measure_theory.function.ess_sup ⟷ Mathlib.MeasureTheory.Function.EssSup

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 -/
 import MeasureTheory.Constructions.BorelSpace.Basic
-import Order.Filter.Ennreal
+import Order.Filter.ENNReal
 
 #align_import measure_theory.function.ess_sup from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
 

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

@@ -86,13 +86,13 @@ theorem essInf_const' [μ.ae.ne_bot] (c : β) : essInf (fun x : α => c) μ = c
 
 #print essSup_const /-
 theorem essSup_const (c : β) (hμ : μ ≠ 0) : essSup (fun x : α => c) μ = c := by
-  rw [← ae_ne_bot] at hμ ; exact essSup_const' _
+  rw [← ae_ne_bot] at hμ; exact essSup_const' _
 #align ess_sup_const essSup_const
 -/
 
 #print essInf_const /-
 theorem essInf_const (c : β) (hμ : μ ≠ 0) : essInf (fun x : α => c) μ = c := by
-  rw [← ae_ne_bot] at hμ ; exact essInf_const' _
+  rw [← ae_ne_bot] at hμ; exact essInf_const' _
 #align ess_inf_const essInf_const
 -/
 
@@ -380,7 +380,7 @@ theorem essSup_map_measure (hg : AEMeasurable g (Measure.map f μ)) (hf : AEMeas
   rw [essSup_congr_ae hg.ae_eq_mk, essSup_map_measure_of_measurable hg.measurable_mk hf]
   refine' essSup_congr_ae _
   have h_eq := ae_of_ae_map hf hg.ae_eq_mk
-  rw [← eventually_eq] at h_eq 
+  rw [← eventually_eq] at h_eq
   exact h_eq.symm
 #align ess_sup_map_measure essSup_map_measure
 -/
@@ -420,19 +420,19 @@ theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → 
           is_bounded_default)
       fun c h_restrict_le => _
   rw [eventually_map] at h_restrict_le ⊢
-  rw [ae_restrict_iff' hs] at h_restrict_le 
+  rw [ae_restrict_iff' hs] at h_restrict_le
   have hc : 0 ≤ c := by
     rsuffices ⟨x, hx⟩ : ∃ x, 0 ≤ f x ∧ f x ≤ c; exact hx.1.trans hx.2
     refine' frequently.exists _
     · exact μ.ae
-    rw [eventually_le, ae_restrict_iff' hs] at hf 
+    rw [eventually_le, ae_restrict_iff' hs] at hf
     have hs' : ∃ᵐ x ∂μ, x ∈ s := by
       contrapose! hs_not_null
-      rw [not_frequently, ae_iff] at hs_not_null 
+      rw [not_frequently, ae_iff] at hs_not_null
       suffices {a : α | ¬a ∉ s} = s by rwa [← this]
       simp
     refine' hs'.mp (hf.mp (h_restrict_le.mono fun x hxs_imp_c hxf_nonneg hxs => _))
-    rw [Pi.zero_apply] at hxf_nonneg 
+    rw [Pi.zero_apply] at hxf_nonneg
     exact ⟨hxf_nonneg hxs, hxs_imp_c hxs⟩
   refine' h_restrict_le.mono fun x hxc => _
   by_cases hxs : x ∈ s

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

@@ -397,7 +397,6 @@ variable [CompleteLinearOrder β]
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
-#print essSup_indicator_eq_essSup_restrict /-
 theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → β}
     (hf : 0 ≤ᵐ[μ.restrict s] f) (hs : MeasurableSet s) (hs_not_null : μ s ≠ 0) :
     essSup (s.indicator f) μ = essSup f (μ.restrict s) :=
@@ -440,7 +439,6 @@ theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → 
   · simpa [hxs] using hxc hxs
   · simpa [hxs] using hc
 #align ess_sup_indicator_eq_ess_sup_restrict essSup_indicator_eq_essSup_restrict
--/
 
 end CompleteLinearOrder
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 -/
-import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
-import Mathbin.Order.Filter.Ennreal
+import MeasureTheory.Constructions.BorelSpace.Basic
+import Order.Filter.Ennreal
 
 #align_import measure_theory.function.ess_sup from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module measure_theory.function.ess_sup
-! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
 import Mathbin.Order.Filter.Ennreal
 
+#align_import measure_theory.function.ess_sup from "leanprover-community/mathlib"@"4280f5f32e16755ec7985ce11e189b6cd6ff6735"
+
 /-!
 # Essential supremum and infimum
 

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

@@ -61,31 +61,43 @@ def essInf {m : MeasurableSpace α} (f : α → β) (μ : Measure α) :=
 #align ess_inf essInf
 -/
 
+#print essSup_congr_ae /-
 theorem essSup_congr_ae {f g : α → β} (hfg : f =ᵐ[μ] g) : essSup f μ = essSup g μ :=
   limsup_congr hfg
 #align ess_sup_congr_ae essSup_congr_ae
+-/
 
+#print essInf_congr_ae /-
 theorem essInf_congr_ae {f g : α → β} (hfg : f =ᵐ[μ] g) : essInf f μ = essInf g μ :=
   @essSup_congr_ae α βᵒᵈ _ _ _ _ _ hfg
 #align ess_inf_congr_ae essInf_congr_ae
+-/
 
+#print essSup_const' /-
 @[simp]
 theorem essSup_const' [μ.ae.ne_bot] (c : β) : essSup (fun x : α => c) μ = c :=
   limsup_const _
 #align ess_sup_const' essSup_const'
+-/
 
+#print essInf_const' /-
 @[simp]
 theorem essInf_const' [μ.ae.ne_bot] (c : β) : essInf (fun x : α => c) μ = c :=
   liminf_const _
 #align ess_inf_const' essInf_const'
+-/
 
+#print essSup_const /-
 theorem essSup_const (c : β) (hμ : μ ≠ 0) : essSup (fun x : α => c) μ = c := by
   rw [← ae_ne_bot] at hμ ; exact essSup_const' _
 #align ess_sup_const essSup_const
+-/
 
+#print essInf_const /-
 theorem essInf_const (c : β) (hμ : μ ≠ 0) : essInf (fun x : α => c) μ = c := by
   rw [← ae_ne_bot] at hμ ; exact essInf_const' _
 #align ess_inf_const essInf_const
+-/
 
 end ConditionallyCompleteLattice
 
@@ -93,15 +105,19 @@ section ConditionallyCompleteLinearOrder
 
 variable [ConditionallyCompleteLinearOrder β] {x : β} {f : α → β}
 
+#print essSup_eq_sInf /-
 theorem essSup_eq_sInf {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
     essSup f μ = sInf {a | μ {x | a < f x} = 0} := by dsimp [essSup, limsup, Limsup];
   simp only [ae_iff, not_le]
 #align ess_sup_eq_Inf essSup_eq_sInf
+-/
 
+#print essInf_eq_sSup /-
 theorem essInf_eq_sSup {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
     essInf f μ = sSup {a | μ {x | f x < a} = 0} := by dsimp [essInf, liminf, Liminf];
   simp only [ae_iff, not_le]
 #align ess_inf_eq_Sup essInf_eq_sSup
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 #print ae_lt_of_essSup_lt /-
@@ -150,20 +166,24 @@ theorem ae_essInf_le
 -/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print meas_essSup_lt /-
 theorem meas_essSup_lt
     (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
       run_tac
         is_bounded_default) :
     μ {y | essSup f μ < f y} = 0 := by simp_rw [← not_le]; exact ae_le_essSup hf
 #align meas_ess_sup_lt meas_essSup_lt
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print meas_lt_essInf /-
 theorem meas_lt_essInf
     (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
       run_tac
         is_bounded_default) :
     μ {y | f y < essInf f μ} = 0 := by simp_rw [← not_le]; exact ae_essInf_le hf
 #align meas_lt_ess_inf meas_lt_essInf
+-/
 
 end ConditionallyCompleteLinearOrder
 
@@ -171,24 +191,33 @@ section CompleteLattice
 
 variable [CompleteLattice β]
 
+#print essSup_measure_zero /-
 @[simp]
 theorem essSup_measure_zero {m : MeasurableSpace α} {f : α → β} : essSup f (0 : Measure α) = ⊥ :=
   le_bot_iff.mp (sInf_le (by simp [Set.mem_setOf_eq, eventually_le, ae_iff]))
 #align ess_sup_measure_zero essSup_measure_zero
+-/
 
+#print essInf_measure_zero /-
 @[simp]
 theorem essInf_measure_zero {m : MeasurableSpace α} {f : α → β} : essInf f (0 : Measure α) = ⊤ :=
   @essSup_measure_zero α βᵒᵈ _ _ _
 #align ess_inf_measure_zero essInf_measure_zero
+-/
 
+#print essSup_mono_ae /-
 theorem essSup_mono_ae {f g : α → β} (hfg : f ≤ᵐ[μ] g) : essSup f μ ≤ essSup g μ :=
   limsup_le_limsup hfg
 #align ess_sup_mono_ae essSup_mono_ae
+-/
 
+#print essInf_mono_ae /-
 theorem essInf_mono_ae {f g : α → β} (hfg : f ≤ᵐ[μ] g) : essInf f μ ≤ essInf g μ :=
   liminf_le_liminf hfg
 #align ess_inf_mono_ae essInf_mono_ae
+-/
 
+#print essSup_le_of_ae_le /-
 theorem essSup_le_of_ae_le {f : α → β} (c : β) (hf : f ≤ᵐ[μ] fun _ => c) : essSup f μ ≤ c :=
   by
   refine' (essSup_mono_ae hf).trans _
@@ -196,20 +225,28 @@ theorem essSup_le_of_ae_le {f : α → β} (c : β) (hf : f ≤ᵐ[μ] fun _ =>
   · simp [hμ]
   · rwa [essSup_const]
 #align ess_sup_le_of_ae_le essSup_le_of_ae_le
+-/
 
+#print le_essInf_of_ae_le /-
 theorem le_essInf_of_ae_le {f : α → β} (c : β) (hf : (fun _ => c) ≤ᵐ[μ] f) : c ≤ essInf f μ :=
   @essSup_le_of_ae_le α βᵒᵈ _ _ _ _ c hf
 #align le_ess_inf_of_ae_le le_essInf_of_ae_le
+-/
 
+#print essSup_const_bot /-
 theorem essSup_const_bot : essSup (fun x : α => (⊥ : β)) μ = (⊥ : β) :=
   limsup_const_bot
 #align ess_sup_const_bot essSup_const_bot
+-/
 
+#print essInf_const_top /-
 theorem essInf_const_top : essInf (fun x : α => (⊤ : β)) μ = (⊤ : β) :=
   liminf_const_top
 #align ess_inf_const_top essInf_const_top
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+#print OrderIso.essSup_apply /-
 theorem OrderIso.essSup_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ] (f : α → β)
     (μ : Measure α) (g : β ≃o γ) : g (essSup f μ) = essSup (fun x => g (f x)) μ :=
   by
@@ -218,13 +255,17 @@ theorem OrderIso.essSup_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ]
     run_tac
       is_bounded_default
 #align order_iso.ess_sup_apply OrderIso.essSup_apply
+-/
 
