measure_theory.measure.open_pos ⟷ Mathlib.MeasureTheory.Measure.OpenPos

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

@@ -119,7 +119,7 @@ theorem eqOn_open_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict U] g) (hU : I
     (hf : ContinuousOn f U) (hg : ContinuousOn g U) : EqOn f g U :=
   by
   replace h := ae_imp_of_ae_restrict h
-  simp only [eventually_eq, ae_iff, not_imp] at h 
+  simp only [eventually_eq, ae_iff, not_imp] at h
   have : IsOpen (U ∩ {a | f a ≠ g a}) :=
     by
     refine' is_open_iff_mem_nhds.mpr fun a ha => inter_mem (hU.mem_nhds ha.1) _

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

@@ -3,7 +3,7 @@ Copyright (c) 2022 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.MeasureTheory.Measure.MeasureSpace
+import MeasureTheory.Measure.MeasureSpace
 
 #align_import measure_theory.measure.open_pos from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
 

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

@@ -2,14 +2,11 @@
 Copyright (c) 2022 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 measure_theory.measure.open_pos
-! 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.MeasureSpace
 
+#align_import measure_theory.measure.open_pos from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
+
 /-!
 # Measures positive on nonempty opens
 

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

@@ -46,34 +46,48 @@ class IsOpenPosMeasure : Prop where
 
 variable [IsOpenPosMeasure μ] {s U : Set X} {x : X}
 
+#print IsOpen.measure_ne_zero /-
 theorem IsOpen.measure_ne_zero (hU : IsOpen U) (hne : U.Nonempty) : μ U ≠ 0 :=
   IsOpenPosMeasure.open_pos U hU hne
 #align is_open.measure_ne_zero IsOpen.measure_ne_zero
+-/
 
+#print IsOpen.measure_pos /-
 theorem IsOpen.measure_pos (hU : IsOpen U) (hne : U.Nonempty) : 0 < μ U :=
   (hU.measure_ne_zero μ hne).bot_lt
 #align is_open.measure_pos IsOpen.measure_pos
+-/
 
+#print IsOpen.measure_pos_iff /-
 theorem IsOpen.measure_pos_iff (hU : IsOpen U) : 0 < μ U ↔ U.Nonempty :=
   ⟨fun h => nonempty_iff_ne_empty.2 fun he => h.ne' <| he.symm ▸ measure_empty, hU.measure_pos μ⟩
 #align is_open.measure_pos_iff IsOpen.measure_pos_iff
+-/
 
+#print IsOpen.measure_eq_zero_iff /-
 theorem IsOpen.measure_eq_zero_iff (hU : IsOpen U) : μ U = 0 ↔ U = ∅ := by
   simpa only [not_lt, nonpos_iff_eq_zero, not_nonempty_iff_eq_empty] using
     not_congr (hU.measure_pos_iff μ)
 #align is_open.measure_eq_zero_iff IsOpen.measure_eq_zero_iff
+-/
 
+#print MeasureTheory.Measure.measure_pos_of_nonempty_interior /-
 theorem measure_pos_of_nonempty_interior (h : (interior s).Nonempty) : 0 < μ s :=
   (isOpen_interior.measure_pos μ h).trans_le (measure_mono interior_subset)
 #align measure_theory.measure.measure_pos_of_nonempty_interior MeasureTheory.Measure.measure_pos_of_nonempty_interior
+-/
 
+#print MeasureTheory.Measure.measure_pos_of_mem_nhds /-
 theorem measure_pos_of_mem_nhds (h : s ∈ 𝓝 x) : 0 < μ s :=
   measure_pos_of_nonempty_interior _ ⟨x, mem_interior_iff_mem_nhds.2 h⟩
 #align measure_theory.measure.measure_pos_of_mem_nhds MeasureTheory.Measure.measure_pos_of_mem_nhds
+-/
 
+#print MeasureTheory.Measure.isOpenPosMeasure_smul /-
 theorem isOpenPosMeasure_smul {c : ℝ≥0∞} (h : c ≠ 0) : IsOpenPosMeasure (c • μ) :=
   ⟨fun U Uo Une => mul_ne_zero h (Uo.measure_ne_zero μ Une)⟩
 #align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.isOpenPosMeasure_smul
+-/
 
 variable {μ ν}
 
@@ -89,14 +103,19 @@ theorem LE.le.isOpenPosMeasure (h : μ ≤ ν) : IsOpenPosMeasure ν :=
 #align has_le.le.is_open_pos_measure LE.le.isOpenPosMeasure
 -/
 
+#print IsOpen.eq_empty_of_measure_zero /-
 theorem IsOpen.eq_empty_of_measure_zero (hU : IsOpen U) (h₀ : μ U = 0) : U = ∅ :=
   (hU.measure_eq_zero_iff μ).mp h₀
 #align is_open.eq_empty_of_measure_zero IsOpen.eq_empty_of_measure_zero
+-/
 
+#print MeasureTheory.Measure.interior_eq_empty_of_null /-
 theorem interior_eq_empty_of_null (hs : μ s = 0) : interior s = ∅ :=
   isOpen_interior.eq_empty_of_measure_zero <| measure_mono_null interior_subset hs
 #align measure_theory.measure.interior_eq_empty_of_null MeasureTheory.Measure.interior_eq_empty_of_null
+-/
 
+#print MeasureTheory.Measure.eqOn_open_of_ae_eq /-
 /-- If two functions are a.e. equal on an open set and are continuous on this set, then they are
 equal on this set. -/
 theorem eqOn_open_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict U] g) (hU : IsOpen U)
@@ -114,13 +133,17 @@ theorem eqOn_open_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict U] g) (hU : I
   replace := (this.eq_empty_of_measure_zero h).le
   exact fun x hx => Classical.not_not.1 fun h => this ⟨hx, h⟩
 #align measure_theory.measure.eq_on_open_of_ae_eq MeasureTheory.Measure.eqOn_open_of_ae_eq
+-/
 
+#print MeasureTheory.Measure.eq_of_ae_eq /-
 /-- If two continuous functions are a.e. equal, then they are equal. -/
 theorem eq_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ] g) (hf : Continuous f) (hg : Continuous g) : f = g :=
   suffices EqOn f g univ from funext fun x => this trivial
   eqOn_open_of_ae_eq (ae_restrict_of_ae h) isOpen_univ hf.ContinuousOn hg.ContinuousOn
 #align measure_theory.measure.eq_of_ae_eq MeasureTheory.Measure.eq_of_ae_eq
+-/
 
+#print MeasureTheory.Measure.eqOn_of_ae_eq /-
 theorem eqOn_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict s] g) (hf : ContinuousOn f s)
     (hg : ContinuousOn g s) (hU : s ⊆ closure (interior s)) : EqOn f g s :=
   have : interior s ⊆ s := interior_subset
@@ -128,13 +151,16 @@ theorem eqOn_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict s] g) (hf : Contin
         (hg.mono this)).of_subset_closure
     hf hg this hU
 #align measure_theory.measure.eq_on_of_ae_eq MeasureTheory.Measure.eqOn_of_ae_eq
+-/
 
 variable (μ)
 
+#print Continuous.ae_eq_iff_eq /-
 theorem Continuous.ae_eq_iff_eq {f g : X → Y} (hf : Continuous f) (hg : Continuous g) :
     f =ᵐ[μ] g ↔ f = g :=
   ⟨fun h => eq_of_ae_eq h hf hg, fun h => h ▸ EventuallyEq.rfl⟩
 #align continuous.ae_eq_iff_eq Continuous.ae_eq_iff_eq
+-/
 
 end Basic
 
@@ -143,44 +169,60 @@ section LinearOrder
 variable {X Y : Type _} [TopologicalSpace X] [LinearOrder X] [OrderTopology X]
   {m : MeasurableSpace X} [TopologicalSpace Y] [T2Space Y] (μ : Measure X) [IsOpenPosMeasure μ]
 
+#print MeasureTheory.Measure.measure_Ioi_pos /-
 theorem measure_Ioi_pos [NoMaxOrder X] (a : X) : 0 < μ (Ioi a) :=
   isOpen_Ioi.measure_pos μ nonempty_Ioi
 #align measure_theory.measure.measure_Ioi_pos MeasureTheory.Measure.measure_Ioi_pos
+-/
 
+#print MeasureTheory.Measure.measure_Iio_pos /-
 theorem measure_Iio_pos [NoMinOrder X] (a : X) : 0 < μ (Iio a) :=
   isOpen_Iio.measure_pos μ nonempty_Iio
 #align measure_theory.measure.measure_Iio_pos MeasureTheory.Measure.measure_Iio_pos
+-/
 
+#print MeasureTheory.Measure.measure_Ioo_pos /-
 theorem measure_Ioo_pos [DenselyOrdered X] {a b : X} : 0 < μ (Ioo a b) ↔ a < b :=
   (isOpen_Ioo.measure_pos_iff μ).trans nonempty_Ioo
 #align measure_theory.measure.measure_Ioo_pos MeasureTheory.Measure.measure_Ioo_pos
+-/
 
+#print MeasureTheory.Measure.measure_Ioo_eq_zero /-
 theorem measure_Ioo_eq_zero [DenselyOrdered X] {a b : X} : μ (Ioo a b) = 0 ↔ b ≤ a :=
   (isOpen_Ioo.measure_eq_zero_iff μ).trans (Ioo_eq_empty_iff.trans not_lt)
 #align measure_theory.measure.measure_Ioo_eq_zero MeasureTheory.Measure.measure_Ioo_eq_zero
+-/
 
+#print MeasureTheory.Measure.eqOn_Ioo_of_ae_eq /-
 theorem eqOn_Ioo_of_ae_eq {a b : X} {f g : X → Y} (hfg : f =ᵐ[μ.restrict (Ioo a b)] g)
     (hf : ContinuousOn f (Ioo a b)) (hg : ContinuousOn g (Ioo a b)) : EqOn f g (Ioo a b) :=
   eqOn_of_ae_eq hfg hf hg Ioo_subset_closure_interior
 #align measure_theory.measure.eq_on_Ioo_of_ae_eq MeasureTheory.Measure.eqOn_Ioo_of_ae_eq
+-/
 
+#print MeasureTheory.Measure.eqOn_Ioc_of_ae_eq /-
 theorem eqOn_Ioc_of_ae_eq [DenselyOrdered X] {a b : X} {f g : X → Y}
     (hfg : f =ᵐ[μ.restrict (Ioc a b)] g) (hf : ContinuousOn f (Ioc a b))
     (hg : ContinuousOn g (Ioc a b)) : EqOn f g (Ioc a b) :=
   eqOn_of_ae_eq hfg hf hg (Ioc_subset_closure_interior _ _)
 #align measure_theory.measure.eq_on_Ioc_of_ae_eq MeasureTheory.Measure.eqOn_Ioc_of_ae_eq
+-/
 
+#print MeasureTheory.Measure.eqOn_Ico_of_ae_eq /-
 theorem eqOn_Ico_of_ae_eq [DenselyOrdered X] {a b : X} {f g : X → Y}
     (hfg : f =ᵐ[μ.restrict (Ico a b)] g) (hf : ContinuousOn f (Ico a b))
     (hg : ContinuousOn g (Ico a b)) : EqOn f g (Ico a b) :=
   eqOn_of_ae_eq hfg hf hg (Ico_subset_closure_interior _ _)
 #align measure_theory.measure.eq_on_Ico_of_ae_eq MeasureTheory.Measure.eqOn_Ico_of_ae_eq
+-/
 
+#print MeasureTheory.Measure.eqOn_Icc_of_ae_eq /-
 theorem eqOn_Icc_of_ae_eq [DenselyOrdered X] {a b : X} (hne : a ≠ b) {f g : X → Y}
     (hfg : f =ᵐ[μ.restrict (Icc a b)] g) (hf : ContinuousOn f (Icc a b))
     (hg : ContinuousOn g (Icc a b)) : EqOn f g (Icc a b) :=
   eqOn_of_ae_eq hfg hf hg (closure_interior_Icc hne).symm.Subset
 #align measure_theory.measure.eq_on_Icc_of_ae_eq MeasureTheory.Measure.eqOn_Icc_of_ae_eq
+-/
 
 end LinearOrder
 
@@ -195,13 +237,17 @@ namespace Metric
 variable {X : Type _} [PseudoMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
   [IsOpenPosMeasure μ]
 
+#print Metric.measure_ball_pos /-
 theorem measure_ball_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (ball x r) :=
   isOpen_ball.measure_pos μ (nonempty_ball.2 hr)
 #align metric.measure_ball_pos Metric.measure_ball_pos
+-/
 
+#print Metric.measure_closedBall_pos /-
 theorem measure_closedBall_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (closedBall x r) :=
   (measure_ball_pos μ x hr).trans_le (measure_mono ball_subset_closedBall)
 #align metric.measure_closed_ball_pos Metric.measure_closedBall_pos
+-/
 
 end Metric
 
@@ -210,13 +256,17 @@ namespace Emetric
 variable {X : Type _} [PseudoEMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
   [IsOpenPosMeasure μ]
 
+#print EMetric.measure_ball_pos /-
 theorem measure_ball_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ (ball x r) :=
   isOpen_ball.measure_pos μ ⟨x, mem_ball_self hr.bot_lt⟩
 #align emetric.measure_ball_pos EMetric.measure_ball_pos
+-/
 
+#print EMetric.measure_closedBall_pos /-
 theorem measure_closedBall_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ (closedBall x r) :=
   (measure_ball_pos μ x hr).trans_le (measure_mono ball_subset_closedBall)
 #align emetric.measure_closed_ball_pos EMetric.measure_closedBall_pos
+-/
 
 end Emetric
 

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

@@ -37,17 +37,17 @@ section Basic
 variable {X Y : Type _} [TopologicalSpace X] {m : MeasurableSpace X} [TopologicalSpace Y]
   [T2Space Y] (μ ν : Measure X)
 
