⟨n + m, _, _⟩⟩
   · exact add_le_add hn (Nat.one_le_of_lt <| pos_iff_ne_zero.2 hm0)
-  · rwa [Set.mem_preimage, ← iterate_add_apply] at hxm
+  · rwa [Set.mem_preimage, ← iterate_add_apply] at hxm 
 #align measure_theory.conservative.frequently_measure_inter_ne_zero MeasureTheory.Conservative.frequently_measure_inter_ne_zero
 
 /-- If `f` is a conservative map and `s` is a measurable set of nonzero measure, then
@@ -215,7 +215,7 @@ protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative (f^[
   /- We take a point `x ∈ s` such that `f^[k] x ∈ s` for infinitely many values of `k`,
     then we choose two of these values `k < l` such that `k ≡ l [MOD (n + 1)]`.
     Then `f^[k] x ∈ s` and `(f^[n + 1])^[(l - k) / (n + 1)] (f^[k] x) = f^[l] x ∈ s`. -/
-  rw [Nat.frequently_atTop_iff_infinite] at hx
+  rw [Nat.frequently_atTop_iff_infinite] at hx 
   rcases Nat.exists_lt_modEq_of_infinite hx n.succ_pos with ⟨k, hk, l, hl, hkl, hn⟩
   set m := (l - k) / (n + 1)
   have : (n + 1) * m = l - k := by
@@ -223,7 +223,7 @@ protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative (f^[
     exact (Nat.modEq_iff_dvd' hkl.le).1 hn
   refine' ⟨(f^[k]) x, hk, m, _, _⟩
   · intro hm
-    rw [hm, MulZeroClass.mul_zero, eq_comm, tsub_eq_zero_iff_le] at this
+    rw [hm, MulZeroClass.mul_zero, eq_comm, tsub_eq_zero_iff_le] at this 
     exact this.not_lt hkl
   · rwa [← iterate_mul, this, ← iterate_add_apply, tsub_add_cancel_of_le]
     exact hkl.le

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

@@ -48,7 +48,7 @@ noncomputable section
 
 open Classical Set Filter MeasureTheory Finset Function TopologicalSpace
 
-open Classical Topology
+open scoped Classical Topology
 
 variable {ι : Type _} {α : Type _} [MeasurableSpace α] {f : α → α} {s : Set α} {μ : Measure α}
 

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

@@ -89,12 +89,6 @@ protected theorem id (μ : Measure α) : Conservative id μ :=
 #align measure_theory.conservative.id MeasureTheory.Conservative.id
 -/
 
-/- warning: measure_theory.conservative.frequently_measure_inter_ne_zero -> MeasureTheory.Conservative.frequently_measure_inter_ne_zero is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.frequently_measure_inter_ne_zero MeasureTheory.Conservative.frequently_measure_inter_ne_zeroₓ'. -/
 /-- If `f` is a conservative map and `s` is a measurable set of nonzero measure, then
 for infinitely many values of `m` a positive measure of points `x ∈ s` returns back to `s`
 after `m` iterations of `f`. -/
@@ -122,12 +116,6 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
   · rwa [Set.mem_preimage, ← iterate_add_apply] at hxm
 #align measure_theory.conservative.frequently_measure_inter_ne_zero MeasureTheory.Conservative.frequently_measure_inter_ne_zero
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.exists_gt_measure_inter_ne_zero MeasureTheory.Conservative.exists_gt_measure_inter_ne_zeroₓ'. -/
 /-- If `f` is a conservative map and `s` is a measurable set of nonzero measure, then
 for an arbitrarily large `m` a positive measure of points `x ∈ s` returns back to `s`
 after `m` iterations of `f`. -/
@@ -138,12 +126,6 @@ theorem exists_gt_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurabl
   ⟨m, hmN, hm⟩
 #align measure_theory.conservative.exists_gt_measure_inter_ne_zero MeasureTheory.Conservative.exists_gt_measure_inter_ne_zero
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.measure_mem_forall_ge_image_not_mem_eq_zero MeasureTheory.Conservative.measure_mem_forall_ge_image_not_mem_eq_zeroₓ'. -/
 /-- Poincaré recurrence theorem: given a conservative map `f` and a measurable set `s`, the set
 of points `x ∈ s` such that `x` does not return to `s` after `≥ n` iterations has measure zero. -/
 theorem measure_mem_forall_ge_image_not_mem_eq_zero (hf : Conservative f μ) (hs : MeasurableSet s)
@@ -173,23 +155,11 @@ theorem ae_mem_imp_frequently_image_mem (hf : Conservative f μ) (hs : Measurabl
 #align measure_theory.conservative.ae_mem_imp_frequently_image_mem MeasureTheory.Conservative.ae_mem_imp_frequently_image_mem
 -/
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.inter_frequently_image_mem_ae_eq MeasureTheory.Conservative.inter_frequently_image_mem_ae_eqₓ'. -/
 theorem inter_frequently_image_mem_ae_eq (hf : Conservative f μ) (hs : MeasurableSet s) :
     (s ∩ { x | ∃ᶠ n in atTop, (f^[n]) x ∈ s } : Set α) =ᵐ[μ] s :=
   inter_eventuallyEq_left.2 <| hf.ae_mem_imp_frequently_image_mem hs
 #align measure_theory.conservative.inter_frequently_image_mem_ae_eq MeasureTheory.Conservative.inter_frequently_image_mem_ae_eq
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.measure_inter_frequently_image_mem_eq MeasureTheory.Conservative.measure_inter_frequently_image_mem_eqₓ'. -/
 theorem measure_inter_frequently_image_mem_eq (hf : Conservative f μ) (hs : MeasurableSet s) :
     μ (s ∩ { x | ∃ᶠ n in atTop, (f^[n]) x ∈ s }) = μ s :=
   measure_congr (hf.inter_frequently_image_mem_ae_eq hs)
@@ -210,12 +180,6 @@ theorem ae_forall_image_mem_imp_frequently_image_mem (hf : Conservative f μ)
 #align measure_theory.conservative.ae_forall_image_mem_imp_frequently_image_mem MeasureTheory.Conservative.ae_forall_image_mem_imp_frequently_image_mem
 -/
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.frequently_ae_mem_and_frequently_image_mem MeasureTheory.Conservative.frequently_ae_mem_and_frequently_image_memₓ'. -/
 /-- If `f` is a conservative self-map and `s` is a measurable set of positive measure, then
 `μ.ae`-frequently we have `x ∈ s` and `s` returns to `s` under infinitely many iterations of `f`. -/
 theorem frequently_ae_mem_and_frequently_image_mem (hf : Conservative f μ) (hs : MeasurableSet s)