+#print OrderIso.essInf_apply /-
 theorem OrderIso.essInf_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ] (f : α → β)
     (μ : Measure α) (g : β ≃o γ) : g (essInf f μ) = essInf (fun x => g (f x)) μ :=
   @OrderIso.essSup_apply α βᵒᵈ _ _ γᵒᵈ _ _ _ g.dual
 #align order_iso.ess_inf_apply OrderIso.essInf_apply
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+#print essSup_mono_measure /-
 theorem essSup_mono_measure {f : α → β} (hμν : ν ≪ μ) : essSup f ν ≤ essSup f μ :=
   by
   refine' limsup_le_limsup_of_le (measure.ae_le_iff_absolutely_continuous.mpr hμν) _ _
@@ -232,14 +273,18 @@ theorem essSup_mono_measure {f : α → β} (hμν : ν ≪ μ) : essSup f ν 
     run_tac
       is_bounded_default
 #align ess_sup_mono_measure essSup_mono_measure
+-/
 
+#print essSup_mono_measure' /-
 theorem essSup_mono_measure' {α : Type _} {β : Type _} {m : MeasurableSpace α}
     {μ ν : MeasureTheory.Measure α} [CompleteLattice β] {f : α → β} (hμν : ν ≤ μ) :
     essSup f ν ≤ essSup f μ :=
   essSup_mono_measure (Measure.absolutelyContinuous_of_le hμν)
 #align ess_sup_mono_measure' essSup_mono_measure'
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+#print essInf_antitone_measure /-
 theorem essInf_antitone_measure {f : α → β} (hμν : μ ≪ ν) : essInf f ν ≤ essInf f μ :=
   by
   refine' liminf_le_liminf_of_le (measure.ae_le_iff_absolutely_continuous.mpr hμν) _ _
@@ -247,7 +292,9 @@ theorem essInf_antitone_measure {f : α → β} (hμν : μ ≪ ν) : essInf f 
     run_tac
       is_bounded_default
 #align ess_inf_antitone_measure essInf_antitone_measure
+-/
 
+#print essSup_smul_measure /-
 theorem essSup_smul_measure {f : α → β} {c : ℝ≥0∞} (hc : c ≠ 0) : essSup f (c • μ) = essSup f μ :=
   by
   simp_rw [essSup]
@@ -256,15 +303,15 @@ theorem essSup_smul_measure {f : α → β} {c : ℝ≥0∞} (hc : c ≠ 0) : es
   simp_rw [mem_ae_iff]
   simp [hc]
 #align ess_sup_smul_measure essSup_smul_measure
+-/
 
 section TopologicalSpace
 
 variable {γ : Type _} {mγ : MeasurableSpace γ} {f : α → γ} {g : γ → β}
 
-include mγ
-
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+#print essSup_comp_le_essSup_map_measure /-
 theorem essSup_comp_le_essSup_map_measure (hf : AEMeasurable f μ) :
     essSup (g ∘ f) μ ≤ essSup g (Measure.map f μ) :=
   by
@@ -281,9 +328,11 @@ theorem essSup_comp_le_essSup_map_measure (hf : AEMeasurable f μ) :
   rw [this]
   exact fun h => mem_ae_of_mem_ae_map hf h
 #align ess_sup_comp_le_ess_sup_map_measure essSup_comp_le_essSup_map_measure
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+#print MeasurableEmbedding.essSup_map_measure /-
 theorem MeasurableEmbedding.essSup_map_measure (hf : MeasurableEmbedding f) :
     essSup g (Measure.map f μ) = essSup (g ∘ f) μ :=
   by
@@ -300,6 +349,7 @@ theorem MeasurableEmbedding.essSup_map_measure (hf : MeasurableEmbedding f) :
   rw [eventually_map] at h_le ⊢
   exact hf.ae_map_iff.mpr h_le
 #align measurable_embedding.ess_sup_map_measure MeasurableEmbedding.essSup_map_measure
+-/
 
 variable [MeasurableSpace β] [TopologicalSpace β] [SecondCountableTopology β]
   [OrderClosedTopology β] [OpensMeasurableSpace β]
@@ -338,8 +388,6 @@ theorem essSup_map_measure (hg : AEMeasurable g (Measure.map f μ)) (hf : AEMeas
 #align ess_sup_map_measure essSup_map_measure
 -/
 
-omit mγ
-
 end TopologicalSpace
 
 end CompleteLattice
@@ -352,6 +400,7 @@ variable [CompleteLinearOrder β]
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+#print essSup_indicator_eq_essSup_restrict /-
 theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → β}
     (hf : 0 ≤ᵐ[μ.restrict s] f) (hs : MeasurableSet s) (hs_not_null : μ s ≠ 0) :
     essSup (s.indicator f) μ = essSup f (μ.restrict s) :=
@@ -394,6 +443,7 @@ theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → 
   · simpa [hxs] using hxc hxs
   · simpa [hxs] using hc
 #align ess_sup_indicator_eq_ess_sup_restrict essSup_indicator_eq_essSup_restrict
+-/
 
 end CompleteLinearOrder
 
@@ -401,39 +451,53 @@ namespace ENNReal
 
 variable {f : α → ℝ≥0∞}
 
+#print ENNReal.ae_le_essSup /-
 theorem ae_le_essSup (f : α → ℝ≥0∞) : ∀ᵐ y ∂μ, f y ≤ essSup f μ :=
   eventually_le_limsup f
 #align ennreal.ae_le_ess_sup ENNReal.ae_le_essSup
+-/
 
+#print ENNReal.essSup_eq_zero_iff /-
 @[simp]
 theorem essSup_eq_zero_iff : essSup f μ = 0 ↔ f =ᵐ[μ] 0 :=
   limsup_eq_zero_iff
 #align ennreal.ess_sup_eq_zero_iff ENNReal.essSup_eq_zero_iff
+-/
 
+#print ENNReal.essSup_const_mul /-
 theorem essSup_const_mul {a : ℝ≥0∞} : essSup (fun x : α => a * f x) μ = a * essSup f μ :=
   limsup_const_mul
 #align ennreal.ess_sup_const_mul ENNReal.essSup_const_mul
+-/
 
+#print ENNReal.essSup_mul_le /-
 theorem essSup_mul_le (f g : α → ℝ≥0∞) : essSup (f * g) μ ≤ essSup f μ * essSup g μ :=
   limsup_mul_le f g
 #align ennreal.ess_sup_mul_le ENNReal.essSup_mul_le
+-/
 
+#print ENNReal.essSup_add_le /-
 theorem essSup_add_le (f g : α → ℝ≥0∞) : essSup (f + g) μ ≤ essSup f μ + essSup g μ :=
   limsup_add_le f g
 #align ennreal.ess_sup_add_le ENNReal.essSup_add_le
+-/
 
+#print ENNReal.essSup_liminf_le /-
 theorem essSup_liminf_le {ι} [Countable ι] [LinearOrder ι] (f : ι → α → ℝ≥0∞) :
     essSup (fun x => atTop.liminf fun n => f n x) μ ≤
       atTop.liminf fun n => essSup (fun x => f n x) μ :=
   by simp_rw [essSup]; exact ENNReal.limsup_liminf_le_liminf_limsup fun a b => f b a
 #align ennreal.ess_sup_liminf_le ENNReal.essSup_liminf_le
+-/
 
+#print ENNReal.coe_essSup /-
 theorem coe_essSup {f : α → ℝ≥0} (hf : IsBoundedUnder (· ≤ ·) μ.ae f) :
     (↑(essSup f μ) : ℝ≥0∞) = essSup (fun x => f x) μ :=
   (ENNReal.coe_sInf <| hf).trans <|
     eq_of_forall_le_iff fun r => by
       simp [essSup, limsup, Limsup, eventually_map, ENNReal.forall_ennreal]
 #align ennreal.coe_ess_sup ENNReal.coe_essSup
+-/
 
 end ENNReal
 

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

@@ -94,12 +94,12 @@ section ConditionallyCompleteLinearOrder
 variable [ConditionallyCompleteLinearOrder β] {x : β} {f : α → β}
 
 theorem essSup_eq_sInf {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
-    essSup f μ = sInf { a | μ { x | a < f x } = 0 } := by dsimp [essSup, limsup, Limsup];
+    essSup f μ = sInf {a | μ {x | a < f x} = 0} := by dsimp [essSup, limsup, Limsup];
   simp only [ae_iff, not_le]
 #align ess_sup_eq_Inf essSup_eq_sInf
 
 theorem essInf_eq_sSup {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
-    essInf f μ = sSup { a | μ { x | f x < a } = 0 } := by dsimp [essInf, liminf, Liminf];
+    essInf f μ = sSup {a | μ {x | f x < a} = 0} := by dsimp [essInf, liminf, Liminf];
   simp only [ae_iff, not_le]
 #align ess_inf_eq_Sup essInf_eq_sSup
 
@@ -154,7 +154,7 @@ theorem meas_essSup_lt
     (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
       run_tac
         is_bounded_default) :
-    μ { y | essSup f μ < f y } = 0 := by simp_rw [← not_le]; exact ae_le_essSup hf
+    μ {y | essSup f μ < f y} = 0 := by simp_rw [← not_le]; exact ae_le_essSup hf
 #align meas_ess_sup_lt meas_essSup_lt
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
@@ -162,7 +162,7 @@ theorem meas_lt_essInf
     (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
       run_tac
         is_bounded_default) :
-    μ { y | f y < essInf f μ } = 0 := by simp_rw [← not_le]; exact ae_essInf_le hf
+    μ {y | f y < essInf f μ} = 0 := by simp_rw [← not_le]; exact ae_essInf_le hf
 #align meas_lt_ess_inf meas_lt_essInf
 
 end ConditionallyCompleteLinearOrder
@@ -384,7 +384,7 @@ theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → 
     have hs' : ∃ᵐ x ∂μ, x ∈ s := by
       contrapose! hs_not_null
       rw [not_frequently, ae_iff] at hs_not_null 
-      suffices { a : α | ¬a ∉ s } = s by rwa [← this]
+      suffices {a : α | ¬a ∉ s} = s by rwa [← this]
       simp
     refine' hs'.mp (hf.mp (h_restrict_le.mono fun x hxs_imp_c hxf_nonneg hxs => _))
     rw [Pi.zero_apply] at hxf_nonneg 

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

@@ -80,11 +80,11 @@ theorem essInf_const' [μ.ae.ne_bot] (c : β) : essInf (fun x : α => c) μ = c
 #align ess_inf_const' essInf_const'
 
 theorem essSup_const (c : β) (hμ : μ ≠ 0) : essSup (fun x : α => c) μ = c := by
-  rw [← ae_ne_bot] at hμ; exact essSup_const' _
+  rw [← ae_ne_bot] at hμ ; exact essSup_const' _
 #align ess_sup_const essSup_const
 
 theorem essInf_const (c : β) (hμ : μ ≠ 0) : essInf (fun x : α => c) μ = c := by
-  rw [← ae_ne_bot] at hμ; exact essInf_const' _
+  rw [← ae_ne_bot] at hμ ; exact essInf_const' _
 #align ess_inf_const essInf_const
 
 end ConditionallyCompleteLattice
@@ -297,7 +297,7 @@ theorem MeasurableEmbedding.essSup_map_measure (hf : MeasurableEmbedding f) :
         run_tac
           is_bounded_default)
       fun c h_le => _
-  rw [eventually_map] at h_le⊢
+  rw [eventually_map] at h_le ⊢
   exact hf.ae_map_iff.mpr h_le
 #align measurable_embedding.ess_sup_map_measure MeasurableEmbedding.essSup_map_measure
 