-#print MeasureTheory.Measure.OpenPosMeasure /-
+#print MeasureTheory.Measure.IsOpenPosMeasure /-
 /-- A measure is said to be `is_open_pos_measure` if it is positive on nonempty open sets. -/
-class OpenPosMeasure : Prop where
+class IsOpenPosMeasure : Prop where
   open_pos : ∀ U : Set X, IsOpen U → U.Nonempty → μ U ≠ 0
-#align measure_theory.measure.is_open_pos_measure MeasureTheory.Measure.OpenPosMeasure
+#align measure_theory.measure.is_open_pos_measure MeasureTheory.Measure.IsOpenPosMeasure
 -/
 
-variable [OpenPosMeasure μ] {s U : Set X} {x : X}
+variable [IsOpenPosMeasure μ] {s U : Set X} {x : X}
 
 theorem IsOpen.measure_ne_zero (hU : IsOpen U) (hne : U.Nonempty) : μ U ≠ 0 :=
-  OpenPosMeasure.open_pos U hU hne
+  IsOpenPosMeasure.open_pos U hU hne
 #align is_open.measure_ne_zero IsOpen.measure_ne_zero
 
 theorem IsOpen.measure_pos (hU : IsOpen U) (hne : U.Nonempty) : 0 < μ U :=
@@ -71,21 +71,21 @@ theorem measure_pos_of_mem_nhds (h : s ∈ 𝓝 x) : 0 < μ s :=
   measure_pos_of_nonempty_interior _ ⟨x, mem_interior_iff_mem_nhds.2 h⟩
 #align measure_theory.measure.measure_pos_of_mem_nhds MeasureTheory.Measure.measure_pos_of_mem_nhds
 
-theorem openPosMeasure_smul {c : ℝ≥0∞} (h : c ≠ 0) : OpenPosMeasure (c • μ) :=
+theorem isOpenPosMeasure_smul {c : ℝ≥0∞} (h : c ≠ 0) : IsOpenPosMeasure (c • μ) :=
   ⟨fun U Uo Une => mul_ne_zero h (Uo.measure_ne_zero μ Une)⟩
-#align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.openPosMeasure_smul
+#align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.isOpenPosMeasure_smul
 
 variable {μ ν}
 
-#print MeasureTheory.Measure.AbsolutelyContinuous.openPosMeasure /-
-protected theorem AbsolutelyContinuous.openPosMeasure (h : μ ≪ ν) : OpenPosMeasure ν :=
+#print MeasureTheory.Measure.AbsolutelyContinuous.isOpenPosMeasure /-
+protected theorem AbsolutelyContinuous.isOpenPosMeasure (h : μ ≪ ν) : IsOpenPosMeasure ν :=
   ⟨fun U ho hne h₀ => ho.measure_ne_zero μ hne (h h₀)⟩
-#align measure_theory.measure.absolutely_continuous.is_open_pos_measure MeasureTheory.Measure.AbsolutelyContinuous.openPosMeasure
+#align measure_theory.measure.absolutely_continuous.is_open_pos_measure MeasureTheory.Measure.AbsolutelyContinuous.isOpenPosMeasure
 -/
 
 #print LE.le.isOpenPosMeasure /-
-theorem LE.le.isOpenPosMeasure (h : μ ≤ ν) : OpenPosMeasure ν :=
-  h.AbsolutelyContinuous.OpenPosMeasure
+theorem LE.le.isOpenPosMeasure (h : μ ≤ ν) : IsOpenPosMeasure ν :=
+  h.AbsolutelyContinuous.IsOpenPosMeasure
 #align has_le.le.is_open_pos_measure LE.le.isOpenPosMeasure
 -/
 
@@ -104,7 +104,7 @@ theorem eqOn_open_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict U] g) (hU : I
   by
   replace h := ae_imp_of_ae_restrict h
   simp only [eventually_eq, ae_iff, not_imp] at h 
-  have : IsOpen (U ∩ { a | f a ≠ g a }) :=
+  have : IsOpen (U ∩ {a | f a ≠ g a}) :=
     by
     refine' is_open_iff_mem_nhds.mpr fun a ha => inter_mem (hU.mem_nhds ha.1) _
     rcases ha with ⟨ha : a ∈ U, ha' : (f a, g a) ∈ diagonal Yᶜ⟩
@@ -141,7 +141,7 @@ end Basic
 section LinearOrder
 
 variable {X Y : Type _} [TopologicalSpace X] [LinearOrder X] [OrderTopology X]
-  {m : MeasurableSpace X} [TopologicalSpace Y] [T2Space Y] (μ : Measure X) [OpenPosMeasure μ]
+  {m : MeasurableSpace X} [TopologicalSpace Y] [T2Space Y] (μ : Measure X) [IsOpenPosMeasure μ]
 
 theorem measure_Ioi_pos [NoMaxOrder X] (a : X) : 0 < μ (Ioi a) :=
   isOpen_Ioi.measure_pos μ nonempty_Ioi
@@ -193,7 +193,7 @@ open MeasureTheory MeasureTheory.Measure
 namespace Metric
 
 variable {X : Type _} [PseudoMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
-  [OpenPosMeasure μ]
+  [IsOpenPosMeasure μ]
 
 theorem measure_ball_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (ball x r) :=
   isOpen_ball.measure_pos μ (nonempty_ball.2 hr)
@@ -208,7 +208,7 @@ end Metric
 namespace Emetric
 
 variable {X : Type _} [PseudoEMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
-  [OpenPosMeasure μ]
+  [IsOpenPosMeasure μ]
 
 theorem measure_ball_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ (ball x r) :=
   isOpen_ball.measure_pos μ ⟨x, mem_ball_self hr.bot_lt⟩

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

@@ -103,7 +103,7 @@ theorem eqOn_open_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict U] g) (hU : I
     (hf : ContinuousOn f U) (hg : ContinuousOn g U) : EqOn f g U :=
   by
   replace h := ae_imp_of_ae_restrict h
-  simp only [eventually_eq, ae_iff, not_imp] at h
+  simp only [eventually_eq, ae_iff, not_imp] at h 
   have : IsOpen (U ∩ { a | f a ≠ g a }) :=
     by
     refine' is_open_iff_mem_nhds.mpr fun a ha => inter_mem (hU.mem_nhds ha.1) _

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

@@ -24,7 +24,7 @@ about these measures.
 -/
 
 
-open Topology ENNReal MeasureTheory
+open scoped Topology ENNReal MeasureTheory
 
 open Set Function Filter
 
@@ -83,9 +83,11 @@ protected theorem AbsolutelyContinuous.openPosMeasure (h : μ ≪ ν) : OpenPosM
 #align measure_theory.measure.absolutely_continuous.is_open_pos_measure MeasureTheory.Measure.AbsolutelyContinuous.openPosMeasure
 -/
 
+#print LE.le.isOpenPosMeasure /-
 theorem LE.le.isOpenPosMeasure (h : μ ≤ ν) : OpenPosMeasure ν :=
   h.AbsolutelyContinuous.OpenPosMeasure
 #align has_le.le.is_open_pos_measure LE.le.isOpenPosMeasure
+-/
 
 theorem IsOpen.eq_empty_of_measure_zero (hU : IsOpen U) (h₀ : μ U = 0) : U = ∅ :=
   (hU.measure_eq_zero_iff μ).mp h₀

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

@@ -46,73 +46,31 @@ class OpenPosMeasure : Prop where
 
 variable [OpenPosMeasure μ] {s U : Set X} {x : X}
 
-/- warning: is_open.measure_ne_zero -> IsOpen.measure_ne_zero is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Set.Nonempty.{u1} X U) -> (Ne.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ U) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Set.Nonempty.{u1} X U) -> (Ne.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) U) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
-Case conversion may be inaccurate. Consider using '#align is_open.measure_ne_zero IsOpen.measure_ne_zeroₓ'. -/
 theorem IsOpen.measure_ne_zero (hU : IsOpen U) (hne : U.Nonempty) : μ U ≠ 0 :=
   OpenPosMeasure.open_pos U hU hne
 #align is_open.measure_ne_zero IsOpen.measure_ne_zero
 
-/- warning: is_open.measure_pos -> IsOpen.measure_pos is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Set.Nonempty.{u1} X U) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ U))
-but is expected to have type
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 theorem IsOpen.measure_pos (hU : IsOpen U) (hne : U.Nonempty) : 0 < μ U :=
   (hU.measure_ne_zero μ hne).bot_lt
 #align is_open.measure_pos IsOpen.measure_pos
 
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 theorem IsOpen.measure_pos_iff (hU : IsOpen U) : 0 < μ U ↔ U.Nonempty :=
   ⟨fun h => nonempty_iff_ne_empty.2 fun he => h.ne' <| he.symm ▸ measure_empty, hU.measure_pos μ⟩
 #align is_open.measure_pos_iff IsOpen.measure_pos_iff
 
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 theorem IsOpen.measure_eq_zero_iff (hU : IsOpen U) : μ U = 0 ↔ U = ∅ := by
   simpa only [not_lt, nonpos_iff_eq_zero, not_nonempty_iff_eq_empty] using
     not_congr (hU.measure_pos_iff μ)
 #align is_open.measure_eq_zero_iff IsOpen.measure_eq_zero_iff
 
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 theorem measure_pos_of_nonempty_interior (h : (interior s).Nonempty) : 0 < μ s :=
   (isOpen_interior.measure_pos μ h).trans_le (measure_mono interior_subset)
 #align measure_theory.measure.measure_pos_of_nonempty_interior MeasureTheory.Measure.measure_pos_of_nonempty_interior
 
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 theorem measure_pos_of_mem_nhds (h : s ∈ 𝓝 x) : 0 < μ s :=
   measure_pos_of_nonempty_interior _ ⟨x, mem_interior_iff_mem_nhds.2 h⟩
 #align measure_theory.measure.measure_pos_of_mem_nhds MeasureTheory.Measure.measure_pos_of_mem_nhds
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.openPosMeasure_smulₓ'. -/
 theorem openPosMeasure_smul {c : ℝ≥0∞} (h : c ≠ 0) : OpenPosMeasure (c • μ) :=
   ⟨fun U Uo Une => mul_ne_zero h (Uo.measure_ne_zero μ Une)⟩
 #align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.openPosMeasure_smul
@@ -125,42 +83,18 @@ protected theorem AbsolutelyContinuous.openPosMeasure (h : μ ≪ ν) : OpenPosM
 #align measure_theory.measure.absolutely_continuous.is_open_pos_measure MeasureTheory.Measure.AbsolutelyContinuous.openPosMeasure
 -/
 
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-Case conversion may be inaccurate. Consider using '#align has_le.le.is_open_pos_measure LE.le.isOpenPosMeasureₓ'. -/
 theorem LE.le.isOpenPosMeasure (h : μ ≤ ν) : OpenPosMeasure ν :=
   h.AbsolutelyContinuous.OpenPosMeasure
 #align has_le.le.is_open_pos_measure LE.le.isOpenPosMeasure
 
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 theorem IsOpen.eq_empty_of_measure_zero (hU : IsOpen U) (h₀ : μ U = 0) : U = ∅ :=
   (hU.measure_eq_zero_iff μ).mp h₀
 #align is_open.eq_empty_of_measure_zero IsOpen.eq_empty_of_measure_zero
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.measure.interior_eq_empty_of_null MeasureTheory.Measure.interior_eq_empty_of_nullₓ'. -/
 theorem interior_eq_empty_of_null (hs : μ s = 0) : interior s = ∅ :=
   isOpen_interior.eq_empty_of_measure_zero <| measure_mono_null interior_subset hs
 #align measure_theory.measure.interior_eq_empty_of_null MeasureTheory.Measure.interior_eq_empty_of_null
 
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 /-- If two functions are a.e. equal on an open set and are continuous on this set, then they are
 equal on this set. -/
 theorem eqOn_open_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict U] g) (hU : IsOpen U)
@@ -179,24 +113,12 @@ theorem eqOn_open_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict U] g) (hU : I
   exact fun x hx => Classical.not_not.1 fun h => this ⟨hx, h⟩
 #align measure_theory.measure.eq_on_open_of_ae_eq MeasureTheory.Measure.eqOn_open_of_ae_eq
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_of_ae_eq MeasureTheory.Measure.eq_of_ae_eqₓ'. -/
 /-- If two continuous functions are a.e. equal, then they are equal. -/
 theorem eq_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ] g) (hf : Continuous f) (hg : Continuous g) : f = g :=
   suffices EqOn f g univ from funext fun x => this trivial
   eqOn_open_of_ae_eq (ae_restrict_of_ae h) isOpen_univ hf.ContinuousOn hg.ContinuousOn
 #align measure_theory.measure.eq_of_ae_eq MeasureTheory.Measure.eq_of_ae_eq
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_of_ae_eq MeasureTheory.Measure.eqOn_of_ae_eqₓ'. -/
 theorem eqOn_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict s] g) (hf : ContinuousOn f s)
     (hg : ContinuousOn g s) (hU : s ⊆ closure (interior s)) : EqOn f g s :=
   have : interior s ⊆ s := interior_subset
@@ -207,12 +129,6 @@ theorem eqOn_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict s] g) (hf : Contin
 
 variable (μ)
 