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

@@ -101,14 +101,11 @@ after `m` iterations of `f`. -/
 theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : MeasurableSet s)
     (h0 : μ s ≠ 0) : ∃ᶠ m in atTop, μ (s ∩ f^[m] ⁻¹' s) ≠ 0 :=
   by
-  by_contra H
-  simp only [not_frequently, eventually_at_top, Ne.def, Classical.not_not] at H
+  by_contra H; simp only [not_frequently, eventually_at_top, Ne.def, Classical.not_not] at H
   rcases H with ⟨N, hN⟩
   induction' N with N ihN
-  · apply h0
-    simpa using hN 0 le_rfl
-  rw [imp_false] at ihN
-  push_neg  at ihN
+  · apply h0; simpa using hN 0 le_rfl
+  rw [imp_false] at ihN; push_neg  at ihN
   rcases ihN with ⟨n, hn, hμn⟩
   set T := s ∩ ⋃ n ≥ N + 1, f^[n] ⁻¹' s
   have hT : MeasurableSet T :=
@@ -116,8 +113,7 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
   have hμT : μ T = 0 :=
     by
     convert(measure_bUnion_null_iff <| to_countable _).2 hN
-    rw [← inter_Union₂]
-    rfl
+    rw [← inter_Union₂]; rfl
   have : μ ((s ∩ f^[n] ⁻¹' s) \ T) ≠ 0 := by rwa [measure_diff_null hμT]
   rcases hf.exists_mem_image_mem ((hs.inter (hf.measurable.iterate n hs)).diffₓ hT) this with
     ⟨x, ⟨⟨hxs, hxn⟩, hxT⟩, m, hm0, ⟨hxms, hxm⟩, hxx⟩
@@ -248,8 +244,7 @@ theorem ae_frequently_mem_of_mem_nhds [TopologicalSpace α] [SecondCountableTopo
 /-- Iteration of a conservative system is a conservative system. -/
 protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative (f^[n]) μ :=
   by
-  cases n
-  · exact conservative.id μ
+  cases n; · exact conservative.id μ
   -- Discharge the trivial case `n = 0`
   refine' ⟨hf.1.iterate _, fun s hs hs0 => _⟩
   rcases(hf.frequently_ae_mem_and_frequently_image_mem hs hs0).exists with ⟨x, hxs, hx⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -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.conservative
-! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.Combinatorics.Pigeonhole
 /-!
 # Conservative systems
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define `f : α → α` to be a *conservative* system w.r.t a measure `μ` if `f` is
 non-singular (`measure_theory.quasi_measure_preserving`) and for every measurable set `s` of
 positive measure at least one point `x ∈ s` returns back to `s` after some number of iterations of

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

@@ -53,6 +53,7 @@ namespace MeasureTheory
 
 open Measure
 
+#print MeasureTheory.Conservative /-
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m «expr ≠ » 0) -/
 /-- We say that a non-singular (`measure_theory.quasi_measure_preserving`) self-map is
 *conservative* if for any measurable set `s` of positive measure there exists `x ∈ s` such that `x`
@@ -63,15 +64,19 @@ structure Conservative (f : α → α)
   exists_mem_image_mem :
     ∀ ⦃s⦄, MeasurableSet s → μ s ≠ 0 → ∃ x ∈ s, ∃ (m : _)(_ : m ≠ 0), (f^[m]) x ∈ s
 #align measure_theory.conservative MeasureTheory.Conservative
+-/
 
+#print MeasureTheory.MeasurePreserving.conservative /-
 /-- A self-map preserving a finite measure is conservative. -/
 protected theorem MeasurePreserving.conservative [FiniteMeasure μ] (h : MeasurePreserving f μ μ) :
     Conservative f μ :=
   ⟨h.QuasiMeasurePreserving, fun s hsm h0 => h.exists_mem_image_mem hsm h0⟩
 #align measure_theory.measure_preserving.conservative MeasureTheory.MeasurePreserving.conservative
+-/
 
 namespace Conservative
 
+#print MeasureTheory.Conservative.id /-
 /-- The identity map is conservative w.r.t. any measure. -/
 protected theorem id (μ : Measure α) : Conservative id μ :=
   { to_quasiMeasurePreserving := QuasiMeasurePreserving.id μ
@@ -79,7 +84,14 @@ protected theorem id (μ : Measure α) : Conservative id μ :=
       let ⟨x, hx⟩ := nonempty_of_measure_ne_zero h0
       ⟨x, hx, 1, one_ne_zero, hx⟩ }
 #align measure_theory.conservative.id MeasureTheory.Conservative.id
+-/
 
+/- warning: measure_theory.conservative.frequently_measure_inter_ne_zero -> MeasureTheory.Conservative.frequently_measure_inter_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (Ne.{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) μ s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Filter.Frequently.{0} Nat (fun (m : Nat) => Ne.{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) μ (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.preimage.{u1, u1} α α (Nat.iterate.{succ u1} α f m) s))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f 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))) -> (Filter.Frequently.{0} Nat (fun (m : Nat) => Ne.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.preimage.{u1, u1} α α (Nat.iterate.{succ u1} α f m) s))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))
+Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.frequently_measure_inter_ne_zero MeasureTheory.Conservative.frequently_measure_inter_ne_zeroₓ'. -/
 /-- If `f` is a conservative map and `s` is a measurable set of nonzero measure, then
 for infinitely many values of `m` a positive measure of points `x ∈ s` returns back to `s`
 after `m` iterations of `f`. -/
@@ -111,6 +123,12 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
   · rwa [Set.mem_preimage, ← iterate_add_apply] at hxm
 #align measure_theory.conservative.frequently_measure_inter_ne_zero MeasureTheory.Conservative.frequently_measure_inter_ne_zero
 