@@ -320,7 +320,7 @@ theorem essSup_map_measure_of_measurable (hg : Measurable g) (hf : AEMeasurable
         run_tac
           is_bounded_default)
       fun c h_le => _
-  rw [eventually_map] at h_le⊢
+  rw [eventually_map] at h_le ⊢
   rw [ae_map_iff hf (measurableSet_le hg measurable_const)]
   exact h_le
 #align ess_sup_map_measure_of_measurable essSup_map_measure_of_measurable
@@ -333,7 +333,7 @@ theorem essSup_map_measure (hg : AEMeasurable g (Measure.map f μ)) (hf : AEMeas
   rw [essSup_congr_ae hg.ae_eq_mk, essSup_map_measure_of_measurable hg.measurable_mk hf]
   refine' essSup_congr_ae _
   have h_eq := ae_of_ae_map hf hg.ae_eq_mk
-  rw [← eventually_eq] at h_eq
+  rw [← eventually_eq] at h_eq 
   exact h_eq.symm
 #align ess_sup_map_measure essSup_map_measure
 -/
@@ -374,20 +374,20 @@ theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → 
         run_tac
           is_bounded_default)
       fun c h_restrict_le => _
-  rw [eventually_map] at h_restrict_le⊢
-  rw [ae_restrict_iff' hs] at h_restrict_le
+  rw [eventually_map] at h_restrict_le ⊢
+  rw [ae_restrict_iff' hs] at h_restrict_le 
   have hc : 0 ≤ c := by
     rsuffices ⟨x, hx⟩ : ∃ x, 0 ≤ f x ∧ f x ≤ c; exact hx.1.trans hx.2
     refine' frequently.exists _
     · exact μ.ae
-    rw [eventually_le, ae_restrict_iff' hs] at hf
+    rw [eventually_le, ae_restrict_iff' hs] at hf 
     have hs' : ∃ᵐ x ∂μ, x ∈ s := by
       contrapose! hs_not_null
-      rw [not_frequently, ae_iff] at hs_not_null
+      rw [not_frequently, ae_iff] at hs_not_null 
       suffices { a : α | ¬a ∉ s } = s by rwa [← this]
       simp
     refine' hs'.mp (hf.mp (h_restrict_le.mono fun x hxs_imp_c hxf_nonneg hxs => _))
-    rw [Pi.zero_apply] at hxf_nonneg
+    rw [Pi.zero_apply] at hxf_nonneg 
     exact ⟨hxf_nonneg hxs, hxs_imp_c hxs⟩
   refine' h_restrict_le.mono fun x hxc => _
   by_cases hxs : x ∈ s

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

@@ -37,7 +37,7 @@ sense). We do not define that quantity here, which is simply the supremum of a m
 
 open MeasureTheory Filter Set TopologicalSpace
 
-open ENNReal MeasureTheory NNReal
+open scoped ENNReal MeasureTheory NNReal
 
 variable {α β : Type _} {m : MeasurableSpace α} {μ ν : Measure α}
 
@@ -104,6 +104,7 @@ theorem essInf_eq_sSup {m : MeasurableSpace α} (μ : Measure α) (f : α → β
 #align ess_inf_eq_Sup essInf_eq_sSup
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print ae_lt_of_essSup_lt /-
 theorem ae_lt_of_essSup_lt (hx : essSup f μ < x)
     (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
       run_tac
@@ -111,8 +112,10 @@ theorem ae_lt_of_essSup_lt (hx : essSup f μ < x)
     ∀ᵐ y ∂μ, f y < x :=
   eventually_lt_of_limsup_lt hx hf
 #align ae_lt_of_ess_sup_lt ae_lt_of_essSup_lt
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print ae_lt_of_lt_essInf /-
 theorem ae_lt_of_lt_essInf (hx : x < essInf f μ)
     (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
       run_tac
@@ -120,10 +123,12 @@ theorem ae_lt_of_lt_essInf (hx : x < essInf f μ)
     ∀ᵐ y ∂μ, x < f y :=
   eventually_lt_of_lt_liminf hx hf
 #align ae_lt_of_lt_ess_inf ae_lt_of_lt_essInf
+-/
 
 variable [TopologicalSpace β] [FirstCountableTopology β] [OrderTopology β]
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print ae_le_essSup /-
 theorem ae_le_essSup
     (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
       run_tac
@@ -131,8 +136,10 @@ theorem ae_le_essSup
     ∀ᵐ y ∂μ, f y ≤ essSup f μ :=
   eventually_le_limsup hf
 #align ae_le_ess_sup ae_le_essSup
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+#print ae_essInf_le /-
 theorem ae_essInf_le
     (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
       run_tac
@@ -140,6 +147,7 @@ theorem ae_essInf_le
     ∀ᵐ y ∂μ, essInf f μ ≤ f y :=
   eventually_liminf_le hf
 #align ae_ess_inf_le ae_essInf_le
+-/
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem meas_essSup_lt
@@ -344,7 +352,6 @@ variable [CompleteLinearOrder β]
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
-#print essSup_indicator_eq_essSup_restrict /-
 theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → β}
     (hf : 0 ≤ᵐ[μ.restrict s] f) (hs : MeasurableSet s) (hs_not_null : μ s ≠ 0) :
     essSup (s.indicator f) μ = essSup f (μ.restrict s) :=
@@ -387,7 +394,6 @@ theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → 
   · simpa [hxs] using hxc hxs
   · simpa [hxs] using hc
 #align ess_sup_indicator_eq_ess_sup_restrict essSup_indicator_eq_essSup_restrict
--/
 
 end CompleteLinearOrder
 

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

@@ -61,64 +61,28 @@ def essInf {m : MeasurableSpace α} (f : α → β) (μ : Measure α) :=
 #align ess_inf essInf
 -/
 
-/- warning: ess_sup_congr_ae -> essSup_congr_ae is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLattice.{u2} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyEq.{u1, u2} α β (MeasureTheory.Measure.ae.{u1} α m μ) f g) -> (Eq.{succ u2} β (essSup.{u1, u2} α β _inst_1 m f μ) (essSup.{u1, u2} α β _inst_1 m g μ))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : ConditionallyCompleteLattice.{u1} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyEq.{u2, u1} α β (MeasureTheory.Measure.ae.{u2} α m μ) f g) -> (Eq.{succ u1} β (essSup.{u2, u1} α β _inst_1 m f μ) (essSup.{u2, u1} α β _inst_1 m g μ))
-Case conversion may be inaccurate. Consider using '#align ess_sup_congr_ae essSup_congr_aeₓ'. -/
 theorem essSup_congr_ae {f g : α → β} (hfg : f =ᵐ[μ] g) : essSup f μ = essSup g μ :=
   limsup_congr hfg
 #align ess_sup_congr_ae essSup_congr_ae
 
-/- warning: ess_inf_congr_ae -> essInf_congr_ae is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLattice.{u2} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyEq.{u1, u2} α β (MeasureTheory.Measure.ae.{u1} α m μ) f g) -> (Eq.{succ u2} β (essInf.{u1, u2} α β _inst_1 m f μ) (essInf.{u1, u2} α β _inst_1 m g μ))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : ConditionallyCompleteLattice.{u1} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyEq.{u2, u1} α β (MeasureTheory.Measure.ae.{u2} α m μ) f g) -> (Eq.{succ u1} β (essInf.{u2, u1} α β _inst_1 m f μ) (essInf.{u2, u1} α β _inst_1 m g μ))
-Case conversion may be inaccurate. Consider using '#align ess_inf_congr_ae essInf_congr_aeₓ'. -/
 theorem essInf_congr_ae {f g : α → β} (hfg : f =ᵐ[μ] g) : essInf f μ = essInf g μ :=
   @essSup_congr_ae α βᵒᵈ _ _ _ _ _ hfg
 #align ess_inf_congr_ae essInf_congr_ae
 
-/- warning: ess_sup_const' -> essSup_const' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : Filter.NeBot.{u1} α (MeasureTheory.Measure.ae.{u1} α m μ)] (c : β), Eq.{succ u2} β (essSup.{u1, u2} α β _inst_1 m (fun (x : α) => c) μ) c
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : ConditionallyCompleteLattice.{u1} β] [_inst_2 : Filter.NeBot.{u2} α (MeasureTheory.Measure.ae.{u2} α m μ)] (c : β), Eq.{succ u1} β (essSup.{u2, u1} α β _inst_1 m (fun (x : α) => c) μ) c
-Case conversion may be inaccurate. Consider using '#align ess_sup_const' essSup_const'ₓ'. -/
 @[simp]
 theorem essSup_const' [μ.ae.ne_bot] (c : β) : essSup (fun x : α => c) μ = c :=
   limsup_const _
 #align ess_sup_const' essSup_const'
 
-/- warning: ess_inf_const' -> essInf_const' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : Filter.NeBot.{u1} α (MeasureTheory.Measure.ae.{u1} α m μ)] (c : β), Eq.{succ u2} β (essInf.{u1, u2} α β _inst_1 m (fun (x : α) => c) μ) c
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align ess_inf_const' essInf_const'ₓ'. -/
 @[simp]
 theorem essInf_const' [μ.ae.ne_bot] (c : β) : essInf (fun x : α => c) μ = c :=
   liminf_const _
 #align ess_inf_const' essInf_const'
 
-/- warning: ess_sup_const -> essSup_const is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align ess_sup_const essSup_constₓ'. -/
 theorem essSup_const (c : β) (hμ : μ ≠ 0) : essSup (fun x : α => c) μ = c := by
   rw [← ae_ne_bot] at hμ; exact essSup_const' _
 #align ess_sup_const essSup_const
 
-/- warning: ess_inf_const -> essInf_const is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align ess_inf_const essInf_constₓ'. -/
 theorem essInf_const (c : β) (hμ : μ ≠ 0) : essInf (fun x : α => c) μ = c := by
   rw [← ae_ne_bot] at hμ; exact essInf_const' _
 #align ess_inf_const essInf_const
@@ -129,31 +93,16 @@ section ConditionallyCompleteLinearOrder
 
 variable [ConditionallyCompleteLinearOrder β] {x : β} {f : α → β}
 
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-Case conversion may be inaccurate. Consider using '#align ess_sup_eq_Inf essSup_eq_sInfₓ'. -/
 theorem essSup_eq_sInf {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
     essSup f μ = sInf { a | μ { x | a < f x } = 0 } := by dsimp [essSup, limsup, Limsup];
   simp only [ae_iff, not_le]
 #align ess_sup_eq_Inf essSup_eq_sInf
 
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-Case conversion may be inaccurate. Consider using '#align ess_inf_eq_Sup essInf_eq_sSupₓ'. -/
 theorem essInf_eq_sSup {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
     essInf f μ = sSup { a | μ { x | f x < a } = 0 } := by dsimp [essInf, liminf, Liminf];
   simp only [ae_iff, not_le]
 #align ess_inf_eq_Sup essInf_eq_sSup
 
-/- warning: ae_lt_of_ess_sup_lt -> ae_lt_of_essSup_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ae_lt_of_ess_sup_lt ae_lt_of_essSup_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_lt_of_essSup_lt (hx : essSup f μ < x)
     (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
@@ -163,9 +112,6 @@ theorem ae_lt_of_essSup_lt (hx : essSup f μ < x)
   eventually_lt_of_limsup_lt hx hf
 #align ae_lt_of_ess_sup_lt ae_lt_of_essSup_lt
 
-/- warning: ae_lt_of_lt_ess_inf -> ae_lt_of_lt_essInf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ae_lt_of_lt_ess_inf ae_lt_of_lt_essInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_lt_of_lt_essInf (hx : x < essInf f μ)
     (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
@@ -177,9 +123,6 @@ theorem ae_lt_of_lt_essInf (hx : x < essInf f μ)
 
 variable [TopologicalSpace β] [FirstCountableTopology β] [OrderTopology β]
 