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-Case conversion may be inaccurate. Consider using '#align continuous.ae_eq_iff_eq Continuous.ae_eq_iff_eqₓ'. -/
 theorem Continuous.ae_eq_iff_eq {f g : X → Y} (hf : Continuous f) (hg : Continuous g) :
     f =ᵐ[μ] g ↔ f = g :=
   ⟨fun h => eq_of_ae_eq h hf hg, fun h => h ▸ EventuallyEq.rfl⟩
@@ -225,84 +141,39 @@ section LinearOrder
 variable {X Y : Type _} [TopologicalSpace X] [LinearOrder X] [OrderTopology X]
   {m : MeasurableSpace X} [TopologicalSpace Y] [T2Space Y] (μ : Measure X) [OpenPosMeasure μ]
 
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 theorem measure_Ioi_pos [NoMaxOrder X] (a : X) : 0 < μ (Ioi a) :=
   isOpen_Ioi.measure_pos μ nonempty_Ioi
 #align measure_theory.measure.measure_Ioi_pos MeasureTheory.Measure.measure_Ioi_pos
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_Iio_pos MeasureTheory.Measure.measure_Iio_posₓ'. -/
 theorem measure_Iio_pos [NoMinOrder X] (a : X) : 0 < μ (Iio a) :=
   isOpen_Iio.measure_pos μ nonempty_Iio
 #align measure_theory.measure.measure_Iio_pos MeasureTheory.Measure.measure_Iio_pos
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_Ioo_pos MeasureTheory.Measure.measure_Ioo_posₓ'. -/
 theorem measure_Ioo_pos [DenselyOrdered X] {a b : X} : 0 < μ (Ioo a b) ↔ a < b :=
   (isOpen_Ioo.measure_pos_iff μ).trans nonempty_Ioo
 #align measure_theory.measure.measure_Ioo_pos MeasureTheory.Measure.measure_Ioo_pos
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_Ioo_eq_zero MeasureTheory.Measure.measure_Ioo_eq_zeroₓ'. -/
 theorem measure_Ioo_eq_zero [DenselyOrdered X] {a b : X} : μ (Ioo a b) = 0 ↔ b ≤ a :=
   (isOpen_Ioo.measure_eq_zero_iff μ).trans (Ioo_eq_empty_iff.trans not_lt)
 #align measure_theory.measure.measure_Ioo_eq_zero MeasureTheory.Measure.measure_Ioo_eq_zero
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Ioo_of_ae_eq MeasureTheory.Measure.eqOn_Ioo_of_ae_eqₓ'. -/
 theorem eqOn_Ioo_of_ae_eq {a b : X} {f g : X → Y} (hfg : f =ᵐ[μ.restrict (Ioo a b)] g)
     (hf : ContinuousOn f (Ioo a b)) (hg : ContinuousOn g (Ioo a b)) : EqOn f g (Ioo a b) :=
   eqOn_of_ae_eq hfg hf hg Ioo_subset_closure_interior
 #align measure_theory.measure.eq_on_Ioo_of_ae_eq MeasureTheory.Measure.eqOn_Ioo_of_ae_eq
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Ioc_of_ae_eq MeasureTheory.Measure.eqOn_Ioc_of_ae_eqₓ'. -/
 theorem eqOn_Ioc_of_ae_eq [DenselyOrdered X] {a b : X} {f g : X → Y}
     (hfg : f =ᵐ[μ.restrict (Ioc a b)] g) (hf : ContinuousOn f (Ioc a b))
     (hg : ContinuousOn g (Ioc a b)) : EqOn f g (Ioc a b) :=
   eqOn_of_ae_eq hfg hf hg (Ioc_subset_closure_interior _ _)
 #align measure_theory.measure.eq_on_Ioc_of_ae_eq MeasureTheory.Measure.eqOn_Ioc_of_ae_eq
 
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-Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Ico_of_ae_eq MeasureTheory.Measure.eqOn_Ico_of_ae_eqₓ'. -/
 theorem eqOn_Ico_of_ae_eq [DenselyOrdered X] {a b : X} {f g : X → Y}
     (hfg : f =ᵐ[μ.restrict (Ico a b)] g) (hf : ContinuousOn f (Ico a b))
     (hg : ContinuousOn g (Ico a b)) : EqOn f g (Ico a b) :=
   eqOn_of_ae_eq hfg hf hg (Ico_subset_closure_interior _ _)
 #align measure_theory.measure.eq_on_Ico_of_ae_eq MeasureTheory.Measure.eqOn_Ico_of_ae_eq
 
-/- warning: measure_theory.measure.eq_on_Icc_of_ae_eq -> MeasureTheory.Measure.eqOn_Icc_of_ae_eq is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Icc_of_ae_eq MeasureTheory.Measure.eqOn_Icc_of_ae_eqₓ'. -/
 theorem eqOn_Icc_of_ae_eq [DenselyOrdered X] {a b : X} (hne : a ≠ b) {f g : X → Y}
     (hfg : f =ᵐ[μ.restrict (Icc a b)] g) (hf : ContinuousOn f (Icc a b))
     (hg : ContinuousOn g (Icc a b)) : EqOn f g (Icc a b) :=
@@ -322,22 +193,10 @@ namespace Metric
 variable {X : Type _} [PseudoMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
   [OpenPosMeasure μ]
 
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-Case conversion may be inaccurate. Consider using '#align metric.measure_ball_pos Metric.measure_ball_posₓ'. -/
 theorem measure_ball_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (ball x r) :=
   isOpen_ball.measure_pos μ (nonempty_ball.2 hr)
 #align metric.measure_ball_pos Metric.measure_ball_pos
 
-/- warning: metric.measure_closed_ball_pos -> Metric.measure_closedBall_pos is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Metric.closedBall.{u1} X _inst_1 x r)))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Metric.closedBall.{u1} X _inst_1 x r)))
-Case conversion may be inaccurate. Consider using '#align metric.measure_closed_ball_pos Metric.measure_closedBall_posₓ'. -/
 theorem measure_closedBall_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (closedBall x r) :=
   (measure_ball_pos μ x hr).trans_le (measure_mono ball_subset_closedBall)
 #align metric.measure_closed_ball_pos Metric.measure_closedBall_pos
@@ -349,22 +208,10 @@ namespace Emetric
 variable {X : Type _} [PseudoEMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
   [OpenPosMeasure μ]
 
-/- warning: emetric.measure_ball_pos -> EMetric.measure_ball_pos is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (EMetric.ball.{u1} X _inst_1 x r)))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (EMetric.ball.{u1} X _inst_1 x r)))
-Case conversion may be inaccurate. Consider using '#align emetric.measure_ball_pos EMetric.measure_ball_posₓ'. -/
 theorem measure_ball_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ (ball x r) :=
   isOpen_ball.measure_pos μ ⟨x, mem_ball_self hr.bot_lt⟩
 #align emetric.measure_ball_pos EMetric.measure_ball_pos
 
-/- warning: emetric.measure_closed_ball_pos -> EMetric.measure_closedBall_pos is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (EMetric.closedBall.{u1} X _inst_1 x r)))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (EMetric.closedBall.{u1} X _inst_1 x r)))
-Case conversion may be inaccurate. Consider using '#align emetric.measure_closed_ball_pos EMetric.measure_closedBall_posₓ'. -/
 theorem measure_closedBall_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ (closedBall x r) :=
   (measure_ball_pos μ x hr).trans_le (measure_mono ball_subset_closedBall)
 #align emetric.measure_closed_ball_pos EMetric.measure_closedBall_pos

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

@@ -301,10 +301,7 @@ theorem eqOn_Ico_of_ae_eq [DenselyOrdered X] {a b : X} {f g : X → Y}
 #align measure_theory.measure.eq_on_Ico_of_ae_eq MeasureTheory.Measure.eqOn_Ico_of_ae_eq
 
 /- warning: measure_theory.measure.eq_on_Icc_of_ae_eq -> MeasureTheory.Measure.eqOn_Icc_of_ae_eq is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} [_inst_4 : TopologicalSpace.{u2} Y] [_inst_5 : T2Space.{u2} Y _inst_4] (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toHasLt.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X}, (Ne.{succ u1} X a b) -> (forall {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 f (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 g (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (Set.EqOn.{u1, u2} X Y f g (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)))
-but is expected to have type
-  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : LinearOrder.{u2} X] [_inst_3 : OrderTopology.{u2} X _inst_1 (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2)))))] {m : MeasurableSpace.{u2} X} [_inst_4 : TopologicalSpace.{u1} Y] [_inst_5 : T2Space.{u1} Y _inst_4] (μ : MeasureTheory.Measure.{u2} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u2} X (Preorder.toLT.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))))] {a : X} {b : X}, (Ne.{succ u2} X a b) -> (forall {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m (MeasureTheory.Measure.restrict.{u2} X m μ (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))) f g) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 f (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 g (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (Set.EqOn.{u2, u1} X Y f g (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)))
+<too large>
 Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Icc_of_ae_eq MeasureTheory.Measure.eqOn_Icc_of_ae_eqₓ'. -/
 theorem eqOn_Icc_of_ae_eq [DenselyOrdered X] {a b : X} (hne : a ≠ b) {f g : X → Y}
     (hfg : f =ᵐ[μ.restrict (Icc a b)] g) (hf : ContinuousOn f (Icc a b))

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

@@ -58,7 +58,7 @@ theorem IsOpen.measure_ne_zero (hU : IsOpen U) (hne : U.Nonempty) : μ U ≠ 0 :
 
 /- warning: is_open.measure_pos -> IsOpen.measure_pos is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Set.Nonempty.{u1} X U) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ U))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Set.Nonempty.{u1} X U) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ U))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Set.Nonempty.{u1} X U) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) U))
 Case conversion may be inaccurate. Consider using '#align is_open.measure_pos IsOpen.measure_posₓ'. -/
@@ -68,7 +68,7 @@ theorem IsOpen.measure_pos (hU : IsOpen U) (hne : U.Nonempty) : 0 < μ U :=
 
 /- warning: is_open.measure_pos_iff -> IsOpen.measure_pos_iff is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Iff (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ U)) (Set.Nonempty.{u1} X U))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Iff (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ U)) (Set.Nonempty.{u1} X U))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Iff (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) U)) (Set.Nonempty.{u1} X U))
 Case conversion may be inaccurate. Consider using '#align is_open.measure_pos_iff IsOpen.measure_pos_iffₓ'. -/
@@ -89,7 +89,7 @@ theorem IsOpen.measure_eq_zero_iff (hU : IsOpen U) : μ U = 0 ↔ U = ∅ := by
 
 /- warning: measure_theory.measure.measure_pos_of_nonempty_interior -> MeasureTheory.Measure.measure_pos_of_nonempty_interior is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X}, (Set.Nonempty.{u1} X (interior.{u1} X _inst_1 s)) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ s))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X}, (Set.Nonempty.{u1} X (interior.{u1} X _inst_1 s)) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ s))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X}, (Set.Nonempty.{u1} X (interior.{u1} X _inst_1 s)) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) s))
 Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_pos_of_nonempty_interior MeasureTheory.Measure.measure_pos_of_nonempty_interiorₓ'. -/
@@ -99,7 +99,7 @@ theorem measure_pos_of_nonempty_interior (h : (interior s).Nonempty) : 0 < μ s
 
 /- warning: measure_theory.measure.measure_pos_of_mem_nhds -> MeasureTheory.Measure.measure_pos_of_mem_nhds is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X} {x : X}, (Membership.Mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (Filter.hasMem.{u1} X) s (nhds.{u1} X _inst_1 x)) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ s))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X} {x : X}, (Membership.Mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (Filter.hasMem.{u1} X) s (nhds.{u1} X _inst_1 x)) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ s))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X} {x : X}, (Membership.mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (instMembershipSetFilter.{u1} X) s (nhds.{u1} X _inst_1 x)) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) s))
 Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_pos_of_mem_nhds MeasureTheory.Measure.measure_pos_of_mem_nhdsₓ'. -/
@@ -125,11 +125,15 @@ protected theorem AbsolutelyContinuous.openPosMeasure (h : μ ≪ ν) : OpenPosM
 #align measure_theory.measure.absolutely_continuous.is_open_pos_measure MeasureTheory.Measure.AbsolutelyContinuous.openPosMeasure
 -/
 
-#print LE.le.isOpenPosMeasure /-
+/- warning: has_le.le.is_open_pos_measure -> LE.le.isOpenPosMeasure is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} {μ : MeasureTheory.Measure.{u1} X m} {ν : MeasureTheory.Measure.{u1} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ], (LE.le.{u1} (MeasureTheory.Measure.{u1} X m) (Preorder.toHasLe.{u1} (MeasureTheory.Measure.{u1} X m) (PartialOrder.toPreorder.{u1} (MeasureTheory.Measure.{u1} X m) (MeasureTheory.Measure.instPartialOrder.{u1} X m))) μ ν) -> (MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m ν)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} {μ : MeasureTheory.Measure.{u1} X m} {ν : MeasureTheory.Measure.{u1} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ], (LE.le.{u1} (MeasureTheory.Measure.{u1} X m) (Preorder.toLE.{u1} (MeasureTheory.Measure.{u1} X m) (PartialOrder.toPreorder.{u1} (MeasureTheory.Measure.{u1} X m) (MeasureTheory.Measure.instPartialOrder.{u1} X m))) μ ν) -> (MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m ν)
+Case conversion may be inaccurate. Consider using '#align has_le.le.is_open_pos_measure LE.le.isOpenPosMeasureₓ'. -/
 theorem LE.le.isOpenPosMeasure (h : μ ≤ ν) : OpenPosMeasure ν :=
   h.AbsolutelyContinuous.OpenPosMeasure
 #align has_le.le.is_open_pos_measure LE.le.isOpenPosMeasure
--/
 
 /- warning: is_open.eq_empty_of_measure_zero -> IsOpen.eq_empty_of_measure_zero is a dubious translation:
 lean 3 declaration is
@@ -223,7 +227,7 @@ variable {X Y : Type _} [TopologicalSpace X] [LinearOrder X] [OrderTopology X]
 