+/- warning: measure_theory.conservative.exists_gt_measure_inter_ne_zero -> MeasureTheory.Conservative.exists_gt_measure_inter_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (Ne.{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) μ s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (N : Nat), Exists.{1} Nat (fun (m : Nat) => Exists.{0} (GT.gt.{0} Nat Nat.hasLt m N) (fun (H : GT.gt.{0} Nat Nat.hasLt m N) => Ne.{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) μ (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Set.preimage.{u1, u1} α α (Nat.iterate.{succ u1} α f m) s))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f 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))) -> (forall (N : Nat), Exists.{1} Nat (fun (m : Nat) => And (GT.gt.{0} Nat instLTNat m N) (Ne.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Set.preimage.{u1, u1} α α (Nat.iterate.{succ u1} α f m) s))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))))
+Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.exists_gt_measure_inter_ne_zero MeasureTheory.Conservative.exists_gt_measure_inter_ne_zeroₓ'. -/
 /-- If `f` is a conservative map and `s` is a measurable set of nonzero measure, then
 for an arbitrarily large `m` a positive measure of points `x ∈ s` returns back to `s`
 after `m` iterations of `f`. -/
@@ -121,6 +139,12 @@ theorem exists_gt_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurabl
   ⟨m, hmN, hm⟩
 #align measure_theory.conservative.exists_gt_measure_inter_ne_zero MeasureTheory.Conservative.exists_gt_measure_inter_ne_zero
 
+/- warning: measure_theory.conservative.measure_mem_forall_ge_image_not_mem_eq_zero -> MeasureTheory.Conservative.measure_mem_forall_ge_image_not_mem_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (forall (n : Nat), 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) μ (Sep.sep.{u1, u1} α (Set.{u1} α) (Set.hasSep.{u1} α) (fun (x : α) => forall (m : Nat), (GE.ge.{0} Nat Nat.hasLe m n) -> (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Nat.iterate.{succ u1} α f m x) s))) s)) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (forall (n : Nat), Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) (setOf.{u1} α (fun (x : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (forall (m : Nat), (GE.ge.{0} Nat instLENat m n) -> (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Nat.iterate.{succ u1} α f m x) s)))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.measure_mem_forall_ge_image_not_mem_eq_zero MeasureTheory.Conservative.measure_mem_forall_ge_image_not_mem_eq_zeroₓ'. -/
 /-- Poincaré recurrence theorem: given a conservative map `f` and a measurable set `s`, the set
 of points `x ∈ s` such that `x` does not return to `s` after `≥ n` iterations has measure zero. -/
 theorem measure_mem_forall_ge_image_not_mem_eq_zero (hf : Conservative f μ) (hs : MeasurableSet s)
@@ -137,6 +161,7 @@ theorem measure_mem_forall_ge_image_not_mem_eq_zero (hf : Conservative f μ) (hs
   exact hxn m hmn.lt.le hxm
 #align measure_theory.conservative.measure_mem_forall_ge_image_not_mem_eq_zero MeasureTheory.Conservative.measure_mem_forall_ge_image_not_mem_eq_zero
 
+#print MeasureTheory.Conservative.ae_mem_imp_frequently_image_mem /-
 /-- Poincaré recurrence theorem: given a conservative map `f` and a measurable set `s`,
 almost every point `x ∈ s` returns back to `s` infinitely many times. -/
 theorem ae_mem_imp_frequently_image_mem (hf : Conservative f μ) (hs : MeasurableSet s) :
@@ -147,17 +172,31 @@ theorem ae_mem_imp_frequently_image_mem (hf : Conservative f μ) (hs : Measurabl
   filter_upwards [measure_zero_iff_ae_nmem.1 (hf.measure_mem_forall_ge_image_not_mem_eq_zero hs n)]
   simp
 #align measure_theory.conservative.ae_mem_imp_frequently_image_mem MeasureTheory.Conservative.ae_mem_imp_frequently_image_mem
+-/
 
+/- warning: measure_theory.conservative.inter_frequently_image_mem_ae_eq -> MeasureTheory.Conservative.inter_frequently_image_mem_ae_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (Filter.EventuallyEq.{u1, 0} α Prop (MeasureTheory.Measure.ae.{u1} α _inst_1 μ) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (setOf.{u1} α (fun (x : α) => Filter.Frequently.{0} Nat (fun (n : Nat) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Nat.iterate.{succ u1} α f n x) s) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))))))) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (Filter.EventuallyEq.{u1, 0} α Prop (MeasureTheory.Measure.ae.{u1} α _inst_1 μ) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (setOf.{u1} α (fun (x : α) => Filter.Frequently.{0} Nat (fun (n : Nat) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Nat.iterate.{succ u1} α f n x) s) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)))))) s)
+Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.inter_frequently_image_mem_ae_eq MeasureTheory.Conservative.inter_frequently_image_mem_ae_eqₓ'. -/
 theorem inter_frequently_image_mem_ae_eq (hf : Conservative f μ) (hs : MeasurableSet s) :
     (s ∩ { x | ∃ᶠ n in atTop, (f^[n]) x ∈ s } : Set α) =ᵐ[μ] s :=
   inter_eventuallyEq_left.2 <| hf.ae_mem_imp_frequently_image_mem hs
 #align measure_theory.conservative.inter_frequently_image_mem_ae_eq MeasureTheory.Conservative.inter_frequently_image_mem_ae_eq
 