-/- warning: ae_le_ess_sup -> ae_le_essSup is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ae_le_ess_sup ae_le_essSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_le_essSup
     (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
@@ -189,9 +132,6 @@ theorem ae_le_essSup
   eventually_le_limsup hf
 #align ae_le_ess_sup ae_le_essSup
 
-/- warning: ae_ess_inf_le -> ae_essInf_le is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ae_ess_inf_le ae_essInf_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_essInf_le
     (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
@@ -201,9 +141,6 @@ theorem ae_essInf_le
   eventually_liminf_le hf
 #align ae_ess_inf_le ae_essInf_le
 
-/- warning: meas_ess_sup_lt -> meas_essSup_lt is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align meas_ess_sup_lt meas_essSup_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem meas_essSup_lt
     (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
@@ -212,9 +149,6 @@ theorem meas_essSup_lt
     μ { y | essSup f μ < f y } = 0 := by simp_rw [← not_le]; exact ae_le_essSup hf
 #align meas_ess_sup_lt meas_essSup_lt
 
-/- warning: meas_lt_ess_inf -> meas_lt_essInf is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align meas_lt_ess_inf meas_lt_essInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem meas_lt_essInf
     (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
@@ -229,54 +163,24 @@ section CompleteLattice
 
 variable [CompleteLattice β]
 
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-Case conversion may be inaccurate. Consider using '#align ess_sup_measure_zero essSup_measure_zeroₓ'. -/
 @[simp]
 theorem essSup_measure_zero {m : MeasurableSpace α} {f : α → β} : essSup f (0 : Measure α) = ⊥ :=
   le_bot_iff.mp (sInf_le (by simp [Set.mem_setOf_eq, eventually_le, ae_iff]))
 #align ess_sup_measure_zero essSup_measure_zero
 
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-Case conversion may be inaccurate. Consider using '#align ess_inf_measure_zero essInf_measure_zeroₓ'. -/
 @[simp]
 theorem essInf_measure_zero {m : MeasurableSpace α} {f : α → β} : essInf f (0 : Measure α) = ⊤ :=
   @essSup_measure_zero α βᵒᵈ _ _ _
 #align ess_inf_measure_zero essInf_measure_zero
 
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-Case conversion may be inaccurate. Consider using '#align ess_sup_mono_ae essSup_mono_aeₓ'. -/
 theorem essSup_mono_ae {f g : α → β} (hfg : f ≤ᵐ[μ] g) : essSup f μ ≤ essSup g μ :=
   limsup_le_limsup hfg
 #align ess_sup_mono_ae essSup_mono_ae
 
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-Case conversion may be inaccurate. Consider using '#align ess_inf_mono_ae essInf_mono_aeₓ'. -/
 theorem essInf_mono_ae {f g : α → β} (hfg : f ≤ᵐ[μ] g) : essInf f μ ≤ essInf g μ :=
   liminf_le_liminf hfg
 #align ess_inf_mono_ae essInf_mono_ae
 
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 theorem essSup_le_of_ae_le {f : α → β} (c : β) (hf : f ≤ᵐ[μ] fun _ => c) : essSup f μ ≤ c :=
   by
   refine' (essSup_mono_ae hf).trans _
@@ -285,39 +189,18 @@ theorem essSup_le_of_ae_le {f : α → β} (c : β) (hf : f ≤ᵐ[μ] fun _ =>
   · rwa [essSup_const]
 #align ess_sup_le_of_ae_le essSup_le_of_ae_le
 
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 theorem le_essInf_of_ae_le {f : α → β} (c : β) (hf : (fun _ => c) ≤ᵐ[μ] f) : c ≤ essInf f μ :=
   @essSup_le_of_ae_le α βᵒᵈ _ _ _ _ c hf
 #align le_ess_inf_of_ae_le le_essInf_of_ae_le
 
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 theorem essSup_const_bot : essSup (fun x : α => (⊥ : β)) μ = (⊥ : β) :=
   limsup_const_bot
 #align ess_sup_const_bot essSup_const_bot
 
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 theorem essInf_const_top : essInf (fun x : α => (⊤ : β)) μ = (⊤ : β) :=
   liminf_const_top
 #align ess_inf_const_top essInf_const_top
 
-/- warning: order_iso.ess_sup_apply -> OrderIso.essSup_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align order_iso.ess_sup_apply OrderIso.essSup_applyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem OrderIso.essSup_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ] (f : α → β)
     (μ : Measure α) (g : β ≃o γ) : g (essSup f μ) = essSup (fun x => g (f x)) μ :=
@@ -328,20 +211,11 @@ theorem OrderIso.essSup_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ]
       is_bounded_default
 #align order_iso.ess_sup_apply OrderIso.essSup_apply
 
-/- warning: order_iso.ess_inf_apply -> OrderIso.essInf_apply is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align order_iso.ess_inf_apply OrderIso.essInf_applyₓ'. -/
 theorem OrderIso.essInf_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ] (f : α → β)
     (μ : Measure α) (g : β ≃o γ) : g (essInf f μ) = essInf (fun x => g (f x)) μ :=
   @OrderIso.essSup_apply α βᵒᵈ _ _ γᵒᵈ _ _ _ g.dual
 #align order_iso.ess_inf_apply OrderIso.essInf_apply
 
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-Case conversion may be inaccurate. Consider using '#align ess_sup_mono_measure essSup_mono_measureₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem essSup_mono_measure {f : α → β} (hμν : ν ≪ μ) : essSup f ν ≤ essSup f μ :=
   by
@@ -351,24 +225,12 @@ theorem essSup_mono_measure {f : α → β} (hμν : ν ≪ μ) : essSup f ν 
       is_bounded_default
 #align ess_sup_mono_measure essSup_mono_measure
 
-/- warning: ess_sup_mono_measure' -> essSup_mono_measure' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ess_sup_mono_measure' essSup_mono_measure'ₓ'. -/
 theorem essSup_mono_measure' {α : Type _} {β : Type _} {m : MeasurableSpace α}
     {μ ν : MeasureTheory.Measure α} [CompleteLattice β] {f : α → β} (hμν : ν ≤ μ) :
     essSup f ν ≤ essSup f μ :=
   essSup_mono_measure (Measure.absolutelyContinuous_of_le hμν)
 #align ess_sup_mono_measure' essSup_mono_measure'
 
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-Case conversion may be inaccurate. Consider using '#align ess_inf_antitone_measure essInf_antitone_measureₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem essInf_antitone_measure {f : α → β} (hμν : μ ≪ ν) : essInf f ν ≤ essInf f μ :=
   by
@@ -378,9 +240,6 @@ theorem essInf_antitone_measure {f : α → β} (hμν : μ ≪ ν) : essInf f 
       is_bounded_default
 #align ess_inf_antitone_measure essInf_antitone_measure
 
-/- warning: ess_sup_smul_measure -> essSup_smul_measure is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align ess_sup_smul_measure essSup_smul_measureₓ'. -/
 theorem essSup_smul_measure {f : α → β} {c : ℝ≥0∞} (hc : c ≠ 0) : essSup f (c • μ) = essSup f μ :=
   by
   simp_rw [essSup]
@@ -396,12 +255,6 @@ variable {γ : Type _} {mγ : MeasurableSpace γ} {f : α → γ} {g : γ → β
 
 include mγ
 
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-Case conversion may be inaccurate. Consider using '#align ess_sup_comp_le_ess_sup_map_measure essSup_comp_le_essSup_map_measureₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem essSup_comp_le_essSup_map_measure (hf : AEMeasurable f μ) :
@@ -421,12 +274,6 @@ theorem essSup_comp_le_essSup_map_measure (hf : AEMeasurable f μ) :
   exact fun h => mem_ae_of_mem_ae_map hf h
 #align ess_sup_comp_le_ess_sup_map_measure essSup_comp_le_essSup_map_measure
 
-/- warning: measurable_embedding.ess_sup_map_measure -> MeasurableEmbedding.essSup_map_measure is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align measurable_embedding.ess_sup_map_measure MeasurableEmbedding.essSup_map_measureₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem MeasurableEmbedding.essSup_map_measure (hf : MeasurableEmbedding f) :
@@ -548,75 +395,33 @@ namespace ENNReal
 
 variable {f : α → ℝ≥0∞}
 
-/- warning: ennreal.ae_le_ess_sup -> ENNReal.ae_le_essSup is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ennreal.ae_le_ess_sup ENNReal.ae_le_essSupₓ'. -/
 theorem ae_le_essSup (f : α → ℝ≥0∞) : ∀ᵐ y ∂μ, f y ≤ essSup f μ :=
   eventually_le_limsup f
 #align ennreal.ae_le_ess_sup ENNReal.ae_le_essSup
 
-/- warning: ennreal.ess_sup_eq_zero_iff -> ENNReal.essSup_eq_zero_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ennreal.ess_sup_eq_zero_iff ENNReal.essSup_eq_zero_iffₓ'. -/
 @[simp]
 theorem essSup_eq_zero_iff : essSup f μ = 0 ↔ f =ᵐ[μ] 0 :=
   limsup_eq_zero_iff
 #align ennreal.ess_sup_eq_zero_iff ENNReal.essSup_eq_zero_iff
 
-/- warning: ennreal.ess_sup_const_mul -> ENNReal.essSup_const_mul is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ennreal.ess_sup_const_mul ENNReal.essSup_const_mulₓ'. -/
 theorem essSup_const_mul {a : ℝ≥0∞} : essSup (fun x : α => a * f x) μ = a * essSup f μ :=
   limsup_const_mul
 #align ennreal.ess_sup_const_mul ENNReal.essSup_const_mul
 
-/- warning: ennreal.ess_sup_mul_le -> ENNReal.essSup_mul_le is a dubious translation:
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-  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} (f : α -> ENNReal) (g : α -> ENNReal), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m (HMul.hMul.{u1, u1, u1} (α -> ENNReal) (α -> ENNReal) (α -> ENNReal) (instHMul.{u1} (α -> ENNReal) (Pi.instMul.{u1, 0} α (fun (ᾰ : α) => ENNReal) (fun (i : α) => CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) f g) μ) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m f μ) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m g μ))
-Case conversion may be inaccurate. Consider using '#align ennreal.ess_sup_mul_le ENNReal.essSup_mul_leₓ'. -/
 theorem essSup_mul_le (f g : α → ℝ≥0∞) : essSup (f * g) μ ≤ essSup f μ * essSup g μ :=
   limsup_mul_le f g
 #align ennreal.ess_sup_mul_le ENNReal.essSup_mul_le
 
-/- warning: ennreal.ess_sup_add_le -> ENNReal.essSup_add_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} (f : α -> ENNReal) (g : α -> ENNReal), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m (HAdd.hAdd.{u1, u1, u1} (α -> ENNReal) (α -> ENNReal) (α -> ENNReal) (instHAdd.{u1} (α -> ENNReal) (Pi.instAdd.{u1, 0} α (fun (ᾰ : α) => ENNReal) (fun (i : α) => Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) f g) μ) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m f μ) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m g μ))
-but is expected to have type
-  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} (f : α -> ENNReal) (g : α -> ENNReal), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m (HAdd.hAdd.{u1, u1, u1} (α -> ENNReal) (α -> ENNReal) (α -> ENNReal) (instHAdd.{u1} (α -> ENNReal) (Pi.instAdd.{u1, 0} α (fun (ᾰ : α) => ENNReal) (fun (i : α) => Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))))) f g) μ) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m f μ) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m g μ))
-Case conversion may be inaccurate. Consider using '#align ennreal.ess_sup_add_le ENNReal.essSup_add_leₓ'. -/
 theorem essSup_add_le (f g : α → ℝ≥0∞) : essSup (f + g) μ ≤ essSup f μ + essSup g μ :=
   limsup_add_le f g
 #align ennreal.ess_sup_add_le ENNReal.essSup_add_le
 