 /- warning: measure_theory.measure.measure_Ioi_pos -> MeasureTheory.Measure.measure_Ioi_pos is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : NoMaxOrder.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] (a : X), 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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Ioi.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : NoMaxOrder.{u1} X (Preorder.toHasLt.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] (a : X), 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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Ioi.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : NoMaxOrder.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))))] (a : X), 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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Set.Ioi.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))) a))
 Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_Ioi_pos MeasureTheory.Measure.measure_Ioi_posₓ'. -/
@@ -233,7 +237,7 @@ theorem measure_Ioi_pos [NoMaxOrder X] (a : X) : 0 < μ (Ioi a) :=
 
 /- warning: measure_theory.measure.measure_Iio_pos -> MeasureTheory.Measure.measure_Iio_pos is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : NoMinOrder.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] (a : X), 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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Iio.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a))
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : NoMinOrder.{u1} X (Preorder.toHasLt.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] (a : X), 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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Iio.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : NoMinOrder.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))))] (a : X), 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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Set.Iio.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))) a))
 Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_Iio_pos MeasureTheory.Measure.measure_Iio_posₓ'. -/
@@ -243,7 +247,7 @@ theorem measure_Iio_pos [NoMinOrder X] (a : X) : 0 < μ (Iio a) :=
 
 /- warning: measure_theory.measure.measure_Ioo_pos -> MeasureTheory.Measure.measure_Ioo_pos is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X}, Iff (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) (LT.lt.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))) a b)
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toHasLt.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X}, Iff (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) (LT.lt.{u1} X (Preorder.toHasLt.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))) a b)
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))))] {a : X} {b : X}, Iff (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))) a b))) (LT.lt.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))) a b)
 Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_Ioo_pos MeasureTheory.Measure.measure_Ioo_posₓ'. -/
@@ -253,7 +257,7 @@ theorem measure_Ioo_pos [DenselyOrdered X] {a b : X} : 0 < μ (Ioo a b) ↔ a <
 
 /- warning: measure_theory.measure.measure_Ioo_eq_zero -> MeasureTheory.Measure.measure_Ioo_eq_zero is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X}, Iff (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (LE.le.{u1} X (Preorder.toLE.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))) b a)
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toHasLt.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X}, Iff (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (LE.le.{u1} X (Preorder.toHasLe.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))) b a)
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))))] {a : X} {b : X}, Iff (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))) a b)) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (LE.le.{u1} X (Preorder.toLE.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))) b a)
 Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_Ioo_eq_zero MeasureTheory.Measure.measure_Ioo_eq_zeroₓ'. -/
@@ -274,7 +278,7 @@ theorem eqOn_Ioo_of_ae_eq {a b : X} {f g : X → Y} (hfg : f =ᵐ[μ.restrict (I
 
 /- warning: measure_theory.measure.eq_on_Ioc_of_ae_eq -> MeasureTheory.Measure.eqOn_Ioc_of_ae_eq is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} [_inst_4 : TopologicalSpace.{u2} Y] [_inst_5 : T2Space.{u2} Y _inst_4] (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 f (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 g (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (Set.EqOn.{u1, u2} X Y f g (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} [_inst_4 : TopologicalSpace.{u2} Y] [_inst_5 : T2Space.{u2} Y _inst_4] (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toHasLt.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 f (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 g (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (Set.EqOn.{u1, u2} X Y f g (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))
 but is expected to have type
   forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : LinearOrder.{u2} X] [_inst_3 : OrderTopology.{u2} X _inst_1 (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2)))))] {m : MeasurableSpace.{u2} X} [_inst_4 : TopologicalSpace.{u1} Y] [_inst_5 : T2Space.{u1} Y _inst_4] (μ : MeasureTheory.Measure.{u2} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u2} X (Preorder.toLT.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))))] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m (MeasureTheory.Measure.restrict.{u2} X m μ (Set.Ioc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))) f g) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 f (Set.Ioc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 g (Set.Ioc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (Set.EqOn.{u2, u1} X Y f g (Set.Ioc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))
 Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Ioc_of_ae_eq MeasureTheory.Measure.eqOn_Ioc_of_ae_eqₓ'. -/
@@ -286,7 +290,7 @@ theorem eqOn_Ioc_of_ae_eq [DenselyOrdered X] {a b : X} {f g : X → Y}
 
 /- warning: measure_theory.measure.eq_on_Ico_of_ae_eq -> MeasureTheory.Measure.eqOn_Ico_of_ae_eq is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} [_inst_4 : TopologicalSpace.{u2} Y] [_inst_5 : T2Space.{u2} Y _inst_4] (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 f (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 g (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (Set.EqOn.{u1, u2} X Y f g (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} [_inst_4 : TopologicalSpace.{u2} Y] [_inst_5 : T2Space.{u2} Y _inst_4] (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toHasLt.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 f (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 g (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (Set.EqOn.{u1, u2} X Y f g (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))
 but is expected to have type
   forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : LinearOrder.{u2} X] [_inst_3 : OrderTopology.{u2} X _inst_1 (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2)))))] {m : MeasurableSpace.{u2} X} [_inst_4 : TopologicalSpace.{u1} Y] [_inst_5 : T2Space.{u1} Y _inst_4] (μ : MeasureTheory.Measure.{u2} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u2} X (Preorder.toLT.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))))] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m (MeasureTheory.Measure.restrict.{u2} X m μ (Set.Ico.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))) f g) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 f (Set.Ico.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 g (Set.Ico.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (Set.EqOn.{u2, u1} X Y f g (Set.Ico.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))
 Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Ico_of_ae_eq MeasureTheory.Measure.eqOn_Ico_of_ae_eqₓ'. -/
@@ -298,7 +302,7 @@ theorem eqOn_Ico_of_ae_eq [DenselyOrdered X] {a b : X} {f g : X → Y}
 
 /- warning: measure_theory.measure.eq_on_Icc_of_ae_eq -> MeasureTheory.Measure.eqOn_Icc_of_ae_eq is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} [_inst_4 : TopologicalSpace.{u2} Y] [_inst_5 : T2Space.{u2} Y _inst_4] (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X}, (Ne.{succ u1} X a b) -> (forall {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 f (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 g (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (Set.EqOn.{u1, u2} X Y f g (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)))
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} [_inst_4 : TopologicalSpace.{u2} Y] [_inst_5 : T2Space.{u2} Y _inst_4] (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toHasLt.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X}, (Ne.{succ u1} X a b) -> (forall {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 f (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 g (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (Set.EqOn.{u1, u2} X Y f g (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)))
 but is expected to have type
   forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : LinearOrder.{u2} X] [_inst_3 : OrderTopology.{u2} X _inst_1 (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2)))))] {m : MeasurableSpace.{u2} X} [_inst_4 : TopologicalSpace.{u1} Y] [_inst_5 : T2Space.{u1} Y _inst_4] (μ : MeasureTheory.Measure.{u2} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u2} X (Preorder.toLT.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))))] {a : X} {b : X}, (Ne.{succ u2} X a b) -> (forall {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m (MeasureTheory.Measure.restrict.{u2} X m μ (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))) f g) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 f (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 g (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (Set.EqOn.{u2, u1} X Y f g (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)))
 Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Icc_of_ae_eq MeasureTheory.Measure.eqOn_Icc_of_ae_eqₓ'. -/
@@ -323,7 +327,7 @@ variable {X : Type _} [PseudoMetricSpace X] {m : MeasurableSpace X} (μ : Measur
 
 /- warning: metric.measure_ball_pos -> Metric.measure_ball_pos is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Metric.ball.{u1} X _inst_1 x r)))
+  forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Metric.ball.{u1} X _inst_1 x r)))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Metric.ball.{u1} X _inst_1 x r)))
 Case conversion may be inaccurate. Consider using '#align metric.measure_ball_pos Metric.measure_ball_posₓ'. -/
@@ -333,7 +337,7 @@ theorem measure_ball_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (ball x r) :=
 
 /- warning: metric.measure_closed_ball_pos -> Metric.measure_closedBall_pos is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Metric.closedBall.{u1} X _inst_1 x r)))
+  forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Metric.closedBall.{u1} X _inst_1 x r)))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Metric.closedBall.{u1} X _inst_1 x r)))
 Case conversion may be inaccurate. Consider using '#align metric.measure_closed_ball_pos Metric.measure_closedBall_posₓ'. -/
@@ -350,7 +354,7 @@ variable {X : Type _} [PseudoEMetricSpace X] {m : MeasurableSpace X} (μ : Measu
 
 /- warning: emetric.measure_ball_pos -> EMetric.measure_ball_pos is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (EMetric.ball.{u1} X _inst_1 x r)))
+  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (EMetric.ball.{u1} X _inst_1 x r)))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (EMetric.ball.{u1} X _inst_1 x r)))
 Case conversion may be inaccurate. Consider using '#align emetric.measure_ball_pos EMetric.measure_ball_posₓ'. -/
@@ -360,7 +364,7 @@ theorem measure_ball_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ (ball
 
 /- warning: emetric.measure_closed_ball_pos -> EMetric.measure_closedBall_pos is a dubious translation:
 lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (EMetric.closedBall.{u1} X _inst_1 x r)))
+  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (EMetric.closedBall.{u1} X _inst_1 x r)))
 but is expected to have type
   forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (EMetric.closedBall.{u1} X _inst_1 x r)))
 Case conversion may be inaccurate. Consider using '#align emetric.measure_closed_ball_pos EMetric.measure_closedBall_posₓ'. -/

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 measure_theory.measure.open_pos
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! 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.MeasureSpace
 /-!
 # Measures positive on nonempty opens
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define a typeclass for measures that are positive on nonempty opens, see
 `measure_theory.measure.is_open_pos_measure`. Examples include (additive) Haar measures, as well as
 measures that have positive density with respect to a Haar measure. We also prove some basic facts

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 measure_theory.measure.open_pos
-! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
+! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
 ! 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.MeasureSpace
 /-!
 # Measures positive on nonempty opens
 
-> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
-> Any changes to this file require a corresponding PR to mathlib4.
-
 In this file we define a typeclass for measures that are positive on nonempty opens, see
 `measure_theory.measure.is_open_pos_measure`. Examples include (additive) Haar measures, as well as
 measures that have positive density with respect to a Haar measure. We also prove some basic facts

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 measure_theory.measure.open_pos
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! 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.MeasureSpace
 /-!
 # Measures positive on nonempty opens
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define a typeclass for measures that are positive on nonempty opens, see
 `measure_theory.measure.is_open_pos_measure`. Examples include (additive) Haar measures, as well as
 measures that have positive density with respect to a Haar measure. We also prove some basic facts

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

@@ -34,60 +34,126 @@ section Basic
 variable {X Y : Type _} [TopologicalSpace X] {m : MeasurableSpace X} [TopologicalSpace Y]
   [T2Space Y] (μ ν : Measure X)
 
+#print MeasureTheory.Measure.OpenPosMeasure /-
 /-- A measure is said to be `is_open_pos_measure` if it is positive on nonempty open sets. -/
-class IsOpenPosMeasure : Prop where
+class OpenPosMeasure : Prop where
   open_pos : ∀ U : Set X, IsOpen U → U.Nonempty → μ U ≠ 0
-#align measure_theory.measure.is_open_pos_measure MeasureTheory.Measure.IsOpenPosMeasure
+#align measure_theory.measure.is_open_pos_measure MeasureTheory.Measure.OpenPosMeasure
+-/
 
-variable [IsOpenPosMeasure μ] {s U : Set X} {x : X}
+variable [OpenPosMeasure μ] {s U : Set X} {x : X}
 
+/- warning: is_open.measure_ne_zero -> IsOpen.measure_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Set.Nonempty.{u1} X U) -> (Ne.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ U) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Set.Nonempty.{u1} X U) -> (Ne.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) U) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align is_open.measure_ne_zero IsOpen.measure_ne_zeroₓ'. -/
 theorem IsOpen.measure_ne_zero (hU : IsOpen U) (hne : U.Nonempty) : μ U ≠ 0 :=
-  IsOpenPosMeasure.open_pos U hU hne
+  OpenPosMeasure.open_pos U hU hne
 #align is_open.measure_ne_zero IsOpen.measure_ne_zero
 
+/- warning: is_open.measure_pos -> IsOpen.measure_pos is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Set.Nonempty.{u1} X U) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ U))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Set.Nonempty.{u1} X U) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) U))
+Case conversion may be inaccurate. Consider using '#align is_open.measure_pos IsOpen.measure_posₓ'. -/
 theorem IsOpen.measure_pos (hU : IsOpen U) (hne : U.Nonempty) : 0 < μ U :=
   (hU.measure_ne_zero μ hne).bot_lt
 #align is_open.measure_pos IsOpen.measure_pos
 
+/- warning: is_open.measure_pos_iff -> IsOpen.measure_pos_iff is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Iff (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ U)) (Set.Nonempty.{u1} X U))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Iff (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) U)) (Set.Nonempty.{u1} X U))
+Case conversion may be inaccurate. Consider using '#align is_open.measure_pos_iff IsOpen.measure_pos_iffₓ'. -/
 theorem IsOpen.measure_pos_iff (hU : IsOpen U) : 0 < μ U ↔ U.Nonempty :=
   ⟨fun h => nonempty_iff_ne_empty.2 fun he => h.ne' <| he.symm ▸ measure_empty, hU.measure_pos μ⟩
 #align is_open.measure_pos_iff IsOpen.measure_pos_iff
 