+/- warning: measure_theory.conservative.measure_inter_frequently_image_mem_eq -> MeasureTheory.Conservative.measure_inter_frequently_image_mem_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f μ) -> (MeasurableSet.{u1} α _inst_1 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) μ (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (setOf.{u1} α (fun (x : α) => Filter.Frequently.{0} Nat (fun (n : Nat) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Nat.iterate.{succ u1} α f n x) s) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))))) (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))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (setOf.{u1} α (fun (x : α) => Filter.Frequently.{0} Nat (fun (n : Nat) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Nat.iterate.{succ u1} α f n x) s) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) s))
+Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.measure_inter_frequently_image_mem_eq MeasureTheory.Conservative.measure_inter_frequently_image_mem_eqₓ'. -/
 theorem measure_inter_frequently_image_mem_eq (hf : Conservative f μ) (hs : MeasurableSet s) :
     μ (s ∩ { x | ∃ᶠ n in atTop, (f^[n]) x ∈ s }) = μ s :=
   measure_congr (hf.inter_frequently_image_mem_ae_eq hs)
 #align measure_theory.conservative.measure_inter_frequently_image_mem_eq MeasureTheory.Conservative.measure_inter_frequently_image_mem_eq
 
+#print MeasureTheory.Conservative.ae_forall_image_mem_imp_frequently_image_mem /-
 /-- Poincaré recurrence theorem: if `f` is a conservative dynamical system and `s` is a measurable
 set, then for `μ`-a.e. `x`, if the orbit of `x` visits `s` at least once, then it visits `s`
 infinitely many times.  -/
@@ -170,7 +209,14 @@ theorem ae_forall_image_mem_imp_frequently_image_mem (hf : Conservative f μ)
   refine' (hx hk).mono fun n hn => _
   rwa [add_comm, iterate_add_apply]
 #align measure_theory.conservative.ae_forall_image_mem_imp_frequently_image_mem MeasureTheory.Conservative.ae_forall_image_mem_imp_frequently_image_mem
+-/
 
+/- warning: measure_theory.conservative.frequently_ae_mem_and_frequently_image_mem -> MeasureTheory.Conservative.frequently_ae_mem_and_frequently_image_mem is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f μ) -> (MeasurableSet.{u1} α _inst_1 s) -> (Ne.{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) μ s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Filter.Frequently.{u1} α (fun (x : α) => And (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (Filter.Frequently.{0} Nat (fun (n : Nat) => Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) (Nat.iterate.{succ u1} α f n x) s) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))))) (MeasureTheory.Measure.ae.{u1} α _inst_1 μ))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {f : α -> α} {s : Set.{u1} α} {μ : MeasureTheory.Measure.{u1} α _inst_1}, (MeasureTheory.Conservative.{u1} α _inst_1 f 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))) -> (Filter.Frequently.{u1} α (fun (x : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (Filter.Frequently.{0} Nat (fun (n : Nat) => Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) (Nat.iterate.{succ u1} α f n x) s) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))))) (MeasureTheory.Measure.ae.{u1} α _inst_1 μ))
+Case conversion may be inaccurate. Consider using '#align measure_theory.conservative.frequently_ae_mem_and_frequently_image_mem MeasureTheory.Conservative.frequently_ae_mem_and_frequently_image_memₓ'. -/
 /-- If `f` is a conservative self-map and `s` is a measurable set of positive measure, then
 `μ.ae`-frequently we have `x ∈ s` and `s` returns to `s` under infinitely many iterations of `f`. -/
 theorem frequently_ae_mem_and_frequently_image_mem (hf : Conservative f μ) (hs : MeasurableSet s)
@@ -179,6 +225,7 @@ theorem frequently_ae_mem_and_frequently_image_mem (hf : Conservative f μ) (hs
     fun x hx => ⟨hx.1, hx.2 hx.1⟩
 #align measure_theory.conservative.frequently_ae_mem_and_frequently_image_mem MeasureTheory.Conservative.frequently_ae_mem_and_frequently_image_mem
 
+#print MeasureTheory.Conservative.ae_frequently_mem_of_mem_nhds /-
 /-- Poincaré recurrence theorem. Let `f : α → α` be a conservative dynamical system on a topological
 space with second countable topology and measurable open sets. Then almost every point `x : α`
 is recurrent: it visits every neighborhood `s ∈ 𝓝 x` infinitely many times. -/
@@ -192,7 +239,9 @@ theorem ae_frequently_mem_of_mem_nhds [TopologicalSpace α] [SecondCountableTopo
   rcases(is_basis_countable_basis α).mem_nhds_iffₓ.1 hs with ⟨o, hoS, hxo, hos⟩
   exact (hx o hoS hxo).mono fun n hn => hos hn
 #align measure_theory.conservative.ae_frequently_mem_of_mem_nhds MeasureTheory.Conservative.ae_frequently_mem_of_mem_nhds
+-/
 
+#print MeasureTheory.Conservative.iterate /-
 /-- Iteration of a conservative system is a conservative system. -/
 protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative (f^[n]) μ :=
   by
@@ -217,6 +266,7 @@ protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative (f^[
   · rwa [← iterate_mul, this, ← iterate_add_apply, tsub_add_cancel_of_le]
     exact hkl.le
 #align measure_theory.conservative.iterate MeasureTheory.Conservative.iterate
+-/
 
 end Conservative
 

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

@@ -4,11 +4,11 @@ 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.conservative
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.MeasureTheory.Constructions.BorelSpace
+import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
 import Mathbin.Dynamics.Ergodic.MeasurePreserving
 import Mathbin.Combinatorics.Pigeonhole
 

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

@@ -97,7 +97,7 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
   rcases ihN with ⟨n, hn, hμn⟩
   set T := s ∩ ⋃ n ≥ N + 1, f^[n] ⁻¹' s
   have hT : MeasurableSet T :=
-    hs.inter (MeasurableSet.bunionᵢ (to_countable _) fun _ _ => hf.measurable.iterate _ hs)
+    hs.inter (MeasurableSet.biUnion (to_countable _) fun _ _ => hf.measurable.iterate _ hs)
   have hμT : μ T = 0 :=
     by
     convert(measure_bUnion_null_iff <| to_countable _).2 hN
@@ -131,7 +131,7 @@ theorem measure_mem_forall_ge_image_not_mem_eq_zero (hf : Conservative f μ) (hs
     by
     simp only [set_of_forall, ← compl_set_of]
     exact
-      hs.inter (MeasurableSet.binterᵢ (to_countable _) fun m _ => hf.measurable.iterate m hs.compl)
+      hs.inter (MeasurableSet.biInter (to_countable _) fun m _ => hf.measurable.iterate m hs.compl)
   rcases(hf.exists_gt_measure_inter_ne_zero this H) n with ⟨m, hmn, hm⟩
   rcases nonempty_of_measure_ne_zero hm with ⟨x, ⟨hxs, hxn⟩, hxm, -⟩
   exact hxn m hmn.lt.le hxm