-/- warning: ennreal.ess_sup_liminf_le -> ENNReal.essSup_liminf_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {ι : Type.{u2}} [_inst_1 : Countable.{succ u2} ι] [_inst_2 : LinearOrder.{u2} ι] (f : ι -> α -> ENNReal), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m (fun (x : α) => Filter.liminf.{0, u2} ENNReal ι (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) (fun (n : ι) => f n x) (Filter.atTop.{u2} ι (PartialOrder.toPreorder.{u2} ι (SemilatticeInf.toPartialOrder.{u2} ι (Lattice.toSemilatticeInf.{u2} ι (LinearOrder.toLattice.{u2} ι _inst_2)))))) μ) (Filter.liminf.{0, u2} ENNReal ι (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) (fun (n : ι) => essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m (fun (x : α) => f n x) μ) (Filter.atTop.{u2} ι (PartialOrder.toPreorder.{u2} ι (SemilatticeInf.toPartialOrder.{u2} ι (Lattice.toSemilatticeInf.{u2} ι (LinearOrder.toLattice.{u2} ι _inst_2))))))
-but is expected to have type
-  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {ι : Type.{u2}} [_inst_1 : Countable.{succ u2} ι] [_inst_2 : LinearOrder.{u2} ι] (f : ι -> α -> ENNReal), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m (fun (x : α) => Filter.liminf.{0, u2} ENNReal ι (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) (fun (n : ι) => f n x) (Filter.atTop.{u2} ι (PartialOrder.toPreorder.{u2} ι (SemilatticeInf.toPartialOrder.{u2} ι (Lattice.toSemilatticeInf.{u2} ι (DistribLattice.toLattice.{u2} ι (instDistribLattice.{u2} ι _inst_2))))))) μ) (Filter.liminf.{0, u2} ENNReal ι (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) (fun (n : ι) => essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m (fun (x : α) => f n x) μ) (Filter.atTop.{u2} ι (PartialOrder.toPreorder.{u2} ι (SemilatticeInf.toPartialOrder.{u2} ι (Lattice.toSemilatticeInf.{u2} ι (DistribLattice.toLattice.{u2} ι (instDistribLattice.{u2} ι _inst_2)))))))
-Case conversion may be inaccurate. Consider using '#align ennreal.ess_sup_liminf_le ENNReal.essSup_liminf_leₓ'. -/
 theorem essSup_liminf_le {ι} [Countable ι] [LinearOrder ι] (f : ι → α → ℝ≥0∞) :
     essSup (fun x => atTop.liminf fun n => f n x) μ ≤
       atTop.liminf fun n => essSup (fun x => f n x) μ :=
   by simp_rw [essSup]; exact ENNReal.limsup_liminf_le_liminf_limsup fun a b => f b a
 #align ennreal.ess_sup_liminf_le ENNReal.essSup_liminf_le
 
-/- warning: ennreal.coe_ess_sup -> ENNReal.coe_essSup is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {f : α -> NNReal}, (Filter.IsBoundedUnder.{0, u1} NNReal α (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))))) (MeasureTheory.Measure.ae.{u1} α m μ) f) -> (Eq.{1} ENNReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (essSup.{u1, 0} α NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) m f μ)) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m (fun (x : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (f x)) μ))
-but is expected to have type
-  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {f : α -> NNReal}, (Filter.IsBoundedUnder.{0, u1} NNReal α (fun (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.3950 : NNReal) (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.3952 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.3950 x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.3952) (MeasureTheory.Measure.ae.{u1} α m μ) f) -> (Eq.{1} ENNReal (ENNReal.some (essSup.{u1, 0} α NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal)) m f μ)) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m (fun (x : α) => ENNReal.some (f x)) μ))
-Case conversion may be inaccurate. Consider using '#align ennreal.coe_ess_sup ENNReal.coe_essSupₓ'. -/
 theorem coe_essSup {f : α → ℝ≥0} (hf : IsBoundedUnder (· ≤ ·) μ.ae f) :
     (↑(essSup f μ) : ℝ≥0∞) = essSup (fun x => f x) μ :=
   (ENNReal.coe_sInf <| hf).trans <|

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

@@ -109,10 +109,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : ConditionallyCompleteLattice.{u1} β] (c : β), (Ne.{succ u2} (MeasureTheory.Measure.{u2} α m) μ (OfNat.ofNat.{u2} (MeasureTheory.Measure.{u2} α m) 0 (Zero.toOfNat0.{u2} (MeasureTheory.Measure.{u2} α m) (MeasureTheory.Measure.instZero.{u2} α m)))) -> (Eq.{succ u1} β (essSup.{u2, u1} α β _inst_1 m (fun (x : α) => c) μ) c)
 Case conversion may be inaccurate. Consider using '#align ess_sup_const essSup_constₓ'. -/
-theorem essSup_const (c : β) (hμ : μ ≠ 0) : essSup (fun x : α => c) μ = c :=
-  by
-  rw [← ae_ne_bot] at hμ
-  exact essSup_const' _
+theorem essSup_const (c : β) (hμ : μ ≠ 0) : essSup (fun x : α => c) μ = c := by
+  rw [← ae_ne_bot] at hμ; exact essSup_const' _
 #align ess_sup_const essSup_const
 
 /- warning: ess_inf_const -> essInf_const is a dubious translation:
@@ -121,10 +119,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : ConditionallyCompleteLattice.{u1} β] (c : β), (Ne.{succ u2} (MeasureTheory.Measure.{u2} α m) μ (OfNat.ofNat.{u2} (MeasureTheory.Measure.{u2} α m) 0 (Zero.toOfNat0.{u2} (MeasureTheory.Measure.{u2} α m) (MeasureTheory.Measure.instZero.{u2} α m)))) -> (Eq.{succ u1} β (essInf.{u2, u1} α β _inst_1 m (fun (x : α) => c) μ) c)
 Case conversion may be inaccurate. Consider using '#align ess_inf_const essInf_constₓ'. -/
-theorem essInf_const (c : β) (hμ : μ ≠ 0) : essInf (fun x : α => c) μ = c :=
-  by
-  rw [← ae_ne_bot] at hμ
-  exact essInf_const' _
+theorem essInf_const (c : β) (hμ : μ ≠ 0) : essInf (fun x : α => c) μ = c := by
+  rw [← ae_ne_bot] at hμ; exact essInf_const' _
 #align ess_inf_const essInf_const
 
 end ConditionallyCompleteLattice
@@ -140,9 +136,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {m : MeasurableSpace.{u2} α} (μ : MeasureTheory.Measure.{u2} α m) (f : α -> β), Eq.{succ u1} β (essSup.{u2, u1} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) m f μ) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)) (setOf.{u1} β (fun (a : β) => Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α m μ) (setOf.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) a (f x)))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))))
 Case conversion may be inaccurate. Consider using '#align ess_sup_eq_Inf essSup_eq_sInfₓ'. -/
 theorem essSup_eq_sInf {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
-    essSup f μ = sInf { a | μ { x | a < f x } = 0 } :=
-  by
-  dsimp [essSup, limsup, Limsup]
+    essSup f μ = sInf { a | μ { x | a < f x } = 0 } := by dsimp [essSup, limsup, Limsup];
   simp only [ae_iff, not_le]
 #align ess_sup_eq_Inf essSup_eq_sInf
 
@@ -153,9 +147,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {m : MeasurableSpace.{u2} α} (μ : MeasureTheory.Measure.{u2} α m) (f : α -> β), Eq.{succ u1} β (essInf.{u2, u1} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) m f μ) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)) (setOf.{u1} β (fun (a : β) => Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α m μ) (setOf.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (f x) a))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))))
 Case conversion may be inaccurate. Consider using '#align ess_inf_eq_Sup essInf_eq_sSupₓ'. -/
 theorem essInf_eq_sSup {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
-    essInf f μ = sSup { a | μ { x | f x < a } = 0 } :=
-  by
-  dsimp [essInf, liminf, Liminf]
+    essInf f μ = sSup { a | μ { x | f x < a } = 0 } := by dsimp [essInf, liminf, Liminf];
   simp only [ae_iff, not_le]
 #align ess_inf_eq_Sup essInf_eq_sSup
 
@@ -217,9 +209,7 @@ theorem meas_essSup_lt
     (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
       run_tac
         is_bounded_default) :
-    μ { y | essSup f μ < f y } = 0 := by
-  simp_rw [← not_le]
-  exact ae_le_essSup hf
+    μ { y | essSup f μ < f y } = 0 := by simp_rw [← not_le]; exact ae_le_essSup hf
 #align meas_ess_sup_lt meas_essSup_lt
 
 /- warning: meas_lt_ess_inf -> meas_lt_essInf is a dubious translation:
@@ -230,9 +220,7 @@ theorem meas_lt_essInf
     (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
       run_tac
         is_bounded_default) :
-    μ { y | f y < essInf f μ } = 0 := by
-  simp_rw [← not_le]
-  exact ae_essInf_le hf
+    μ { y | f y < essInf f μ } = 0 := by simp_rw [← not_le]; exact ae_essInf_le hf
 #align meas_lt_ess_inf meas_lt_essInf
 
 end ConditionallyCompleteLinearOrder
@@ -428,9 +416,7 @@ theorem essSup_comp_le_essSup_map_measure (hf : AEMeasurable f μ) :
         run_tac
           is_bounded_default)
   simp_rw [Filter.mem_map]
-  have : g ∘ f ⁻¹' t = f ⁻¹' (g ⁻¹' t) := by
-    ext1 x
-    simp_rw [Set.mem_preimage]
+  have : g ∘ f ⁻¹' t = f ⁻¹' (g ⁻¹' t) := by ext1 x; simp_rw [Set.mem_preimage]
   rw [this]
   exact fun h => mem_ae_of_mem_ae_map hf h
 #align ess_sup_comp_le_ess_sup_map_measure essSup_comp_le_essSup_map_measure
@@ -537,8 +523,7 @@ theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → 
   rw [eventually_map] at h_restrict_le⊢
   rw [ae_restrict_iff' hs] at h_restrict_le
   have hc : 0 ≤ c := by
-    rsuffices ⟨x, hx⟩ : ∃ x, 0 ≤ f x ∧ f x ≤ c
-    exact hx.1.trans hx.2
+    rsuffices ⟨x, hx⟩ : ∃ x, 0 ≤ f x ∧ f x ≤ c; exact hx.1.trans hx.2
     refine' frequently.exists _
     · exact μ.ae
     rw [eventually_le, ae_restrict_iff' hs] at hf
@@ -623,9 +608,7 @@ Case conversion may be inaccurate. Consider using '#align ennreal.ess_sup_liminf
 theorem essSup_liminf_le {ι} [Countable ι] [LinearOrder ι] (f : ι → α → ℝ≥0∞) :
     essSup (fun x => atTop.liminf fun n => f n x) μ ≤
       atTop.liminf fun n => essSup (fun x => f n x) μ :=
-  by
-  simp_rw [essSup]
-  exact ENNReal.limsup_liminf_le_liminf_limsup fun a b => f b a
+  by simp_rw [essSup]; exact ENNReal.limsup_liminf_le_liminf_limsup fun a b => f b a
 #align ennreal.ess_sup_liminf_le ENNReal.essSup_liminf_le
 
 /- warning: ennreal.coe_ess_sup -> ENNReal.coe_essSup is a dubious translation:

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

@@ -160,10 +160,7 @@ theorem essInf_eq_sSup {m : MeasurableSpace α} (μ : Measure α) (f : α → β
 #align ess_inf_eq_Sup essInf_eq_sSup
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ae_lt_of_ess_sup_lt ae_lt_of_essSup_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_lt_of_essSup_lt (hx : essSup f μ < x)
@@ -175,10 +172,7 @@ theorem ae_lt_of_essSup_lt (hx : essSup f μ < x)
 #align ae_lt_of_ess_sup_lt ae_lt_of_essSup_lt
 
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ae_lt_of_lt_ess_inf ae_lt_of_lt_essInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_lt_of_lt_essInf (hx : x < essInf f μ)
@@ -192,10 +186,7 @@ theorem ae_lt_of_lt_essInf (hx : x < essInf f μ)
 variable [TopologicalSpace β] [FirstCountableTopology β] [OrderTopology β]
 
 /- warning: ae_le_ess_sup -> ae_le_essSup is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ae_le_ess_sup ae_le_essSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_le_essSup
@@ -207,10 +198,7 @@ theorem ae_le_essSup
 #align ae_le_ess_sup ae_le_essSup
 
 /- warning: ae_ess_inf_le -> ae_essInf_le is a dubious translation:
-lean 3 declaration is
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ae_ess_inf_le ae_essInf_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_essInf_le
@@ -222,10 +210,7 @@ theorem ae_essInf_le
 #align ae_ess_inf_le ae_essInf_le
 
 /- warning: meas_ess_sup_lt -> meas_essSup_lt is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align meas_ess_sup_lt meas_essSup_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem meas_essSup_lt
@@ -238,10 +223,7 @@ theorem meas_essSup_lt
 #align meas_ess_sup_lt meas_essSup_lt
 
 /- warning: meas_lt_ess_inf -> meas_lt_essInf is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align meas_lt_ess_inf meas_lt_essInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem meas_lt_essInf
@@ -346,10 +328,7 @@ theorem essInf_const_top : essInf (fun x : α => (⊤ : β)) μ = (⊤ : β) :=
 #align ess_inf_const_top essInf_const_top
 
 /- warning: order_iso.ess_sup_apply -> OrderIso.essSup_apply is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align order_iso.ess_sup_apply OrderIso.essSup_applyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem OrderIso.essSup_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ] (f : α → β)
@@ -362,10 +341,7 @@ theorem OrderIso.essSup_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ]
 #align order_iso.ess_sup_apply OrderIso.essSup_apply
 
 /- warning: order_iso.ess_inf_apply -> OrderIso.essInf_apply is a dubious translation:
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(OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (OmegaCompletePartialOrder.toPartialOrder.{u2} γ (CompleteLattice.instOmegaCompletePartialOrder.{u2} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (OmegaCompletePartialOrder.toPartialOrder.{u2} γ (CompleteLattice.instOmegaCompletePartialOrder.{u2} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u2} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (OmegaCompletePartialOrder.toPartialOrder.{u2} γ (CompleteLattice.instOmegaCompletePartialOrder.{u2} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (f x)) μ)
+<too large>
 Case conversion may be inaccurate. Consider using '#align order_iso.ess_inf_apply OrderIso.essInf_applyₓ'. -/
 theorem OrderIso.essInf_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ] (f : α → β)
     (μ : Measure α) (g : β ≃o γ) : g (essInf f μ) = essInf (fun x => g (f x)) μ :=
@@ -415,10 +391,7 @@ theorem essInf_antitone_measure {f : α → β} (hμν : μ ≪ ν) : essInf f 
 #align ess_inf_antitone_measure essInf_antitone_measure
 
 /- warning: ess_sup_smul_measure -> essSup_smul_measure is a dubious translation:
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+<too large>
 Case conversion may be inaccurate. Consider using '#align ess_sup_smul_measure essSup_smul_measureₓ'. -/
 theorem essSup_smul_measure {f : α → β} {c : ℝ≥0∞} (hc : c ≠ 0) : essSup f (c • μ) = essSup f μ :=
   by

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 
 ! This file was ported from Lean 3 source module measure_theory.function.ess_sup
-! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
+! leanprover-community/mathlib commit 4280f5f32e16755ec7985ce11e189b6cd6ff6735
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Order.Filter.Ennreal
 
 /-!
 # Essential supremum and infimum
+
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
 We define the essential supremum and infimum of a function `f : α → β` with respect to a measure
 `μ` on `α`. The essential supremum is the infimum of the constants `c : β` such that `f x ≤ c`
 almost everywhere.

mathlib commit https://github.com/leanprover-community/mathlib/commit/33c67ae661dd8988516ff7f247b0be3018cdd952

@@ -42,42 +42,82 @@ section ConditionallyCompleteLattice
 
 variable [ConditionallyCompleteLattice β]
 
+#print essSup /-
 /-- Essential supremum of `f` with respect to measure `μ`: the smallest `c : β` such that
 `f x ≤ c` a.e. -/
 def essSup {m : MeasurableSpace α} (f : α → β) (μ : Measure α) :=
   μ.ae.limsup f
 #align ess_sup essSup
+-/
 
+#print essInf /-
 /-- Essential infimum of `f` with respect to measure `μ`: the greatest `c : β` such that
 `c ≤ f x` a.e. -/
 def essInf {m : MeasurableSpace α} (f : α → β) (μ : Measure α) :=
   μ.ae.liminf f
 #align ess_inf essInf
+-/
 
+/- warning: ess_sup_congr_ae -> essSup_congr_ae is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLattice.{u2} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyEq.{u1, u2} α β (MeasureTheory.Measure.ae.{u1} α m μ) f g) -> (Eq.{succ u2} β (essSup.{u1, u2} α β _inst_1 m f μ) (essSup.{u1, u2} α β _inst_1 m g μ))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : ConditionallyCompleteLattice.{u1} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyEq.{u2, u1} α β (MeasureTheory.Measure.ae.{u2} α m μ) f g) -> (Eq.{succ u1} β (essSup.{u2, u1} α β _inst_1 m f μ) (essSup.{u2, u1} α β _inst_1 m g μ))
+Case conversion may be inaccurate. Consider using '#align ess_sup_congr_ae essSup_congr_aeₓ'. -/
 theorem essSup_congr_ae {f g : α → β} (hfg : f =ᵐ[μ] g) : essSup f μ = essSup g μ :=
   limsup_congr hfg
 #align ess_sup_congr_ae essSup_congr_ae
 
+/- warning: ess_inf_congr_ae -> essInf_congr_ae is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLattice.{u2} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyEq.{u1, u2} α β (MeasureTheory.Measure.ae.{u1} α m μ) f g) -> (Eq.{succ u2} β (essInf.{u1, u2} α β _inst_1 m f μ) (essInf.{u1, u2} α β _inst_1 m g μ))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : ConditionallyCompleteLattice.{u1} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyEq.{u2, u1} α β (MeasureTheory.Measure.ae.{u2} α m μ) f g) -> (Eq.{succ u1} β (essInf.{u2, u1} α β _inst_1 m f μ) (essInf.{u2, u1} α β _inst_1 m g μ))
+Case conversion may be inaccurate. Consider using '#align ess_inf_congr_ae essInf_congr_aeₓ'. -/
 theorem essInf_congr_ae {f g : α → β} (hfg : f =ᵐ[μ] g) : essInf f μ = essInf g μ :=
   @essSup_congr_ae α βᵒᵈ _ _ _ _ _ hfg
 #align ess_inf_congr_ae essInf_congr_ae
 
+/- warning: ess_sup_const' -> essSup_const' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : Filter.NeBot.{u1} α (MeasureTheory.Measure.ae.{u1} α m μ)] (c : β), Eq.{succ u2} β (essSup.{u1, u2} α β _inst_1 m (fun (x : α) => c) μ) c
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ess_sup_const' essSup_const'ₓ'. -/
 @[simp]
 theorem essSup_const' [μ.ae.ne_bot] (c : β) : essSup (fun x : α => c) μ = c :=
   limsup_const _
 #align ess_sup_const' essSup_const'
 
+/- warning: ess_inf_const' -> essInf_const' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLattice.{u2} β] [_inst_2 : Filter.NeBot.{u1} α (MeasureTheory.Measure.ae.{u1} α m μ)] (c : β), Eq.{succ u2} β (essInf.{u1, u2} α β _inst_1 m (fun (x : α) => c) μ) c
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ess_inf_const' essInf_const'ₓ'. -/
 @[simp]
 theorem essInf_const' [μ.ae.ne_bot] (c : β) : essInf (fun x : α => c) μ = c :=
   liminf_const _
 #align ess_inf_const' essInf_const'
 
+/- warning: ess_sup_const -> essSup_const is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : ConditionallyCompleteLattice.{u1} β] (c : β), (Ne.{succ u2} (MeasureTheory.Measure.{u2} α m) μ (OfNat.ofNat.{u2} (MeasureTheory.Measure.{u2} α m) 0 (Zero.toOfNat0.{u2} (MeasureTheory.Measure.{u2} α m) (MeasureTheory.Measure.instZero.{u2} α m)))) -> (Eq.{succ u1} β (essSup.{u2, u1} α β _inst_1 m (fun (x : α) => c) μ) c)
+Case conversion may be inaccurate. Consider using '#align ess_sup_const essSup_constₓ'. -/
 theorem essSup_const (c : β) (hμ : μ ≠ 0) : essSup (fun x : α => c) μ = c :=
   by
   rw [← ae_ne_bot] at hμ
   exact essSup_const' _
 #align ess_sup_const essSup_const
 
+/- warning: ess_inf_const -> essInf_const is a dubious translation:
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+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLattice.{u2} β] (c : β), (Ne.{succ u1} (MeasureTheory.Measure.{u1} α m) μ (OfNat.ofNat.{u1} (MeasureTheory.Measure.{u1} α m) 0 (OfNat.mk.{u1} (MeasureTheory.Measure.{u1} α m) 0 (Zero.zero.{u1} (MeasureTheory.Measure.{u1} α m) (MeasureTheory.Measure.instZero.{u1} α m))))) -> (Eq.{succ u2} β (essInf.{u1, u2} α β _inst_1 m (fun (x : α) => c) μ) c)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : ConditionallyCompleteLattice.{u1} β] (c : β), (Ne.{succ u2} (MeasureTheory.Measure.{u2} α m) μ (OfNat.ofNat.{u2} (MeasureTheory.Measure.{u2} α m) 0 (Zero.toOfNat0.{u2} (MeasureTheory.Measure.{u2} α m) (MeasureTheory.Measure.instZero.{u2} α m)))) -> (Eq.{succ u1} β (essInf.{u2, u1} α β _inst_1 m (fun (x : α) => c) μ) c)
+Case conversion may be inaccurate. Consider using '#align ess_inf_const essInf_constₓ'. -/
 theorem essInf_const (c : β) (hμ : μ ≠ 0) : essInf (fun x : α => c) μ = c :=
   by
   rw [← ae_ne_bot] at hμ
@@ -90,6 +130,12 @@ section ConditionallyCompleteLinearOrder
 
 variable [ConditionallyCompleteLinearOrder β] {x : β} {f : α → β}
 
+/- warning: ess_sup_eq_Inf -> essSup_eq_sInf is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {m : MeasurableSpace.{u1} α} (μ : MeasureTheory.Measure.{u1} α m) (f : α -> β), Eq.{succ u2} β (essSup.{u1, u2} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ) (InfSet.sInf.{u2} β (ConditionallyCompleteLattice.toHasInf.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)) (setOf.{u2} β (fun (a : β) => Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α m) (fun (_x : MeasureTheory.Measure.{u1} α m) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α m) μ (setOf.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) a (f x)))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {m : MeasurableSpace.{u2} α} (μ : MeasureTheory.Measure.{u2} α m) (f : α -> β), Eq.{succ u1} β (essSup.{u2, u1} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) m f μ) (InfSet.sInf.{u1} β (ConditionallyCompleteLattice.toInfSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)) (setOf.{u1} β (fun (a : β) => Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α m μ) (setOf.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) a (f x)))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))))
+Case conversion may be inaccurate. Consider using '#align ess_sup_eq_Inf essSup_eq_sInfₓ'. -/
 theorem essSup_eq_sInf {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
     essSup f μ = sInf { a | μ { x | a < f x } = 0 } :=
   by
@@ -97,6 +143,12 @@ theorem essSup_eq_sInf {m : MeasurableSpace α} (μ : Measure α) (f : α → β
   simp only [ae_iff, not_le]
 #align ess_sup_eq_Inf essSup_eq_sInf
 