+/- warning: is_open.measure_eq_zero_iff -> IsOpen.measure_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Iff (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ U) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Eq.{succ u1} (Set.{u1} X) U (EmptyCollection.emptyCollection.{u1} (Set.{u1} X) (Set.hasEmptyc.{u1} X))))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Iff (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) U) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Eq.{succ u1} (Set.{u1} X) U (EmptyCollection.emptyCollection.{u1} (Set.{u1} X) (Set.instEmptyCollectionSet.{u1} X))))
+Case conversion may be inaccurate. Consider using '#align is_open.measure_eq_zero_iff IsOpen.measure_eq_zero_iffₓ'. -/
 theorem IsOpen.measure_eq_zero_iff (hU : IsOpen U) : μ U = 0 ↔ U = ∅ := by
   simpa only [not_lt, nonpos_iff_eq_zero, not_nonempty_iff_eq_empty] using
     not_congr (hU.measure_pos_iff μ)
 #align is_open.measure_eq_zero_iff IsOpen.measure_eq_zero_iff
 
+/- warning: measure_theory.measure.measure_pos_of_nonempty_interior -> MeasureTheory.Measure.measure_pos_of_nonempty_interior is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X}, (Set.Nonempty.{u1} X (interior.{u1} X _inst_1 s)) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ s))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X}, (Set.Nonempty.{u1} X (interior.{u1} X _inst_1 s)) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) s))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_pos_of_nonempty_interior MeasureTheory.Measure.measure_pos_of_nonempty_interiorₓ'. -/
 theorem measure_pos_of_nonempty_interior (h : (interior s).Nonempty) : 0 < μ s :=
   (isOpen_interior.measure_pos μ h).trans_le (measure_mono interior_subset)
 #align measure_theory.measure.measure_pos_of_nonempty_interior MeasureTheory.Measure.measure_pos_of_nonempty_interior
 
+/- warning: measure_theory.measure.measure_pos_of_mem_nhds -> MeasureTheory.Measure.measure_pos_of_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X} {x : X}, (Membership.Mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (Filter.hasMem.{u1} X) s (nhds.{u1} X _inst_1 x)) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ s))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X} {x : X}, (Membership.mem.{u1, u1} (Set.{u1} X) (Filter.{u1} X) (instMembershipSetFilter.{u1} X) s (nhds.{u1} X _inst_1 x)) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) s))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_pos_of_mem_nhds MeasureTheory.Measure.measure_pos_of_mem_nhdsₓ'. -/
 theorem measure_pos_of_mem_nhds (h : s ∈ 𝓝 x) : 0 < μ s :=
   measure_pos_of_nonempty_interior _ ⟨x, mem_interior_iff_mem_nhds.2 h⟩
 #align measure_theory.measure.measure_pos_of_mem_nhds MeasureTheory.Measure.measure_pos_of_mem_nhds
 
-theorem isOpenPosMeasure_smul {c : ℝ≥0∞} (h : c ≠ 0) : IsOpenPosMeasure (c • μ) :=
+/- warning: measure_theory.measure.is_open_pos_measure_smul -> MeasureTheory.Measure.openPosMeasure_smul is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {c : ENNReal}, (Ne.{1} ENNReal c (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m (SMul.smul.{0, u1} ENNReal (MeasureTheory.Measure.{u1} X m) (MeasureTheory.Measure.instSMul.{u1, 0} X ENNReal (SMulZeroClass.toHasSmul.{0, 0} ENNReal ENNReal (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (SMulWithZero.toSmulZeroClass.{0, 0} ENNReal ENNReal (MulZeroClass.toHasZero.{0} ENNReal (MulZeroOneClass.toMulZeroClass.{0} ENNReal (MonoidWithZero.toMulZeroOneClass.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (CommSemiring.toSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (MulActionWithZero.toSMulWithZero.{0, 0} ENNReal ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (CommSemiring.toSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))) (AddZeroClass.toHasZero.{0} ENNReal (AddMonoid.toAddZeroClass.{0} ENNReal (AddCommMonoid.toAddMonoid.{0} ENNReal (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) (Module.toMulActionWithZero.{0, 0} ENNReal ENNReal (CommSemiring.toSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)) (NonUnitalNonAssocSemiring.toAddCommMonoid.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))) (Algebra.toModule.{0, 0} ENNReal ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring) (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (IsScalarTower.right.{0, 0} ENNReal ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring) (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))) m) c μ))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {c : ENNReal}, (Ne.{1} ENNReal c (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m (HSMul.hSMul.{0, u1, u1} ENNReal (MeasureTheory.Measure.{u1} X m) (MeasureTheory.Measure.{u1} X m) (instHSMul.{0, u1} ENNReal (MeasureTheory.Measure.{u1} X m) (MeasureTheory.Measure.instSMul.{u1, 0} X ENNReal (Algebra.toSMul.{0, 0} ENNReal ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) (IsScalarTower.right.{0, 0} ENNReal ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (CommSemiring.toSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (Algebra.id.{0} ENNReal (CanonicallyOrderedCommSemiring.toCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) m)) c μ))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.openPosMeasure_smulₓ'. -/
+theorem openPosMeasure_smul {c : ℝ≥0∞} (h : c ≠ 0) : OpenPosMeasure (c • μ) :=
   ⟨fun U Uo Une => mul_ne_zero h (Uo.measure_ne_zero μ Une)⟩
-#align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.isOpenPosMeasure_smul
+#align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.openPosMeasure_smul
 
 variable {μ ν}
 
-protected theorem AbsolutelyContinuous.isOpenPosMeasure (h : μ ≪ ν) : IsOpenPosMeasure ν :=
+#print MeasureTheory.Measure.AbsolutelyContinuous.openPosMeasure /-
+protected theorem AbsolutelyContinuous.openPosMeasure (h : μ ≪ ν) : OpenPosMeasure ν :=
   ⟨fun U ho hne h₀ => ho.measure_ne_zero μ hne (h h₀)⟩
-#align measure_theory.measure.absolutely_continuous.is_open_pos_measure MeasureTheory.Measure.AbsolutelyContinuous.isOpenPosMeasure
+#align measure_theory.measure.absolutely_continuous.is_open_pos_measure MeasureTheory.Measure.AbsolutelyContinuous.openPosMeasure
+-/
 
-theorem LE.le.isOpenPosMeasure (h : μ ≤ ν) : IsOpenPosMeasure ν :=
-  h.AbsolutelyContinuous.IsOpenPosMeasure
+#print LE.le.isOpenPosMeasure /-
+theorem LE.le.isOpenPosMeasure (h : μ ≤ ν) : OpenPosMeasure ν :=
+  h.AbsolutelyContinuous.OpenPosMeasure
 #align has_le.le.is_open_pos_measure LE.le.isOpenPosMeasure
+-/
 
+/- warning: is_open.eq_empty_of_measure_zero -> IsOpen.eq_empty_of_measure_zero is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} {μ : MeasureTheory.Measure.{u1} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ U) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Eq.{succ u1} (Set.{u1} X) U (EmptyCollection.emptyCollection.{u1} (Set.{u1} X) (Set.hasEmptyc.{u1} X)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} {μ : MeasureTheory.Measure.{u1} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X}, (IsOpen.{u1} X _inst_1 U) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) U) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Eq.{succ u1} (Set.{u1} X) U (EmptyCollection.emptyCollection.{u1} (Set.{u1} X) (Set.instEmptyCollectionSet.{u1} X)))
+Case conversion may be inaccurate. Consider using '#align is_open.eq_empty_of_measure_zero IsOpen.eq_empty_of_measure_zeroₓ'. -/
 theorem IsOpen.eq_empty_of_measure_zero (hU : IsOpen U) (h₀ : μ U = 0) : U = ∅ :=
   (hU.measure_eq_zero_iff μ).mp h₀
 #align is_open.eq_empty_of_measure_zero IsOpen.eq_empty_of_measure_zero
 
+/- warning: measure_theory.measure.interior_eq_empty_of_null -> MeasureTheory.Measure.interior_eq_empty_of_null is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} {μ : MeasureTheory.Measure.{u1} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X}, (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Eq.{succ u1} (Set.{u1} X) (interior.{u1} X _inst_1 s) (EmptyCollection.emptyCollection.{u1} (Set.{u1} X) (Set.hasEmptyc.{u1} X)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} {μ : MeasureTheory.Measure.{u1} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X}, (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Eq.{succ u1} (Set.{u1} X) (interior.{u1} X _inst_1 s) (EmptyCollection.emptyCollection.{u1} (Set.{u1} X) (Set.instEmptyCollectionSet.{u1} X)))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.interior_eq_empty_of_null MeasureTheory.Measure.interior_eq_empty_of_nullₓ'. -/
 theorem interior_eq_empty_of_null (hs : μ s = 0) : interior s = ∅ :=
   isOpen_interior.eq_empty_of_measure_zero <| measure_mono_null interior_subset hs
 #align measure_theory.measure.interior_eq_empty_of_null MeasureTheory.Measure.interior_eq_empty_of_null
 
+/- warning: measure_theory.measure.eq_on_open_of_ae_eq -> MeasureTheory.Measure.eqOn_open_of_ae_eq is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} [_inst_2 : TopologicalSpace.{u2} Y] [_inst_3 : T2Space.{u2} Y _inst_2] {μ : MeasureTheory.Measure.{u1} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {U : Set.{u1} X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ U)) f g) -> (IsOpen.{u1} X _inst_1 U) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_2 f U) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_2 g U) -> (Set.EqOn.{u1, u2} X Y f g U)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] {m : MeasurableSpace.{u2} X} [_inst_2 : TopologicalSpace.{u1} Y] [_inst_3 : T2Space.{u1} Y _inst_2] {μ : MeasureTheory.Measure.{u2} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] {U : Set.{u2} X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m (MeasureTheory.Measure.restrict.{u2} X m μ U)) f g) -> (IsOpen.{u2} X _inst_1 U) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_2 f U) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_2 g U) -> (Set.EqOn.{u2, u1} X Y f g U)
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_open_of_ae_eq MeasureTheory.Measure.eqOn_open_of_ae_eqₓ'. -/
 /-- If two functions are a.e. equal on an open set and are continuous on this set, then they are
 equal on this set. -/
 theorem eqOn_open_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict U] g) (hU : IsOpen U)
@@ -106,12 +172,24 @@ theorem eqOn_open_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict U] g) (hU : I
   exact fun x hx => Classical.not_not.1 fun h => this ⟨hx, h⟩
 #align measure_theory.measure.eq_on_open_of_ae_eq MeasureTheory.Measure.eqOn_open_of_ae_eq
 
+/- warning: measure_theory.measure.eq_of_ae_eq -> MeasureTheory.Measure.eq_of_ae_eq is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} [_inst_2 : TopologicalSpace.{u2} Y] [_inst_3 : T2Space.{u2} Y _inst_2] {μ : MeasureTheory.Measure.{u1} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m μ) f g) -> (Continuous.{u1, u2} X Y _inst_1 _inst_2 f) -> (Continuous.{u1, u2} X Y _inst_1 _inst_2 g) -> (Eq.{max (succ u1) (succ u2)} (X -> Y) f g)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] {m : MeasurableSpace.{u2} X} [_inst_2 : TopologicalSpace.{u1} Y] [_inst_3 : T2Space.{u1} Y _inst_2] {μ : MeasureTheory.Measure.{u2} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m μ) f g) -> (Continuous.{u2, u1} X Y _inst_1 _inst_2 f) -> (Continuous.{u2, u1} X Y _inst_1 _inst_2 g) -> (Eq.{max (succ u2) (succ u1)} (X -> Y) f g)
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_of_ae_eq MeasureTheory.Measure.eq_of_ae_eqₓ'. -/
 /-- If two continuous functions are a.e. equal, then they are equal. -/
 theorem eq_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ] g) (hf : Continuous f) (hg : Continuous g) : f = g :=
   suffices EqOn f g univ from funext fun x => this trivial
   eqOn_open_of_ae_eq (ae_restrict_of_ae h) isOpen_univ hf.ContinuousOn hg.ContinuousOn
 #align measure_theory.measure.eq_of_ae_eq MeasureTheory.Measure.eq_of_ae_eq
 
+/- warning: measure_theory.measure.eq_on_of_ae_eq -> MeasureTheory.Measure.eqOn_of_ae_eq is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} [_inst_2 : TopologicalSpace.{u2} Y] [_inst_3 : T2Space.{u2} Y _inst_2] {μ : MeasureTheory.Measure.{u1} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {s : Set.{u1} X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ s)) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_2 f s) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_2 g s) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.hasSubset.{u1} X) s (closure.{u1} X _inst_1 (interior.{u1} X _inst_1 s))) -> (Set.EqOn.{u1, u2} X Y f g s)
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] {m : MeasurableSpace.{u2} X} [_inst_2 : TopologicalSpace.{u1} Y] [_inst_3 : T2Space.{u1} Y _inst_2] {μ : MeasureTheory.Measure.{u2} X m} [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] {s : Set.{u2} X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m (MeasureTheory.Measure.restrict.{u2} X m μ s)) f g) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_2 f s) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_2 g s) -> (HasSubset.Subset.{u2} (Set.{u2} X) (Set.instHasSubsetSet.{u2} X) s (closure.{u2} X _inst_1 (interior.{u2} X _inst_1 s))) -> (Set.EqOn.{u2, u1} X Y f g s)
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_of_ae_eq MeasureTheory.Measure.eqOn_of_ae_eqₓ'. -/
 theorem eqOn_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict s] g) (hf : ContinuousOn f s)
     (hg : ContinuousOn g s) (hU : s ⊆ closure (interior s)) : EqOn f g s :=
   have : interior s ⊆ s := interior_subset
@@ -122,6 +200,12 @@ theorem eqOn_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict s] g) (hf : Contin
 
 variable (μ)
 