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

@@ -65,7 +65,7 @@ structure Conservative (f : α → α)
 #align measure_theory.conservative MeasureTheory.Conservative
 
 /-- A self-map preserving a finite measure is conservative. -/
-protected theorem MeasurePreserving.conservative [IsFiniteMeasure μ] (h : MeasurePreserving f μ μ) :
+protected theorem MeasurePreserving.conservative [FiniteMeasure μ] (h : MeasurePreserving f μ μ) :
     Conservative f μ :=
   ⟨h.QuasiMeasurePreserving, fun s hsm h0 => h.exists_mem_image_mem hsm h0⟩
 #align measure_theory.measure_preserving.conservative MeasureTheory.MeasurePreserving.conservative

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

@@ -74,7 +74,7 @@ namespace Conservative
 
 /-- The identity map is conservative w.r.t. any measure. -/
 protected theorem id (μ : Measure α) : Conservative id μ :=
-  { toQuasiMeasurePreserving := QuasiMeasurePreserving.id μ
+  { to_quasiMeasurePreserving := QuasiMeasurePreserving.id μ
     exists_mem_image_mem := fun s hs h0 =>
       let ⟨x, hx⟩ := nonempty_of_measure_ne_zero h0
       ⟨x, hx, 1, one_ne_zero, hx⟩ }

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

@@ -100,7 +100,7 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
     hs.inter (MeasurableSet.bunionᵢ (to_countable _) fun _ _ => hf.measurable.iterate _ hs)
   have hμT : μ T = 0 :=
     by
-    convert (measure_bUnion_null_iff <| to_countable _).2 hN
+    convert(measure_bUnion_null_iff <| to_countable _).2 hN
     rw [← inter_Union₂]
     rfl
   have : μ ((s ∩ f^[n] ⁻¹' s) \ T) ≠ 0 := by rwa [measure_diff_null hμT]

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

@@ -212,7 +212,7 @@ protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative (f^[
     exact (Nat.modEq_iff_dvd' hkl.le).1 hn
   refine' ⟨(f^[k]) x, hk, m, _, _⟩
   · intro hm
-    rw [hm, mul_zero, eq_comm, tsub_eq_zero_iff_le] at this
+    rw [hm, MulZeroClass.mul_zero, eq_comm, tsub_eq_zero_iff_le] at this
     exact this.not_lt hkl
   · rwa [← iterate_mul, this, ← iterate_add_apply, tsub_add_cancel_of_le]
     exact hkl.le

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

@@ -53,7 +53,7 @@ namespace MeasureTheory
 
 open Measure
 
-/- ./././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) -/
 /-- We say that a non-singular (`measure_theory.quasi_measure_preserving`) self-map is
 *conservative* if for any measurable set `s` of positive measure there exists `x ∈ s` such that `x`
 returns back to `s` under some iteration of `f`. -/

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

@@ -83,7 +83,7 @@ after `m` iterations of `f`. -/
 theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : MeasurableSet s)
     (h0 : μ s ≠ 0) : ∃ᶠ m in atTop, μ (s ∩ f^[m] ⁻¹' s) ≠ 0 := by
   by_contra H
-  simp only [not_frequently, eventually_atTop, Ne.def, Classical.not_not] at H
+  simp only [not_frequently, eventually_atTop, Ne, Classical.not_not] at H
   rcases H with ⟨N, hN⟩
   induction' N with N ihN
   · apply h0

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -40,9 +40,11 @@ conservative dynamical system, Poincare recurrence theorem
 
 noncomputable section
 
-open Classical Set Filter MeasureTheory Finset Function TopologicalSpace
+open scoped Classical
+open Set Filter MeasureTheory Finset Function TopologicalSpace
 
-open Classical Topology
+open scoped Classical
+open Topology
 
 variable {ι : Type*} {α : Type*} [MeasurableSpace α] {f : α → α} {s : Set α} {μ : Measure α}
 

@@ -56,8 +56,7 @@ returns back to `s` under some iteration of `f`. -/
 structure Conservative (f : α → α) (μ : Measure α) extends QuasiMeasurePreserving f μ μ : Prop where
   /-- If `f` is a conservative self-map and `s` is a measurable set of nonzero measure,
   then there exists a point `x ∈ s` that returns to `s` under a non-zero iteration of `f`. -/
-  exists_mem_iterate_mem :
-    ∀ ⦃s⦄, MeasurableSet s → μ s ≠ 0 → ∃ x ∈ s, ∃ m, m ≠ 0 ∧ f^[m] x ∈ s
+  exists_mem_iterate_mem : ∀ ⦃s⦄, MeasurableSet s → μ s ≠ 0 → ∃ x ∈ s, ∃ m ≠ 0, f^[m] x ∈ s
 #align measure_theory.conservative MeasureTheory.Conservative
 
 /-- A self-map preserving a finite measure is conservative. -/

• 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?

@@ -54,14 +54,16 @@ open Measure
 *conservative* if for any measurable set `s` of positive measure there exists `x ∈ s` such that `x`
 returns back to `s` under some iteration of `f`. -/
 structure Conservative (f : α → α) (μ : Measure α) extends QuasiMeasurePreserving f μ μ : Prop where
-  exists_mem_image_mem :
-    ∀ ⦃s⦄, MeasurableSet s → μ s ≠ 0 → ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), f^[m] x ∈ s
+  /-- If `f` is a conservative self-map and `s` is a measurable set of nonzero measure,
+  then there exists a point `x ∈ s` that returns to `s` under a non-zero iteration of `f`. -/
+  exists_mem_iterate_mem :
+    ∀ ⦃s⦄, MeasurableSet s → μ s ≠ 0 → ∃ x ∈ s, ∃ m, m ≠ 0 ∧ f^[m] x ∈ s
 #align measure_theory.conservative MeasureTheory.Conservative
 