+/- warning: ess_inf_eq_Sup -> essInf_eq_sSup is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {m : MeasurableSpace.{u1} α} (μ : MeasureTheory.Measure.{u1} α m) (f : α -> β), Eq.{succ u2} β (essInf.{u1, u2} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ) (SupSet.sSup.{u2} β (ConditionallyCompleteLattice.toHasSup.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)) (setOf.{u2} β (fun (a : β) => Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α m) (fun (_x : MeasureTheory.Measure.{u1} α m) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α m) μ (setOf.{u1} α (fun (x : α) => LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (f x) a))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : ConditionallyCompleteLinearOrder.{u1} β] {m : MeasurableSpace.{u2} α} (μ : MeasureTheory.Measure.{u2} α m) (f : α -> β), Eq.{succ u1} β (essInf.{u2, u1} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1) m f μ) (SupSet.sSup.{u1} β (ConditionallyCompleteLattice.toSupSet.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)) (setOf.{u1} β (fun (a : β) => Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α m μ) (setOf.{u2} α (fun (x : α) => LT.lt.{u1} β (Preorder.toLT.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeInf.toPartialOrder.{u1} β (Lattice.toSemilatticeInf.{u1} β (ConditionallyCompleteLattice.toLattice.{u1} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u1} β _inst_1)))))) (f x) a))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))))
+Case conversion may be inaccurate. Consider using '#align ess_inf_eq_Sup essInf_eq_sSupₓ'. -/
 theorem essInf_eq_sSup {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
     essInf f μ = sSup { a | μ { x | f x < a } = 0 } :=
   by
@@ -104,6 +156,12 @@ theorem essInf_eq_sSup {m : MeasurableSpace α} (μ : Measure α) (f : α → β
   simp only [ae_iff, not_le]
 #align ess_inf_eq_Sup essInf_eq_sSup
 
+/- warning: ae_lt_of_ess_sup_lt -> ae_lt_of_essSup_lt is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align ae_lt_of_ess_sup_lt ae_lt_of_essSup_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_lt_of_essSup_lt (hx : essSup f μ < x)
     (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
@@ -113,6 +171,12 @@ theorem ae_lt_of_essSup_lt (hx : essSup f μ < x)
   eventually_lt_of_limsup_lt hx hf
 #align ae_lt_of_ess_sup_lt ae_lt_of_essSup_lt
 
+/- warning: ae_lt_of_lt_ess_inf -> ae_lt_of_lt_essInf is a dubious translation:
+lean 3 declaration is
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(One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Name.mk_string (String.str (String.str (String.str (String.str (String.str (String.str String.empty (Char.ofNat (OfNat.ofNat.{0} Nat 102 (OfNat.mk.{0} Nat 102 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 105 (OfNat.mk.{0} Nat 105 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (y : α) => LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) x (f y)) (MeasureTheory.Measure.ae.{u1} α m μ))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {x : β} {f : α -> β}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) x (essInf.{u1, u2} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ)) -> (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.734 : β) (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.736 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.734 x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.736) (MeasureTheory.Measure.ae.{u1} α m μ) f) _auto._@.Mathlib.MeasureTheory.Function.EssSup._hyg.706) -> (Filter.Eventually.{u1} α (fun (y : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) x (f y)) (MeasureTheory.Measure.ae.{u1} α m μ))
+Case conversion may be inaccurate. Consider using '#align ae_lt_of_lt_ess_inf ae_lt_of_lt_essInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_lt_of_lt_essInf (hx : x < essInf f μ)
     (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
@@ -124,6 +188,12 @@ theorem ae_lt_of_lt_essInf (hx : x < essInf f μ)
 
 variable [TopologicalSpace β] [FirstCountableTopology β] [OrderTopology β]
 
+/- warning: ae_le_ess_sup -> ae_le_essSup is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : α -> β} [_inst_2 : TopologicalSpace.{u2} β] [_inst_3 : TopologicalSpace.FirstCountableTopology.{u2} β _inst_2] [_inst_4 : OrderTopology.{u2} β _inst_2 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))], (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) (MeasureTheory.Measure.ae.{u1} α m μ) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str 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Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Filter.Eventually.{u1} α (fun (y : α) => LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (f y) (essSup.{u1, u2} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ)) (MeasureTheory.Measure.ae.{u1} α m μ))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : α -> β} [_inst_2 : TopologicalSpace.{u2} β] [_inst_3 : TopologicalSpace.FirstCountableTopology.{u2} β _inst_2] [_inst_4 : OrderTopology.{u2} β _inst_2 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))], (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.868 : β) (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.870 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.868 x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.870) (MeasureTheory.Measure.ae.{u1} α m μ) f) _auto._@.Mathlib.MeasureTheory.Function.EssSup._hyg.840) -> (Filter.Eventually.{u1} α (fun (y : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (f y) (essSup.{u1, u2} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ)) (MeasureTheory.Measure.ae.{u1} α m μ))
+Case conversion may be inaccurate. Consider using '#align ae_le_ess_sup ae_le_essSupₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_le_essSup
     (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
@@ -133,6 +203,12 @@ theorem ae_le_essSup
   eventually_le_limsup hf
 #align ae_le_ess_sup ae_le_essSup
 
+/- warning: ae_ess_inf_le -> ae_essInf_le is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : α -> β} [_inst_2 : TopologicalSpace.{u2} β] [_inst_3 : TopologicalSpace.FirstCountableTopology.{u2} β _inst_2] [_inst_4 : OrderTopology.{u2} β _inst_2 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))], (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.973 : β) (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.975 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.973 x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.975) (MeasureTheory.Measure.ae.{u1} α m μ) f) _auto._@.Mathlib.MeasureTheory.Function.EssSup._hyg.945) -> (Filter.Eventually.{u1} α (fun (y : α) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (essInf.{u1, u2} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ) (f y)) (MeasureTheory.Measure.ae.{u1} α m μ))
+Case conversion may be inaccurate. Consider using '#align ae_ess_inf_le ae_essInf_leₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_essInf_le
     (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
@@ -142,6 +218,12 @@ theorem ae_essInf_le
   eventually_liminf_le hf
 #align ae_ess_inf_le ae_essInf_le
 
+/- warning: meas_ess_sup_lt -> meas_essSup_lt is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : α -> β} [_inst_2 : TopologicalSpace.{u2} β] [_inst_3 : TopologicalSpace.FirstCountableTopology.{u2} β _inst_2] [_inst_4 : OrderTopology.{u2} β _inst_2 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))], (autoParamₓ.{0} (Filter.IsBoundedUnder.{u2, u1} β α (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1))))))) (MeasureTheory.Measure.ae.{u1} α m μ) f) (Name.mk_string (String.str (String.str (String.str (String.str (String.str 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+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : α -> β} [_inst_2 : TopologicalSpace.{u2} β] [_inst_3 : TopologicalSpace.FirstCountableTopology.{u2} β _inst_2] [_inst_4 : OrderTopology.{u2} β _inst_2 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))], (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.1076 : β) (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.1078 : β) => LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.1076 x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.1078) (MeasureTheory.Measure.ae.{u1} α m μ) f) _auto._@.Mathlib.MeasureTheory.Function.EssSup._hyg.1048) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α m μ) (setOf.{u1} α (fun (y : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (essSup.{u1, u2} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ) (f y)))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align meas_ess_sup_lt meas_essSup_ltₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem meas_essSup_lt
     (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
@@ -152,6 +234,12 @@ theorem meas_essSup_lt
   exact ae_le_essSup hf
 #align meas_ess_sup_lt meas_essSup_lt
 
+/- warning: meas_lt_ess_inf -> meas_lt_essInf is a dubious translation:
+lean 3 declaration is
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108 (OfNat.mk.{0} Nat 108 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 116 (OfNat.mk.{0} Nat 116 (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 101 (OfNat.mk.{0} Nat 101 (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) (Char.ofNat (OfNat.ofNat.{0} Nat 114 (OfNat.mk.{0} Nat 114 (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit0.{0} Nat Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (bit1.{0} Nat Nat.hasOne Nat.hasAdd (One.one.{0} Nat Nat.hasOne))))))))))) Name.anonymous))) -> (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α m) (fun (_x : MeasureTheory.Measure.{u1} α m) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α m) μ (setOf.{u1} α (fun (y : α) => LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (f y) (essInf.{u1, u2} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ)))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : ConditionallyCompleteLinearOrder.{u2} β] {f : α -> β} [_inst_2 : TopologicalSpace.{u2} β] [_inst_3 : TopologicalSpace.FirstCountableTopology.{u2} β _inst_2] [_inst_4 : OrderTopology.{u2} β _inst_2 (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))], (autoParam.{0} (Filter.IsBoundedUnder.{u2, u1} β α (fun (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.1178 : β) (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.1180 : β) => GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.1178 x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.1180) (MeasureTheory.Measure.ae.{u1} α m μ) f) _auto._@.Mathlib.MeasureTheory.Function.EssSup._hyg.1150) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α m μ) (setOf.{u1} α (fun (y : α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (ConditionallyCompleteLattice.toLattice.{u2} β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1)))))) (f y) (essInf.{u1, u2} α β (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ)))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align meas_lt_ess_inf meas_lt_essInfₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem meas_lt_essInf
     (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
@@ -168,24 +256,54 @@ section CompleteLattice
 
 variable [CompleteLattice β]
 
+/- warning: ess_sup_measure_zero -> essSup_measure_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u2} β] {m : MeasurableSpace.{u1} α} {f : α -> β}, Eq.{succ u2} β (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f (OfNat.ofNat.{u1} (MeasureTheory.Measure.{u1} α m) 0 (OfNat.mk.{u1} (MeasureTheory.Measure.{u1} α m) 0 (Zero.zero.{u1} (MeasureTheory.Measure.{u1} α m) (MeasureTheory.Measure.instZero.{u1} α m))))) (Bot.bot.{u2} β (CompleteLattice.toHasBot.{u2} β _inst_1))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u1} β] {m : MeasurableSpace.{u2} α} {f : α -> β}, Eq.{succ u1} β (essSup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m f (OfNat.ofNat.{u2} (MeasureTheory.Measure.{u2} α m) 0 (Zero.toOfNat0.{u2} (MeasureTheory.Measure.{u2} α m) (MeasureTheory.Measure.instZero.{u2} α m)))) (Bot.bot.{u1} β (CompleteLattice.toBot.{u1} β _inst_1))
+Case conversion may be inaccurate. Consider using '#align ess_sup_measure_zero essSup_measure_zeroₓ'. -/
 @[simp]
 theorem essSup_measure_zero {m : MeasurableSpace α} {f : α → β} : essSup f (0 : Measure α) = ⊥ :=
   le_bot_iff.mp (sInf_le (by simp [Set.mem_setOf_eq, eventually_le, ae_iff]))
 #align ess_sup_measure_zero essSup_measure_zero
 