+/- warning: continuous.ae_eq_iff_eq -> Continuous.ae_eq_iff_eq is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] {m : MeasurableSpace.{u1} X} [_inst_2 : TopologicalSpace.{u2} Y] [_inst_3 : T2Space.{u2} Y _inst_2] (μ : MeasureTheory.Measure.{u1} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {f : X -> Y} {g : X -> Y}, (Continuous.{u1, u2} X Y _inst_1 _inst_2 f) -> (Continuous.{u1, u2} X Y _inst_1 _inst_2 g) -> (Iff (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m μ) f g) (Eq.{max (succ u1) (succ u2)} (X -> Y) f g))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] {m : MeasurableSpace.{u2} X} [_inst_2 : TopologicalSpace.{u1} Y] [_inst_3 : T2Space.{u1} Y _inst_2] (μ : MeasureTheory.Measure.{u2} X m) [_inst_4 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] {f : X -> Y} {g : X -> Y}, (Continuous.{u2, u1} X Y _inst_1 _inst_2 f) -> (Continuous.{u2, u1} X Y _inst_1 _inst_2 g) -> (Iff (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m μ) f g) (Eq.{max (succ u2) (succ u1)} (X -> Y) f g))
+Case conversion may be inaccurate. Consider using '#align continuous.ae_eq_iff_eq Continuous.ae_eq_iff_eqₓ'. -/
 theorem Continuous.ae_eq_iff_eq {f g : X → Y} (hf : Continuous f) (hg : Continuous g) :
     f =ᵐ[μ] g ↔ f = g :=
   ⟨fun h => eq_of_ae_eq h hf hg, fun h => h ▸ EventuallyEq.rfl⟩
@@ -132,41 +216,89 @@ end Basic
 section LinearOrder
 
 variable {X Y : Type _} [TopologicalSpace X] [LinearOrder X] [OrderTopology X]
-  {m : MeasurableSpace X} [TopologicalSpace Y] [T2Space Y] (μ : Measure X) [IsOpenPosMeasure μ]
-
+  {m : MeasurableSpace X} [TopologicalSpace Y] [T2Space Y] (μ : Measure X) [OpenPosMeasure μ]
+
+/- warning: measure_theory.measure.measure_Ioi_pos -> MeasureTheory.Measure.measure_Ioi_pos is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : NoMaxOrder.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] (a : X), 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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Ioi.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : NoMaxOrder.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))))] (a : X), 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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Set.Ioi.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))) a))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_Ioi_pos MeasureTheory.Measure.measure_Ioi_posₓ'. -/
 theorem measure_Ioi_pos [NoMaxOrder X] (a : X) : 0 < μ (Ioi a) :=
   isOpen_Ioi.measure_pos μ nonempty_Ioi
 #align measure_theory.measure.measure_Ioi_pos MeasureTheory.Measure.measure_Ioi_pos
 
+/- warning: measure_theory.measure.measure_Iio_pos -> MeasureTheory.Measure.measure_Iio_pos is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : NoMinOrder.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] (a : X), 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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Iio.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : NoMinOrder.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))))] (a : X), 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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Set.Iio.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))) a))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_Iio_pos MeasureTheory.Measure.measure_Iio_posₓ'. -/
 theorem measure_Iio_pos [NoMinOrder X] (a : X) : 0 < μ (Iio a) :=
   isOpen_Iio.measure_pos μ nonempty_Iio
 #align measure_theory.measure.measure_Iio_pos MeasureTheory.Measure.measure_Iio_pos
 
+/- warning: measure_theory.measure.measure_Ioo_pos -> MeasureTheory.Measure.measure_Ioo_pos is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X}, Iff (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) (LT.lt.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))) a b)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))))] {a : X} {b : X}, Iff (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))) a b))) (LT.lt.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))) a b)
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_Ioo_pos MeasureTheory.Measure.measure_Ioo_posₓ'. -/
 theorem measure_Ioo_pos [DenselyOrdered X] {a b : X} : 0 < μ (Ioo a b) ↔ a < b :=
   (isOpen_Ioo.measure_pos_iff μ).trans nonempty_Ioo
 #align measure_theory.measure.measure_Ioo_pos MeasureTheory.Measure.measure_Ioo_pos
 
+/- warning: measure_theory.measure.measure_Ioo_eq_zero -> MeasureTheory.Measure.measure_Ioo_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X}, Iff (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (LE.le.{u1} X (Preorder.toLE.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))) b a)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))))] {a : X} {b : X}, Iff (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2))))) a b)) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (LE.le.{u1} X (Preorder.toLE.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (DistribLattice.toLattice.{u1} X (instDistribLattice.{u1} X _inst_2)))))) b a)
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.measure_Ioo_eq_zero MeasureTheory.Measure.measure_Ioo_eq_zeroₓ'. -/
 theorem measure_Ioo_eq_zero [DenselyOrdered X] {a b : X} : μ (Ioo a b) = 0 ↔ b ≤ a :=
   (isOpen_Ioo.measure_eq_zero_iff μ).trans (Ioo_eq_empty_iff.trans not_lt)
 #align measure_theory.measure.measure_Ioo_eq_zero MeasureTheory.Measure.measure_Ioo_eq_zero
 
+/- warning: measure_theory.measure.eq_on_Ioo_of_ae_eq -> MeasureTheory.Measure.eqOn_Ioo_of_ae_eq is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} [_inst_4 : TopologicalSpace.{u2} Y] [_inst_5 : T2Space.{u2} Y _inst_4] (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 f (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 g (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (Set.EqOn.{u1, u2} X Y f g (Set.Ioo.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : LinearOrder.{u2} X] [_inst_3 : OrderTopology.{u2} X _inst_1 (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2)))))] {m : MeasurableSpace.{u2} X} [_inst_4 : TopologicalSpace.{u1} Y] [_inst_5 : T2Space.{u1} Y _inst_4] (μ : MeasureTheory.Measure.{u2} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m (MeasureTheory.Measure.restrict.{u2} X m μ (Set.Ioo.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))) f g) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 f (Set.Ioo.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 g (Set.Ioo.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (Set.EqOn.{u2, u1} X Y f g (Set.Ioo.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Ioo_of_ae_eq MeasureTheory.Measure.eqOn_Ioo_of_ae_eqₓ'. -/
 theorem eqOn_Ioo_of_ae_eq {a b : X} {f g : X → Y} (hfg : f =ᵐ[μ.restrict (Ioo a b)] g)
     (hf : ContinuousOn f (Ioo a b)) (hg : ContinuousOn g (Ioo a b)) : EqOn f g (Ioo a b) :=
   eqOn_of_ae_eq hfg hf hg Ioo_subset_closure_interior
 #align measure_theory.measure.eq_on_Ioo_of_ae_eq MeasureTheory.Measure.eqOn_Ioo_of_ae_eq
 
+/- warning: measure_theory.measure.eq_on_Ioc_of_ae_eq -> MeasureTheory.Measure.eqOn_Ioc_of_ae_eq is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} [_inst_4 : TopologicalSpace.{u2} Y] [_inst_5 : T2Space.{u2} Y _inst_4] (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 f (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 g (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (Set.EqOn.{u1, u2} X Y f g (Set.Ioc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : LinearOrder.{u2} X] [_inst_3 : OrderTopology.{u2} X _inst_1 (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2)))))] {m : MeasurableSpace.{u2} X} [_inst_4 : TopologicalSpace.{u1} Y] [_inst_5 : T2Space.{u1} Y _inst_4] (μ : MeasureTheory.Measure.{u2} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u2} X (Preorder.toLT.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))))] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m (MeasureTheory.Measure.restrict.{u2} X m μ (Set.Ioc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))) f g) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 f (Set.Ioc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 g (Set.Ioc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (Set.EqOn.{u2, u1} X Y f g (Set.Ioc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Ioc_of_ae_eq MeasureTheory.Measure.eqOn_Ioc_of_ae_eqₓ'. -/
 theorem eqOn_Ioc_of_ae_eq [DenselyOrdered X] {a b : X} {f g : X → Y}
     (hfg : f =ᵐ[μ.restrict (Ioc a b)] g) (hf : ContinuousOn f (Ioc a b))
     (hg : ContinuousOn g (Ioc a b)) : EqOn f g (Ioc a b) :=
   eqOn_of_ae_eq hfg hf hg (Ioc_subset_closure_interior _ _)
 #align measure_theory.measure.eq_on_Ioc_of_ae_eq MeasureTheory.Measure.eqOn_Ioc_of_ae_eq
 
+/- warning: measure_theory.measure.eq_on_Ico_of_ae_eq -> MeasureTheory.Measure.eqOn_Ico_of_ae_eq is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} [_inst_4 : TopologicalSpace.{u2} Y] [_inst_5 : T2Space.{u2} Y _inst_4] (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 f (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 g (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (Set.EqOn.{u1, u2} X Y f g (Set.Ico.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : LinearOrder.{u2} X] [_inst_3 : OrderTopology.{u2} X _inst_1 (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2)))))] {m : MeasurableSpace.{u2} X} [_inst_4 : TopologicalSpace.{u1} Y] [_inst_5 : T2Space.{u1} Y _inst_4] (μ : MeasureTheory.Measure.{u2} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u2} X (Preorder.toLT.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))))] {a : X} {b : X} {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m (MeasureTheory.Measure.restrict.{u2} X m μ (Set.Ico.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))) f g) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 f (Set.Ico.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 g (Set.Ico.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (Set.EqOn.{u2, u1} X Y f g (Set.Ico.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Ico_of_ae_eq MeasureTheory.Measure.eqOn_Ico_of_ae_eqₓ'. -/
 theorem eqOn_Ico_of_ae_eq [DenselyOrdered X] {a b : X} {f g : X → Y}
     (hfg : f =ᵐ[μ.restrict (Ico a b)] g) (hf : ContinuousOn f (Ico a b))
     (hg : ContinuousOn g (Ico a b)) : EqOn f g (Ico a b) :=
   eqOn_of_ae_eq hfg hf hg (Ico_subset_closure_interior _ _)
 #align measure_theory.measure.eq_on_Ico_of_ae_eq MeasureTheory.Measure.eqOn_Ico_of_ae_eq
 
+/- warning: measure_theory.measure.eq_on_Icc_of_ae_eq -> MeasureTheory.Measure.eqOn_Icc_of_ae_eq is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} {Y : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} X] [_inst_2 : LinearOrder.{u1} X] [_inst_3 : OrderTopology.{u1} X _inst_1 (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2))))] {m : MeasurableSpace.{u1} X} [_inst_4 : TopologicalSpace.{u2} Y] [_inst_5 : T2Space.{u2} Y _inst_4] (μ : MeasureTheory.Measure.{u1} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u1} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u1} X (Preorder.toLT.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))))] {a : X} {b : X}, (Ne.{succ u1} X a b) -> (forall {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u1, u2} X Y (MeasureTheory.Measure.ae.{u1} X m (MeasureTheory.Measure.restrict.{u1} X m μ (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b))) f g) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 f (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (ContinuousOn.{u1, u2} X Y _inst_1 _inst_4 g (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)) -> (Set.EqOn.{u1, u2} X Y f g (Set.Icc.{u1} X (PartialOrder.toPreorder.{u1} X (SemilatticeInf.toPartialOrder.{u1} X (Lattice.toSemilatticeInf.{u1} X (LinearOrder.toLattice.{u1} X _inst_2)))) a b)))
+but is expected to have type
+  forall {X : Type.{u2}} {Y : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} X] [_inst_2 : LinearOrder.{u2} X] [_inst_3 : OrderTopology.{u2} X _inst_1 (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2)))))] {m : MeasurableSpace.{u2} X} [_inst_4 : TopologicalSpace.{u1} Y] [_inst_5 : T2Space.{u1} Y _inst_4] (μ : MeasureTheory.Measure.{u2} X m) [_inst_6 : MeasureTheory.Measure.OpenPosMeasure.{u2} X _inst_1 m μ] [_inst_7 : DenselyOrdered.{u2} X (Preorder.toLT.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))))] {a : X} {b : X}, (Ne.{succ u2} X a b) -> (forall {f : X -> Y} {g : X -> Y}, (Filter.EventuallyEq.{u2, u1} X Y (MeasureTheory.Measure.ae.{u2} X m (MeasureTheory.Measure.restrict.{u2} X m μ (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b))) f g) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 f (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (ContinuousOn.{u2, u1} X Y _inst_1 _inst_4 g (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)) -> (Set.EqOn.{u2, u1} X Y f g (Set.Icc.{u2} X (PartialOrder.toPreorder.{u2} X (SemilatticeInf.toPartialOrder.{u2} X (Lattice.toSemilatticeInf.{u2} X (DistribLattice.toLattice.{u2} X (instDistribLattice.{u2} X _inst_2))))) a b)))
+Case conversion may be inaccurate. Consider using '#align measure_theory.measure.eq_on_Icc_of_ae_eq MeasureTheory.Measure.eqOn_Icc_of_ae_eqₓ'. -/
 theorem eqOn_Icc_of_ae_eq [DenselyOrdered X] {a b : X} (hne : a ≠ b) {f g : X → Y}
     (hfg : f =ᵐ[μ.restrict (Icc a b)] g) (hf : ContinuousOn f (Icc a b))
     (hg : ContinuousOn g (Icc a b)) : EqOn f g (Icc a b) :=
@@ -184,12 +316,24 @@ open MeasureTheory MeasureTheory.Measure
 namespace Metric
 
 variable {X : Type _} [PseudoMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
-  [IsOpenPosMeasure μ]
-
+  [OpenPosMeasure μ]
+
+/- warning: metric.measure_ball_pos -> Metric.measure_ball_pos is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Metric.ball.{u1} X _inst_1 x r)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Metric.ball.{u1} X _inst_1 x r)))
+Case conversion may be inaccurate. Consider using '#align metric.measure_ball_pos Metric.measure_ball_posₓ'. -/
 theorem measure_ball_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (ball x r) :=
   isOpen_ball.measure_pos μ (nonempty_ball.2 hr)
 #align metric.measure_ball_pos Metric.measure_ball_pos
 