 /-- A self-map preserving a finite measure is conservative. -/
 protected theorem MeasurePreserving.conservative [IsFiniteMeasure μ] (h : MeasurePreserving f μ μ) :
     Conservative f μ :=
-  ⟨h.quasiMeasurePreserving, fun _ hsm h0 => h.exists_mem_image_mem hsm h0⟩
+  ⟨h.quasiMeasurePreserving, fun _ hsm h0 => h.exists_mem_iterate_mem hsm h0⟩
 #align measure_theory.measure_preserving.conservative MeasureTheory.MeasurePreserving.conservative
 
 namespace Conservative
@@ -69,7 +71,7 @@ namespace Conservative
 /-- The identity map is conservative w.r.t. any measure. -/
 protected theorem id (μ : Measure α) : Conservative id μ :=
   { toQuasiMeasurePreserving := QuasiMeasurePreserving.id μ
-    exists_mem_image_mem := fun _ _ h0 =>
+    exists_mem_iterate_mem := fun _ _ h0 =>
       let ⟨x, hx⟩ := nonempty_of_measure_ne_zero h0
       ⟨x, hx, 1, one_ne_zero, hx⟩ }
 #align measure_theory.conservative.id MeasureTheory.Conservative.id
@@ -96,7 +98,7 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
     rw [← inter_iUnion₂]
     rfl
   have : μ ((s ∩ f^[n] ⁻¹' s) \ T) ≠ 0 := by rwa [measure_diff_null hμT]
-  rcases hf.exists_mem_image_mem ((hs.inter (hf.measurable.iterate n hs)).diff hT) this with
+  rcases hf.exists_mem_iterate_mem ((hs.inter (hf.measurable.iterate n hs)).diff hT) this with
     ⟨x, ⟨⟨hxs, _⟩, hxT⟩, m, hm0, ⟨_, hxm⟩, _⟩
   refine' hxT ⟨hxs, mem_iUnion₂.2 ⟨n + m, _, _⟩⟩
   · exact add_le_add hn (Nat.one_le_of_lt <| pos_iff_ne_zero.2 hm0)

Replace rcases( with rcases (. Same thing for convert( and congrm(. No other change.

@@ -92,7 +92,7 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
   have hT : MeasurableSet T :=
     hs.inter (MeasurableSet.biUnion (to_countable _) fun _ _ => hf.measurable.iterate _ hs)
   have hμT : μ T = 0 := by
-    convert(measure_biUnion_null_iff <| to_countable _).2 hN
+    convert (measure_biUnion_null_iff <| to_countable _).2 hN
     rw [← inter_iUnion₂]
     rfl
   have : μ ((s ∩ f^[n] ⁻¹' s) \ T) ≠ 0 := by rwa [measure_diff_null hμT]
@@ -122,7 +122,7 @@ theorem measure_mem_forall_ge_image_not_mem_eq_zero (hf : Conservative f μ) (hs
     simp only [setOf_forall, ← compl_setOf]
     exact
       hs.inter (MeasurableSet.biInter (to_countable _) fun m _ => hf.measurable.iterate m hs.compl)
-  rcases(hf.exists_gt_measure_inter_ne_zero this H) n with ⟨m, hmn, hm⟩
+  rcases (hf.exists_gt_measure_inter_ne_zero this H) n with ⟨m, hmn, hm⟩
   rcases nonempty_of_measure_ne_zero hm with ⟨x, ⟨_, hxn⟩, hxm, -⟩
   exact hxn m hmn.lt.le hxm
 #align measure_theory.conservative.measure_mem_forall_ge_image_not_mem_eq_zero MeasureTheory.Conservative.measure_mem_forall_ge_image_not_mem_eq_zero
@@ -186,7 +186,7 @@ protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative f^[n
   · exact Conservative.id μ
   -- Discharge the trivial case `n = 0`
   refine' ⟨hf.1.iterate _, fun s hs hs0 => _⟩
-  rcases(hf.frequently_ae_mem_and_frequently_image_mem hs hs0).exists with ⟨x, _, hx⟩
+  rcases (hf.frequently_ae_mem_and_frequently_image_mem hs hs0).exists with ⟨x, _, hx⟩
   /- We take a point `x ∈ s` such that `f^[k] x ∈ s` for infinitely many values of `k`,
     then we choose two of these values `k < l` such that `k ≡ l [MOD (n + 1)]`.
     Then `f^[k] x ∈ s` and `f^[n + 1]^[(l - k) / (n + 1)] (f^[k] x) = f^[l] x ∈ s`. -/

Search&replace MulZeroClass.mul_zero -> mul_zero, MulZeroClass.zero_mul -> zero_mul.

These were introduced by Mathport, as the full name of mul_zero is actually MulZeroClass.mul_zero (it's exported with the short name).

@@ -198,7 +198,7 @@ protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative f^[n
     exact (Nat.modEq_iff_dvd' hkl.le).1 hn
   refine' ⟨f^[k] x, hk, m, _, _⟩
   · intro hm
-    rw [hm, MulZeroClass.mul_zero, eq_comm, tsub_eq_zero_iff_le] at this
+    rw [hm, mul_zero, eq_comm, tsub_eq_zero_iff_le] at this
     exact this.not_lt hkl
   · rwa [← iterate_mul, this, ← iterate_add_apply, tsub_add_cancel_of_le]
     exact hkl.le

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

This has nice performance benefits.

@@ -44,7 +44,7 @@ open Classical Set Filter MeasureTheory Finset Function TopologicalSpace
 
 open Classical Topology
 
-variable {ι : Type _} {α : Type _} [MeasurableSpace α] {f : α → α} {s : Set α} {μ : Measure α}
+variable {ι : Type*} {α : Type*} [MeasurableSpace α] {f : α → α} {s : Set α} {μ : Measure α}
 
 namespace MeasureTheory
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 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.conservative
-! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
 import Mathlib.Dynamics.Ergodic.MeasurePreserving
 import Mathlib.Combinatorics.Pigeonhole
 
+#align_import dynamics.ergodic.conservative from "leanprover-community/mathlib"@"bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf"
+
 /-!
 # Conservative systems
 

@@ -23,7 +23,7 @@ from it:
 
 * `MeasureTheory.Conservative.frequently_measure_inter_ne_zero`,
   `MeasureTheory.Conservative.exists_gt_measure_inter_ne_zero`: if `μ s ≠ 0`, then for infinitely
-  many `n`, the measure of `s ∩ (f^[n]) ⁻¹' s` is positive.
+  many `n`, the measure of `s ∩ f^[n] ⁻¹' s` is positive.
 