+/- warning: metric.measure_closed_ball_pos -> Metric.measure_closedBall_pos is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (Metric.closedBall.{u1} X _inst_1 x r)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : PseudoMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : Real}, (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) r) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (Metric.closedBall.{u1} X _inst_1 x r)))
+Case conversion may be inaccurate. Consider using '#align metric.measure_closed_ball_pos Metric.measure_closedBall_posₓ'. -/
 theorem measure_closedBall_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (closedBall x r) :=
   (measure_ball_pos μ x hr).trans_le (measure_mono ball_subset_closedBall)
 #align metric.measure_closed_ball_pos Metric.measure_closedBall_pos
@@ -199,15 +343,27 @@ end Metric
 namespace Emetric
 
 variable {X : Type _} [PseudoEMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
-  [IsOpenPosMeasure μ]
-
+  [OpenPosMeasure μ]
+
+/- warning: emetric.measure_ball_pos -> EMetric.measure_ball_pos is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (EMetric.ball.{u1} X _inst_1 x r)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (EMetric.ball.{u1} X _inst_1 x r)))
+Case conversion may be inaccurate. Consider using '#align emetric.measure_ball_pos EMetric.measure_ball_posₓ'. -/
 theorem measure_ball_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ (ball x r) :=
   isOpen_ball.measure_pos μ ⟨x, mem_ball_self hr.bot_lt⟩
-#align emetric.measure_ball_pos Emetric.measure_ball_pos
-
+#align emetric.measure_ball_pos EMetric.measure_ball_pos
+
+/- warning: emetric.measure_closed_ball_pos -> EMetric.measure_closedBall_pos is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} X m) (fun (_x : MeasureTheory.Measure.{u1} X m) => (Set.{u1} X) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} X m) μ (EMetric.closedBall.{u1} X _inst_1 x r)))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} X] {m : MeasurableSpace.{u1} X} (μ : MeasureTheory.Measure.{u1} X m) [_inst_2 : MeasureTheory.Measure.OpenPosMeasure.{u1} X (UniformSpace.toTopologicalSpace.{u1} X (PseudoEMetricSpace.toUniformSpace.{u1} X _inst_1)) m μ] (x : X) {r : ENNReal}, (Ne.{1} ENNReal r (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (MeasureTheory.OuterMeasure.measureOf.{u1} X (MeasureTheory.Measure.toOuterMeasure.{u1} X m μ) (EMetric.closedBall.{u1} X _inst_1 x r)))
+Case conversion may be inaccurate. Consider using '#align emetric.measure_closed_ball_pos EMetric.measure_closedBall_posₓ'. -/
 theorem measure_closedBall_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ (closedBall x r) :=
   (measure_ball_pos μ x hr).trans_le (measure_mono ball_subset_closedBall)
-#align emetric.measure_closed_ball_pos Emetric.measure_closedBall_pos
+#align emetric.measure_closed_ball_pos EMetric.measure_closedBall_pos
 
 end Emetric
 

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

@@ -66,9 +66,9 @@ theorem measure_pos_of_mem_nhds (h : s ∈ 𝓝 x) : 0 < μ s :=
   measure_pos_of_nonempty_interior _ ⟨x, mem_interior_iff_mem_nhds.2 h⟩
 #align measure_theory.measure.measure_pos_of_mem_nhds MeasureTheory.Measure.measure_pos_of_mem_nhds
 
-theorem isOpenPosMeasureSmul {c : ℝ≥0∞} (h : c ≠ 0) : IsOpenPosMeasure (c • μ) :=
+theorem isOpenPosMeasure_smul {c : ℝ≥0∞} (h : c ≠ 0) : IsOpenPosMeasure (c • μ) :=
   ⟨fun U Uo Une => mul_ne_zero h (Uo.measure_ne_zero μ Une)⟩
-#align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.isOpenPosMeasureSmul
+#align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.isOpenPosMeasure_smul
 
 variable {μ ν}
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

@@ -198,7 +198,7 @@ end Metric
 
 namespace Emetric
 
-variable {X : Type _} [PseudoEmetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
+variable {X : Type _} [PseudoEMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
   [IsOpenPosMeasure μ]
 
 theorem measure_ball_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ (ball x r) :=

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

@@ -21,7 +21,7 @@ about these measures.
 -/
 
 
-open Topology Ennreal MeasureTheory
+open Topology ENNReal MeasureTheory
 
 open Set Function Filter
 

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

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

@@ -89,6 +89,7 @@ theorem _root_.IsOpen.ae_eq_empty_iff_eq (hU : IsOpen U) :
     U =ᵐ[μ] (∅ : Set X) ↔ U = ∅ := by
   rw [ae_eq_empty, hU.measure_zero_iff_eq_empty]
 
+/-- An open null set w.r.t. an `IsOpenPosMeasure` is empty. -/
 theorem _root_.IsOpen.eq_empty_of_measure_zero (hU : IsOpen U) (h₀ : μ U = 0) : U = ∅ :=
   (hU.measure_eq_zero_iff μ).mp h₀
 #align is_open.eq_empty_of_measure_zero IsOpen.eq_empty_of_measure_zero
@@ -108,6 +109,7 @@ theorem _root_.IsClosed.measure_eq_one_iff_eq_univ [OpensMeasurableSpace X] [IsP
     μ F = 1 ↔ F = univ := by
   rw [← measure_univ (μ := μ), hF.measure_eq_univ_iff_eq]
 
+/-- A null set has empty interior. -/
 theorem interior_eq_empty_of_null (hs : μ s = 0) : interior s = ∅ :=
   isOpen_interior.eq_empty_of_measure_zero <| measure_mono_null interior_subset hs
 #align measure_theory.measure.interior_eq_empty_of_null MeasureTheory.Measure.interior_eq_empty_of_null
@@ -251,3 +253,39 @@ theorem measure_closedBall_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ
 #align emetric.measure_closed_ball_pos EMetric.measure_closedBall_pos
 
 end EMetric
+
+section MeasureZero
+/-! ## Meagre sets and measure zero
+In general, neither of meagre and measure zero implies the other.
+- The set of Liouville numbers is a Lebesgue measure zero subset of ℝ, but is not meagre.
+(In fact, its complement is meagre. See `Real.disjoint_residual_ae`.)
+
+- The complement of the set of Liouville numbers in $[0,1]$ is meagre and has measure 1.
+For another counterexample, for all $α ∈ (0,1)$, there is a generalised Cantor set $C ⊆ [0,1]$
+of measure `α`. Cantor sets are nowhere dense (hence meagre). Taking a countable union of
+fat Cantor sets whose measure approaches 1 even yields a meagre set of measure 1.
+
+However, with respect to a measure which is positive on non-empty open sets, *closed* measure
+zero sets are nowhere dense and σ-compact measure zero sets in a Hausdorff space are meagre.
+-/
+
+variable {X : Type*} [TopologicalSpace X] [MeasurableSpace X] [BorelSpace X] {s : Set X}
+  {μ : Measure X} [IsOpenPosMeasure μ]
+
+/-- A *closed* measure zero subset is nowhere dense. (Closedness is required: for instance, the
+rational numbers are countable (thus have measure zero), but are dense (hence not nowhere dense). -/
+lemma IsNowhereDense.of_isClosed_null (h₁s : IsClosed s) (h₂s : μ s = 0) :
+    IsNowhereDense s := h₁s.isNowhereDense_iff.mpr (interior_eq_empty_of_null h₂s)
+
+/-- A σ-compact measure zero subset is meagre.
+(More generally, every Fσ set of measure zero is meagre.) -/
+lemma IsMeagre.of_isSigmaCompact_null [T2Space X] (h₁s : IsSigmaCompact s) (h₂s : μ s = 0) :
+    IsMeagre s := by
+  rcases h₁s with ⟨K, hcompact, hcover⟩
+  have h (n : ℕ) : IsNowhereDense (K n) := by
+    have : μ (K n) = 0 := measure_mono_null (hcover ▸ subset_iUnion K n) h₂s
+    exact .of_isClosed_null (hcompact n).isClosed this
+  rw [isMeagre_iff_countable_union_isNowhereDense]
+  exact ⟨range K, fun t ⟨n, hn⟩ ↦ hn ▸ h n, countable_range K, hcover.symm.subset⟩
+
+end MeasureZero

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

This has nice performance benefits.

@@ -29,7 +29,7 @@ namespace Measure
 
 section Basic
 
-variable {X Y : Type _} [TopologicalSpace X] {m : MeasurableSpace X} [TopologicalSpace Y]
+variable {X Y : Type*} [TopologicalSpace X] {m : MeasurableSpace X} [TopologicalSpace Y]
   [T2Space Y] (μ ν : Measure X)
 
 /-- A measure is said to be `IsOpenPosMeasure` if it is positive on nonempty open sets. -/
@@ -152,7 +152,7 @@ theorem _root_.Continuous.ae_eq_iff_eq {f g : X → Y} (hf : Continuous f) (hg :
 variable {μ}
 
 theorem _root_.Continuous.isOpenPosMeasure_map [OpensMeasurableSpace X]
-    {Z : Type _} [TopologicalSpace Z] [MeasurableSpace Z] [BorelSpace Z]
+    {Z : Type*} [TopologicalSpace Z] [MeasurableSpace Z] [BorelSpace Z]
     {f : X → Z} (hf : Continuous f) (hf_surj : Function.Surjective f) :
     (Measure.map f μ).IsOpenPosMeasure := by
   refine' ⟨fun U hUo hUne => _⟩
@@ -164,7 +164,7 @@ end Basic
 
 section LinearOrder
 
-variable {X Y : Type _} [TopologicalSpace X] [LinearOrder X] [OrderTopology X]
+variable {X Y : Type*} [TopologicalSpace X] [LinearOrder X] [OrderTopology X]
   {m : MeasurableSpace X} [TopologicalSpace Y] [T2Space Y] (μ : Measure X) [IsOpenPosMeasure μ]
 
 theorem measure_Ioi_pos [NoMaxOrder X] (a : X) : 0 < μ (Ioi a) :=
@@ -216,7 +216,7 @@ open MeasureTheory MeasureTheory.Measure
 
 namespace Metric
 
-variable {X : Type _} [PseudoMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
+variable {X : Type*} [PseudoMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
   [IsOpenPosMeasure μ]
 
 theorem measure_ball_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (ball x r) :=
@@ -228,7 +228,7 @@ theorem measure_closedBall_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (closedBa
   (measure_ball_pos μ x hr).trans_le (measure_mono ball_subset_closedBall)
 #align metric.measure_closed_ball_pos Metric.measure_closedBall_pos
 
-@[simp] lemma measure_closedBall_pos_iff {X : Type _} [MetricSpace X] {m : MeasurableSpace X}
+@[simp] lemma measure_closedBall_pos_iff {X : Type*} [MetricSpace X] {m : MeasurableSpace X}
     (μ : Measure X) [IsOpenPosMeasure μ] [NoAtoms μ] {x : X} {r : ℝ} :
     0 < μ (closedBall x r) ↔ 0 < r := by
   refine' ⟨fun h ↦ _, measure_closedBall_pos μ x⟩
@@ -239,7 +239,7 @@ end Metric
 
 namespace EMetric
 
-variable {X : Type _} [PseudoEMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
+variable {X : Type*} [PseudoEMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
   [IsOpenPosMeasure μ]
 
 theorem measure_ball_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ (ball x r) :=

Assume NeZero μ instead of μ.ae.NeBot everywhere, and sometimes instead of μ ≠ 0.

API changes

• Convex.average_mem, Convex.set_average_mem, ConvexOn.average_mem_epigraph, ConcaveOn.average_mem_hypograph, ConvexOn.map_average_le, ConcaveOn.le_map_average: assume [NeZero μ] instead of μ ≠ 0;
• MeasureTheory.condexp_bot', essSup_const', essInf_const', MeasureTheory.laverage_const, MeasureTheory.laverage_one, MeasureTheory.average_const: assume [NeZero μ] instead of [μ.ae.NeBot]
• MeasureTheory.Measure.measure_ne_zero: replace with an instance;
• remove @[simp] from MeasureTheory.ae_restrict_neBot, use ≠ 0 in the RHS;
• turn MeasureTheory.IsProbabilityMeasure.ae_neBot into a theorem because inferInstance can find it now;
• add instances:
  • [NeZero μ] : NeZero (μ univ);
  • [NeZero (μ s)] : NeZero (μ.restrict s);
  • [NeZero μ] : μ.ae.NeBot;
  • [IsProbabilityMeasure μ] : NeZero μ;
  • [IsFiniteMeasure μ] [NeZero μ] : IsProbabilityMeasure ((μ univ)⁻¹ • μ) this was a theorem MeasureTheory.isProbabilityMeasureSmul assuming μ ≠ 0;

@@ -47,8 +47,8 @@ theorem _root_.IsOpen.measure_pos (hU : IsOpen U) (hne : U.Nonempty) : 0 < μ U
   (hU.measure_ne_zero μ hne).bot_lt
 #align is_open.measure_pos IsOpen.measure_pos
 
-@[simp] lemma measure_ne_zero [Nonempty X] : μ ≠ 0 := by
-  simpa only [← measure_univ_pos] using isOpen_univ.measure_pos μ univ_nonempty
+instance (priority := 100) [Nonempty X] : NeZero μ :=
+  ⟨measure_univ_pos.mp <| isOpen_univ.measure_pos μ univ_nonempty⟩
 
 theorem _root_.IsOpen.measure_pos_iff (hU : IsOpen U) : 0 < μ U ↔ U.Nonempty :=
   ⟨fun h => nonempty_iff_ne_empty.2 fun he => h.ne' <| he.symm ▸ measure_empty, hU.measure_pos μ⟩