 * `MeasureTheory.Conservative.measure_mem_forall_ge_image_not_mem_eq_zero`,
   `MeasureTheory.Conservative.ae_mem_imp_frequently_image_mem`: a.e. every point of `s` visits `s`
@@ -58,7 +58,7 @@ open Measure
 returns back to `s` under some iteration of `f`. -/
 structure Conservative (f : α → α) (μ : Measure α) extends QuasiMeasurePreserving f μ μ : Prop where
   exists_mem_image_mem :
-    ∀ ⦃s⦄, MeasurableSet s → μ s ≠ 0 → ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), (f^[m]) x ∈ s
+    ∀ ⦃s⦄, MeasurableSet s → μ s ≠ 0 → ∃ x ∈ s, ∃ (m : _) (_ : m ≠ 0), f^[m] x ∈ s
 #align measure_theory.conservative MeasureTheory.Conservative
 
 /-- A self-map preserving a finite measure is conservative. -/
@@ -119,9 +119,9 @@ theorem exists_gt_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurabl
 /-- Poincaré recurrence theorem: given a conservative map `f` and a measurable set `s`, the set
 of points `x ∈ s` such that `x` does not return to `s` after `≥ n` iterations has measure zero. -/
 theorem measure_mem_forall_ge_image_not_mem_eq_zero (hf : Conservative f μ) (hs : MeasurableSet s)
-    (n : ℕ) : μ ({ x ∈ s | ∀ m ≥ n, (f^[m]) x ∉ s }) = 0 := by
+    (n : ℕ) : μ ({ x ∈ s | ∀ m ≥ n, f^[m] x ∉ s }) = 0 := by
   by_contra H
-  have : MeasurableSet (s ∩ { x | ∀ m ≥ n, (f^[m]) x ∉ s }) := by
+  have : MeasurableSet (s ∩ { x | ∀ m ≥ n, f^[m] x ∉ s }) := by
     simp only [setOf_forall, ← compl_setOf]
     exact
       hs.inter (MeasurableSet.biInter (to_countable _) fun m _ => hf.measurable.iterate m hs.compl)
@@ -133,7 +133,7 @@ theorem measure_mem_forall_ge_image_not_mem_eq_zero (hf : Conservative f μ) (hs
 /-- Poincaré recurrence theorem: given a conservative map `f` and a measurable set `s`,
 almost every point `x ∈ s` returns back to `s` infinitely many times. -/
 theorem ae_mem_imp_frequently_image_mem (hf : Conservative f μ) (hs : MeasurableSet s) :
-    ∀ᵐ x ∂μ, x ∈ s → ∃ᶠ n in atTop, (f^[n]) x ∈ s := by
+    ∀ᵐ x ∂μ, x ∈ s → ∃ᶠ n in atTop, f^[n] x ∈ s := by
   simp only [frequently_atTop, @forall_swap (_ ∈ s), ae_all_iff]
   intro n
   filter_upwards [measure_zero_iff_ae_nmem.1 (hf.measure_mem_forall_ge_image_not_mem_eq_zero hs n)]
@@ -141,12 +141,12 @@ theorem ae_mem_imp_frequently_image_mem (hf : Conservative f μ) (hs : Measurabl
 #align measure_theory.conservative.ae_mem_imp_frequently_image_mem MeasureTheory.Conservative.ae_mem_imp_frequently_image_mem
 
 theorem inter_frequently_image_mem_ae_eq (hf : Conservative f μ) (hs : MeasurableSet s) :
-    (s ∩ { x | ∃ᶠ n in atTop, (f^[n]) x ∈ s } : Set α) =ᵐ[μ] s :=
+    (s ∩ { x | ∃ᶠ n in atTop, f^[n] x ∈ s } : Set α) =ᵐ[μ] s :=
   inter_eventuallyEq_left.2 <| hf.ae_mem_imp_frequently_image_mem hs
 #align measure_theory.conservative.inter_frequently_image_mem_ae_eq MeasureTheory.Conservative.inter_frequently_image_mem_ae_eq
 
 theorem measure_inter_frequently_image_mem_eq (hf : Conservative f μ) (hs : MeasurableSet s) :
-    μ (s ∩ { x | ∃ᶠ n in atTop, (f^[n]) x ∈ s }) = μ s :=
+    μ (s ∩ { x | ∃ᶠ n in atTop, f^[n] x ∈ s }) = μ s :=
   measure_congr (hf.inter_frequently_image_mem_ae_eq hs)
 #align measure_theory.conservative.measure_inter_frequently_image_mem_eq MeasureTheory.Conservative.measure_inter_frequently_image_mem_eq
 