@@ -47,6 +47,9 @@ theorem _root_.IsOpen.measure_pos (hU : IsOpen U) (hne : U.Nonempty) : 0 < μ U
   (hU.measure_ne_zero μ hne).bot_lt
 #align is_open.measure_pos IsOpen.measure_pos
 
+@[simp] lemma measure_ne_zero [Nonempty X] : μ ≠ 0 := by
+  simpa only [← measure_univ_pos] using isOpen_univ.measure_pos μ univ_nonempty
+
 theorem _root_.IsOpen.measure_pos_iff (hU : IsOpen U) : 0 < μ U ↔ U.Nonempty :=
   ⟨fun h => nonempty_iff_ne_empty.2 fun he => h.ne' <| he.symm ▸ measure_empty, hU.measure_pos μ⟩
 #align is_open.measure_pos_iff IsOpen.measure_pos_iff
@@ -220,10 +223,18 @@ theorem measure_ball_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (ball x r) :=
   isOpen_ball.measure_pos μ (nonempty_ball.2 hr)
 #align metric.measure_ball_pos Metric.measure_ball_pos
 
+/-- See also `Metric.measure_closedBall_pos_iff`. -/
 theorem measure_closedBall_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (closedBall x r) :=
   (measure_ball_pos μ x hr).trans_le (measure_mono ball_subset_closedBall)
 #align metric.measure_closed_ball_pos Metric.measure_closedBall_pos
 
+@[simp] lemma measure_closedBall_pos_iff {X : Type _} [MetricSpace X] {m : MeasurableSpace X}
+    (μ : Measure X) [IsOpenPosMeasure μ] [NoAtoms μ] {x : X} {r : ℝ} :
+    0 < μ (closedBall x r) ↔ 0 < r := by
+  refine' ⟨fun h ↦ _, measure_closedBall_pos μ x⟩
+  contrapose! h
+  rw [(subsingleton_closedBall x h).measure_zero μ]
+
 end Metric
 
 namespace EMetric

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 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 measure_theory.measure.open_pos
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Measure.MeasureSpace
 import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
 
+#align_import measure_theory.measure.open_pos from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Measures positive on nonempty opens
 

Also invert the import order so that MeasureTheory.Measure.OpenPos imports MeasureTheory.Constructions.BorelSpace.Basic rather than the other way around.

@@ -9,6 +9,7 @@ Authors: Yury Kudryashov
 ! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Measure.MeasureSpace
+import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
 
 /-!
 # Measures positive on nonempty opens
@@ -39,7 +40,7 @@ class IsOpenPosMeasure : Prop where
   open_pos : ∀ U : Set X, IsOpen U → U.Nonempty → μ U ≠ 0
 #align measure_theory.measure.is_open_pos_measure MeasureTheory.Measure.IsOpenPosMeasure
 
-variable [IsOpenPosMeasure μ] {s U : Set X} {x : X}
+variable [IsOpenPosMeasure μ] {s U F : Set X} {x : X}
 
 theorem _root_.IsOpen.measure_ne_zero (hU : IsOpen U) (hne : U.Nonempty) : μ U ≠ 0 :=
   IsOpenPosMeasure.open_pos U hU hne
@@ -80,10 +81,33 @@ theorem _root_.LE.le.isOpenPosMeasure (h : μ ≤ ν) : IsOpenPosMeasure ν :=
   h.absolutelyContinuous.isOpenPosMeasure
 #align has_le.le.is_open_pos_measure LE.le.isOpenPosMeasure
 
+theorem _root_.IsOpen.measure_zero_iff_eq_empty (hU : IsOpen U) :
+    μ U = 0 ↔ U = ∅ :=
+  ⟨fun h ↦ (hU.measure_eq_zero_iff μ).mp h, fun h ↦ by simp [h]⟩
+
+theorem _root_.IsOpen.ae_eq_empty_iff_eq (hU : IsOpen U) :
+    U =ᵐ[μ] (∅ : Set X) ↔ U = ∅ := by
+  rw [ae_eq_empty, hU.measure_zero_iff_eq_empty]
+
 theorem _root_.IsOpen.eq_empty_of_measure_zero (hU : IsOpen U) (h₀ : μ U = 0) : U = ∅ :=
   (hU.measure_eq_zero_iff μ).mp h₀
 #align is_open.eq_empty_of_measure_zero IsOpen.eq_empty_of_measure_zero
 
+theorem _root_.IsClosed.ae_eq_univ_iff_eq (hF : IsClosed F) :
+    F =ᵐ[μ] univ ↔ F = univ := by
+  refine' ⟨fun h ↦ _, fun h ↦ by rw [h]⟩
+  rwa [ae_eq_univ, hF.isOpen_compl.measure_eq_zero_iff μ, compl_empty_iff] at h
+
+theorem _root_.IsClosed.measure_eq_univ_iff_eq [OpensMeasurableSpace X] [IsFiniteMeasure μ]
+    (hF : IsClosed F) :
+    μ F = μ univ ↔ F = univ := by
+  rw [← ae_eq_univ_iff_measure_eq hF.measurableSet.nullMeasurableSet, hF.ae_eq_univ_iff_eq]
+
+theorem _root_.IsClosed.measure_eq_one_iff_eq_univ [OpensMeasurableSpace X] [IsProbabilityMeasure μ]
+    (hF : IsClosed F) :
+    μ F = 1 ↔ F = univ := by
+  rw [← measure_univ (μ := μ), hF.measure_eq_univ_iff_eq]
+
 theorem interior_eq_empty_of_null (hs : μ s = 0) : interior s = ∅ :=
   isOpen_interior.eq_empty_of_measure_zero <| measure_mono_null interior_subset hs
 #align measure_theory.measure.interior_eq_empty_of_null MeasureTheory.Measure.interior_eq_empty_of_null
@@ -125,6 +149,17 @@ theorem _root_.Continuous.ae_eq_iff_eq {f g : X → Y} (hf : Continuous f) (hg :
   ⟨fun h => eq_of_ae_eq h hf hg, fun h => h ▸ EventuallyEq.rfl⟩
 #align continuous.ae_eq_iff_eq Continuous.ae_eq_iff_eq
 
+variable {μ}
+
+theorem _root_.Continuous.isOpenPosMeasure_map [OpensMeasurableSpace X]
+    {Z : Type _} [TopologicalSpace Z] [MeasurableSpace Z] [BorelSpace Z]
+    {f : X → Z} (hf : Continuous f) (hf_surj : Function.Surjective f) :
+    (Measure.map f μ).IsOpenPosMeasure := by
+  refine' ⟨fun U hUo hUne => _⟩
+  rw [Measure.map_apply hf.measurable hUo.measurableSet]
+  exact (hUo.preimage hf).measure_ne_zero μ (hf_surj.nonempty_preimage.mpr hUne)
+#align continuous.is_open_pos_measure_map Continuous.isOpenPosMeasure_map
+
 end Basic
 
 section LinearOrder

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -96,7 +96,7 @@ theorem eqOn_open_of_ae_eq {f g : X → Y} (h : f =ᵐ[μ.restrict U] g) (hU : I
   simp only [EventuallyEq, ae_iff, not_imp] at h
   have : IsOpen (U ∩ { a | f a ≠ g a }) := by
     refine' isOpen_iff_mem_nhds.mpr fun a ha => inter_mem (hU.mem_nhds ha.1) _
-    rcases ha with ⟨ha : a ∈ U, ha' : (f a, g a) ∈ diagonal Yᶜ⟩
+    rcases ha with ⟨ha : a ∈ U, ha' : (f a, g a) ∈ (diagonal Y)ᶜ⟩
     exact
       (hf.continuousAt (hU.mem_nhds ha)).prod_mk_nhds (hg.continuousAt (hU.mem_nhds ha))
         (isClosed_diagonal.isOpen_compl.mem_nhds ha')

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.

@@ -14,7 +14,7 @@ import Mathlib.MeasureTheory.Measure.MeasureSpace
 # Measures positive on nonempty opens
 
 In this file we define a typeclass for measures that are positive on nonempty opens, see
-`MeasureTheory.Measure.OpenPosMeasure`. Examples include (additive) Haar measures, as well as
+`MeasureTheory.Measure.IsOpenPosMeasure`. Examples include (additive) Haar measures, as well as
 measures that have positive density with respect to a Haar measure. We also prove some basic facts
 about these measures.
 
@@ -34,15 +34,15 @@ section Basic
 variable {X Y : Type _} [TopologicalSpace X] {m : MeasurableSpace X} [TopologicalSpace Y]
   [T2Space Y] (μ ν : Measure X)
 
-/-- A measure is said to be `OpenPosMeasure` if it is positive on nonempty open sets. -/
-class OpenPosMeasure : Prop where
+/-- A measure is said to be `IsOpenPosMeasure` if it is positive on nonempty open sets. -/
+class IsOpenPosMeasure : Prop where
   open_pos : ∀ U : Set X, IsOpen U → U.Nonempty → μ U ≠ 0
-#align measure_theory.measure.is_open_pos_measure MeasureTheory.Measure.OpenPosMeasure
+#align measure_theory.measure.is_open_pos_measure MeasureTheory.Measure.IsOpenPosMeasure
 
-variable [OpenPosMeasure μ] {s U : Set X} {x : X}
+variable [IsOpenPosMeasure μ] {s U : Set X} {x : X}
 
 theorem _root_.IsOpen.measure_ne_zero (hU : IsOpen U) (hne : U.Nonempty) : μ U ≠ 0 :=
-  OpenPosMeasure.open_pos U hU hne
+  IsOpenPosMeasure.open_pos U hU hne
 #align is_open.measure_ne_zero IsOpen.measure_ne_zero
 
 theorem _root_.IsOpen.measure_pos (hU : IsOpen U) (hne : U.Nonempty) : 0 < μ U :=
@@ -66,18 +66,18 @@ theorem measure_pos_of_mem_nhds (h : s ∈ 𝓝 x) : 0 < μ s :=
   measure_pos_of_nonempty_interior _ ⟨x, mem_interior_iff_mem_nhds.2 h⟩
 #align measure_theory.measure.measure_pos_of_mem_nhds MeasureTheory.Measure.measure_pos_of_mem_nhds
 
-theorem openPosMeasure_smul {c : ℝ≥0∞} (h : c ≠ 0) : OpenPosMeasure (c • μ) :=
+theorem isOpenPosMeasure_smul {c : ℝ≥0∞} (h : c ≠ 0) : IsOpenPosMeasure (c • μ) :=
   ⟨fun _U Uo Une => mul_ne_zero h (Uo.measure_ne_zero μ Une)⟩
-#align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.openPosMeasure_smul
+#align measure_theory.measure.is_open_pos_measure_smul MeasureTheory.Measure.isOpenPosMeasure_smul
 
 variable {μ ν}
 
-protected theorem AbsolutelyContinuous.openPosMeasure (h : μ ≪ ν) : OpenPosMeasure ν :=
+protected theorem AbsolutelyContinuous.isOpenPosMeasure (h : μ ≪ ν) : IsOpenPosMeasure ν :=
   ⟨fun _U ho hne h₀ => ho.measure_ne_zero μ hne (h h₀)⟩
-#align measure_theory.measure.absolutely_continuous.is_open_pos_measure MeasureTheory.Measure.AbsolutelyContinuous.openPosMeasure
+#align measure_theory.measure.absolutely_continuous.is_open_pos_measure MeasureTheory.Measure.AbsolutelyContinuous.isOpenPosMeasure
 
-theorem _root_.LE.le.isOpenPosMeasure (h : μ ≤ ν) : OpenPosMeasure ν :=
-  h.absolutelyContinuous.openPosMeasure
+theorem _root_.LE.le.isOpenPosMeasure (h : μ ≤ ν) : IsOpenPosMeasure ν :=
+  h.absolutelyContinuous.isOpenPosMeasure
 #align has_le.le.is_open_pos_measure LE.le.isOpenPosMeasure
 
 theorem _root_.IsOpen.eq_empty_of_measure_zero (hU : IsOpen U) (h₀ : μ U = 0) : U = ∅ :=
@@ -130,7 +130,7 @@ end Basic
 section LinearOrder
 
 variable {X Y : Type _} [TopologicalSpace X] [LinearOrder X] [OrderTopology X]
-  {m : MeasurableSpace X} [TopologicalSpace Y] [T2Space Y] (μ : Measure X) [OpenPosMeasure μ]
+  {m : MeasurableSpace X} [TopologicalSpace Y] [T2Space Y] (μ : Measure X) [IsOpenPosMeasure μ]
 
 theorem measure_Ioi_pos [NoMaxOrder X] (a : X) : 0 < μ (Ioi a) :=
   isOpen_Ioi.measure_pos μ nonempty_Ioi
@@ -182,7 +182,7 @@ open MeasureTheory MeasureTheory.Measure
 namespace Metric
 
 variable {X : Type _} [PseudoMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
-  [OpenPosMeasure μ]
+  [IsOpenPosMeasure μ]
 
 theorem measure_ball_pos (x : X) {r : ℝ} (hr : 0 < r) : 0 < μ (ball x r) :=
   isOpen_ball.measure_pos μ (nonempty_ball.2 hr)
@@ -197,7 +197,7 @@ end Metric
 namespace EMetric
 
 variable {X : Type _} [PseudoEMetricSpace X] {m : MeasurableSpace X} (μ : Measure X)
-  [OpenPosMeasure μ]
+  [IsOpenPosMeasure μ]
 
 theorem measure_ball_pos (x : X) {r : ℝ≥0∞} (hr : r ≠ 0) : 0 < μ (ball x r) :=
   isOpen_ball.measure_pos μ ⟨x, mem_ball_self hr.bot_lt⟩

Co-authored-by: Komyyy <pol_tta@outlook.jp> Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>