@@ -154,7 +154,7 @@ theorem measure_inter_frequently_image_mem_eq (hf : Conservative f μ) (hs : Mea
 set, then for `μ`-a.e. `x`, if the orbit of `x` visits `s` at least once, then it visits `s`
 infinitely many times.  -/
 theorem ae_forall_image_mem_imp_frequently_image_mem (hf : Conservative f μ)
-    (hs : MeasurableSet s) : ∀ᵐ x ∂μ, ∀ k, (f^[k]) x ∈ s → ∃ᶠ n in atTop, (f^[n]) x ∈ s := by
+    (hs : MeasurableSet s) : ∀ᵐ x ∂μ, ∀ k, f^[k] x ∈ s → ∃ᶠ n in atTop, f^[n] x ∈ s := by
   refine' ae_all_iff.2 fun k => _
   refine' (hf.ae_mem_imp_frequently_image_mem (hf.measurable.iterate k hs)).mono fun x hx hk => _
   rw [← map_add_atTop_eq_nat k, frequently_map]
@@ -165,7 +165,7 @@ theorem ae_forall_image_mem_imp_frequently_image_mem (hf : Conservative f μ)
 /-- If `f` is a conservative self-map and `s` is a measurable set of positive measure, then
 `μ.ae`-frequently we have `x ∈ s` and `s` returns to `s` under infinitely many iterations of `f`. -/
 theorem frequently_ae_mem_and_frequently_image_mem (hf : Conservative f μ) (hs : MeasurableSet s)
-    (h0 : μ s ≠ 0) : ∃ᵐ x ∂μ, x ∈ s ∧ ∃ᶠ n in atTop, (f^[n]) x ∈ s :=
+    (h0 : μ s ≠ 0) : ∃ᵐ x ∂μ, x ∈ s ∧ ∃ᶠ n in atTop, f^[n] x ∈ s :=
   ((frequently_ae_mem_iff.2 h0).and_eventually (hf.ae_mem_imp_frequently_image_mem hs)).mono
     fun _ hx => ⟨hx.1, hx.2 hx.1⟩
 #align measure_theory.conservative.frequently_ae_mem_and_frequently_image_mem MeasureTheory.Conservative.frequently_ae_mem_and_frequently_image_mem
@@ -175,8 +175,8 @@ space with second countable topology and measurable open sets. Then almost every
 is recurrent: it visits every neighborhood `s ∈ 𝓝 x` infinitely many times. -/
 theorem ae_frequently_mem_of_mem_nhds [TopologicalSpace α] [SecondCountableTopology α]
     [OpensMeasurableSpace α] {f : α → α} {μ : Measure α} (h : Conservative f μ) :
-    ∀ᵐ x ∂μ, ∀ s ∈ 𝓝 x, ∃ᶠ n in atTop, (f^[n]) x ∈ s := by
-  have : ∀ s ∈ countableBasis α, ∀ᵐ x ∂μ, x ∈ s → ∃ᶠ n in atTop, (f^[n]) x ∈ s := fun s hs =>
+    ∀ᵐ x ∂μ, ∀ s ∈ 𝓝 x, ∃ᶠ n in atTop, f^[n] x ∈ s := by
+  have : ∀ s ∈ countableBasis α, ∀ᵐ x ∂μ, x ∈ s → ∃ᶠ n in atTop, f^[n] x ∈ s := fun s hs =>
     h.ae_mem_imp_frequently_image_mem (isOpen_of_mem_countableBasis hs).measurableSet
   refine' ((ae_ball_iff <| countable_countableBasis α).2 this).mono fun x hx s hs => _
   rcases (isBasis_countableBasis α).mem_nhds_iff.1 hs with ⟨o, hoS, hxo, hos⟩
@@ -184,7 +184,7 @@ theorem ae_frequently_mem_of_mem_nhds [TopologicalSpace α] [SecondCountableTopo
 #align measure_theory.conservative.ae_frequently_mem_of_mem_nhds MeasureTheory.Conservative.ae_frequently_mem_of_mem_nhds
 
 /-- Iteration of a conservative system is a conservative system. -/
-protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative (f^[n]) μ := by
+protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative f^[n] μ := by
   cases' n with n
   · exact Conservative.id μ
   -- Discharge the trivial case `n = 0`
@@ -192,14 +192,14 @@ protected theorem iterate (hf : Conservative f μ) (n : ℕ) : Conservative (f^[
   rcases(hf.frequently_ae_mem_and_frequently_image_mem hs hs0).exists with ⟨x, _, hx⟩
   /- We take a point `x ∈ s` such that `f^[k] x ∈ s` for infinitely many values of `k`,
     then we choose two of these values `k < l` such that `k ≡ l [MOD (n + 1)]`.
-    Then `f^[k] x ∈ s` and `(f^[n + 1])^[(l - k) / (n + 1)] (f^[k] x) = f^[l] x ∈ s`. -/
+    Then `f^[k] x ∈ s` and `f^[n + 1]^[(l - k) / (n + 1)] (f^[k] x) = f^[l] x ∈ s`. -/
   rw [Nat.frequently_atTop_iff_infinite] at hx
   rcases Nat.exists_lt_modEq_of_infinite hx n.succ_pos with ⟨k, hk, l, hl, hkl, hn⟩
   set m := (l - k) / (n + 1)
   have : (n + 1) * m = l - k := by
     apply Nat.mul_div_cancel'
     exact (Nat.modEq_iff_dvd' hkl.le).1 hn
-  refine' ⟨(f^[k]) x, hk, m, _, _⟩
+  refine' ⟨f^[k] x, hk, m, _, _⟩
   · intro hm
     rw [hm, MulZeroClass.mul_zero, eq_comm, tsub_eq_zero_iff_le] at this
     exact this.not_lt hkl

Changes are of the form

• some_tactic at h⊢ -> some_tactic at h ⊢
• some_tactic at h -> some_tactic at h

@@ -89,7 +89,7 @@ theorem frequently_measure_inter_ne_zero (hf : Conservative f μ) (hs : Measurab
   · apply h0
     simpa using hN 0 le_rfl
   rw [imp_false] at ihN
-  push_neg  at ihN
+  push_neg at ihN
   rcases ihN with ⟨n, hn, hμn⟩
   set T := s ∩ ⋃ n ≥ N + 1, f^[n] ⁻¹' s
   have hT : MeasurableSet T :=

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.

@@ -62,7 +62,7 @@ structure Conservative (f : α → α) (μ : Measure α) extends QuasiMeasurePre
 #align measure_theory.conservative MeasureTheory.Conservative
 
 /-- A self-map preserving a finite measure is conservative. -/
-protected theorem MeasurePreserving.conservative [FiniteMeasure μ] (h : MeasurePreserving f μ μ) :
+protected theorem MeasurePreserving.conservative [IsFiniteMeasure μ] (h : MeasurePreserving f μ μ) :
     Conservative f μ :=
   ⟨h.quasiMeasurePreserving, fun _ hsm h0 => h.exists_mem_image_mem hsm h0⟩
 #align measure_theory.measure_preserving.conservative MeasureTheory.MeasurePreserving.conservative