+/- warning: ess_inf_measure_zero -> essInf_measure_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : CompleteLattice.{u2} β] {m : MeasurableSpace.{u1} α} {f : α -> β}, Eq.{succ u2} β (essInf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f (OfNat.ofNat.{u1} (MeasureTheory.Measure.{u1} α m) 0 (OfNat.mk.{u1} (MeasureTheory.Measure.{u1} α m) 0 (Zero.zero.{u1} (MeasureTheory.Measure.{u1} α m) (MeasureTheory.Measure.instZero.{u1} α m))))) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β _inst_1))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : CompleteLattice.{u1} β] {m : MeasurableSpace.{u2} α} {f : α -> β}, Eq.{succ u1} β (essInf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m f (OfNat.ofNat.{u2} (MeasureTheory.Measure.{u2} α m) 0 (Zero.toOfNat0.{u2} (MeasureTheory.Measure.{u2} α m) (MeasureTheory.Measure.instZero.{u2} α m)))) (Top.top.{u1} β (CompleteLattice.toTop.{u1} β _inst_1))
+Case conversion may be inaccurate. Consider using '#align ess_inf_measure_zero essInf_measure_zeroₓ'. -/
 @[simp]
 theorem essInf_measure_zero {m : MeasurableSpace α} {f : α → β} : essInf f (0 : Measure α) = ⊤ :=
   @essSup_measure_zero α βᵒᵈ _ _ _
 #align ess_inf_measure_zero essInf_measure_zero
 
+/- warning: ess_sup_mono_ae -> essSup_mono_ae is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_1)))) (MeasureTheory.Measure.ae.{u1} α m μ) f g) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_1)))) (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ) (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m g μ))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : CompleteLattice.{u1} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) (MeasureTheory.Measure.ae.{u2} α m μ) f g) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) (essSup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m f μ) (essSup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m g μ))
+Case conversion may be inaccurate. Consider using '#align ess_sup_mono_ae essSup_mono_aeₓ'. -/
 theorem essSup_mono_ae {f g : α → β} (hfg : f ≤ᵐ[μ] g) : essSup f μ ≤ essSup g μ :=
   limsup_le_limsup hfg
 #align ess_sup_mono_ae essSup_mono_ae
 
+/- warning: ess_inf_mono_ae -> essInf_mono_ae is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_1)))) (MeasureTheory.Measure.ae.{u1} α m μ) f g) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_1)))) (essInf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ) (essInf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m g μ))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : CompleteLattice.{u1} β] {f : α -> β} {g : α -> β}, (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) (MeasureTheory.Measure.ae.{u2} α m μ) f g) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) (essInf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m f μ) (essInf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m g μ))
+Case conversion may be inaccurate. Consider using '#align ess_inf_mono_ae essInf_mono_aeₓ'. -/
 theorem essInf_mono_ae {f g : α → β} (hfg : f ≤ᵐ[μ] g) : essInf f μ ≤ essInf g μ :=
   liminf_le_liminf hfg
 #align ess_inf_mono_ae essInf_mono_ae
 
+/- warning: ess_sup_le_of_ae_le -> essSup_le_of_ae_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β] {f : α -> β} (c : β), (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_1)))) (MeasureTheory.Measure.ae.{u1} α m μ) f (fun (_x : α) => c)) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_1)))) (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ) c)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : CompleteLattice.{u1} β] {f : α -> β} (c : β), (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) (MeasureTheory.Measure.ae.{u2} α m μ) f (fun (_x : α) => c)) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) (essSup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m f μ) c)
+Case conversion may be inaccurate. Consider using '#align ess_sup_le_of_ae_le essSup_le_of_ae_leₓ'. -/
 theorem essSup_le_of_ae_le {f : α → β} (c : β) (hf : f ≤ᵐ[μ] fun _ => c) : essSup f μ ≤ c :=
   by
   refine' (essSup_mono_ae hf).trans _
@@ -194,18 +312,42 @@ theorem essSup_le_of_ae_le {f : α → β} (c : β) (hf : f ≤ᵐ[μ] fun _ =>
   · rwa [essSup_const]
 #align ess_sup_le_of_ae_le essSup_le_of_ae_le
 
+/- warning: le_ess_inf_of_ae_le -> le_essInf_of_ae_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β] {f : α -> β} (c : β), (Filter.EventuallyLE.{u1, u2} α β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_1)))) (MeasureTheory.Measure.ae.{u1} α m μ) (fun (_x : α) => c) f) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_1)))) c (essInf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} [_inst_1 : CompleteLattice.{u1} β] {f : α -> β} (c : β), (Filter.EventuallyLE.{u2, u1} α β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) (MeasureTheory.Measure.ae.{u2} α m μ) (fun (_x : α) => c) f) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) c (essInf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m f μ))
+Case conversion may be inaccurate. Consider using '#align le_ess_inf_of_ae_le le_essInf_of_ae_leₓ'. -/
 theorem le_essInf_of_ae_le {f : α → β} (c : β) (hf : (fun _ => c) ≤ᵐ[μ] f) : c ≤ essInf f μ :=
   @essSup_le_of_ae_le α βᵒᵈ _ _ _ _ c hf
 #align le_ess_inf_of_ae_le le_essInf_of_ae_le
 
+/- warning: ess_sup_const_bot -> essSup_const_bot is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β], Eq.{succ u2} β (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m (fun (x : α) => Bot.bot.{u2} β (CompleteLattice.toHasBot.{u2} β _inst_1)) μ) (Bot.bot.{u2} β (CompleteLattice.toHasBot.{u2} β _inst_1))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β], Eq.{succ u2} β (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m (fun (x : α) => Bot.bot.{u2} β (CompleteLattice.toBot.{u2} β _inst_1)) μ) (Bot.bot.{u2} β (CompleteLattice.toBot.{u2} β _inst_1))
+Case conversion may be inaccurate. Consider using '#align ess_sup_const_bot essSup_const_botₓ'. -/
 theorem essSup_const_bot : essSup (fun x : α => (⊥ : β)) μ = (⊥ : β) :=
   limsup_const_bot
 #align ess_sup_const_bot essSup_const_bot
 
+/- warning: ess_inf_const_top -> essInf_const_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β], Eq.{succ u2} β (essInf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m (fun (x : α) => Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β _inst_1)) μ) (Top.top.{u2} β (CompleteLattice.toHasTop.{u2} β _inst_1))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β], Eq.{succ u2} β (essInf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m (fun (x : α) => Top.top.{u2} β (CompleteLattice.toTop.{u2} β _inst_1)) μ) (Top.top.{u2} β (CompleteLattice.toTop.{u2} β _inst_1))
+Case conversion may be inaccurate. Consider using '#align ess_inf_const_top essInf_const_topₓ'. -/
 theorem essInf_const_top : essInf (fun x : α => (⊤ : β)) μ = (⊤ : β) :=
   liminf_const_top
 #align ess_inf_const_top essInf_const_top
 
+/- warning: order_iso.ess_sup_apply -> OrderIso.essSup_apply is a dubious translation:
+lean 3 declaration is
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+but is expected to have type
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x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (f x)) μ)
+Case conversion may be inaccurate. Consider using '#align order_iso.ess_sup_apply OrderIso.essSup_applyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem OrderIso.essSup_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ] (f : α → β)
     (μ : Measure α) (g : β ≃o γ) : g (essSup f μ) = essSup (fun x => g (f x)) μ :=
@@ -216,11 +358,23 @@ theorem OrderIso.essSup_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ]
       is_bounded_default
 #align order_iso.ess_sup_apply OrderIso.essSup_apply
 
+/- warning: order_iso.ess_inf_apply -> OrderIso.essInf_apply is a dubious translation:
+lean 3 declaration is
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(PartialOrder.toPreorder.{u2} γ (OmegaCompletePartialOrder.toPartialOrder.{u2} γ (CompleteLattice.instOmegaCompletePartialOrder.{u2} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (OmegaCompletePartialOrder.toPartialOrder.{u2} γ (CompleteLattice.instOmegaCompletePartialOrder.{u2} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u2} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (OmegaCompletePartialOrder.toPartialOrder.{u2} γ (CompleteLattice.instOmegaCompletePartialOrder.{u2} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (essInf.{u3, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m f μ)) (essInf.{u3, u2} α γ (CompleteLattice.toConditionallyCompleteLattice.{u2} γ _inst_2) m (fun (x : α) => FunLike.coe.{max (succ u1) (succ u2), succ u1, succ u2} (RelIso.{u1, u2} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (OmegaCompletePartialOrder.toPartialOrder.{u2} γ (CompleteLattice.instOmegaCompletePartialOrder.{u2} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β (fun (_x : β) => γ) (RelHomClass.toFunLike.{max u1 u2, u1, u2} (RelIso.{u1, u2} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (OmegaCompletePartialOrder.toPartialOrder.{u2} γ (CompleteLattice.instOmegaCompletePartialOrder.{u2} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302)) β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (OmegaCompletePartialOrder.toPartialOrder.{u2} γ (CompleteLattice.instOmegaCompletePartialOrder.{u2} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302) (RelIso.instRelHomClassRelIso.{u1, u2} β γ (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1285 : β) (x._@.Mathlib.Order.Hom.Basic._hyg.1287 : β) => LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) x._@.Mathlib.Order.Hom.Basic._hyg.1285 x._@.Mathlib.Order.Hom.Basic._hyg.1287) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.1300 : γ) (x._@.Mathlib.Order.Hom.Basic._hyg.1302 : γ) => LE.le.{u2} γ (Preorder.toLE.{u2} γ (PartialOrder.toPreorder.{u2} γ (OmegaCompletePartialOrder.toPartialOrder.{u2} γ (CompleteLattice.instOmegaCompletePartialOrder.{u2} γ _inst_2)))) x._@.Mathlib.Order.Hom.Basic._hyg.1300 x._@.Mathlib.Order.Hom.Basic._hyg.1302))) g (f x)) μ)
+Case conversion may be inaccurate. Consider using '#align order_iso.ess_inf_apply OrderIso.essInf_applyₓ'. -/
 theorem OrderIso.essInf_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ] (f : α → β)
     (μ : Measure α) (g : β ≃o γ) : g (essInf f μ) = essInf (fun x => g (f x)) μ :=
   @OrderIso.essSup_apply α βᵒᵈ _ _ γᵒᵈ _ _ _ g.dual
 #align order_iso.ess_inf_apply OrderIso.essInf_apply
 
+/- warning: ess_sup_mono_measure -> essSup_mono_measure is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {ν : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β] {f : α -> β}, (MeasureTheory.Measure.AbsolutelyContinuous.{u1} α m ν μ) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_1)))) (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f ν) (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} {ν : MeasureTheory.Measure.{u2} α m} [_inst_1 : CompleteLattice.{u1} β] {f : α -> β}, (MeasureTheory.Measure.AbsolutelyContinuous.{u2} α m ν μ) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) (essSup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m f ν) (essSup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m f μ))
+Case conversion may be inaccurate. Consider using '#align ess_sup_mono_measure essSup_mono_measureₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem essSup_mono_measure {f : α → β} (hμν : ν ≪ μ) : essSup f ν ≤ essSup f μ :=
   by
@@ -230,12 +384,24 @@ theorem essSup_mono_measure {f : α → β} (hμν : ν ≪ μ) : essSup f ν 
       is_bounded_default
 #align ess_sup_mono_measure essSup_mono_measure
 
+/- warning: ess_sup_mono_measure' -> essSup_mono_measure' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {ν : MeasureTheory.Measure.{u1} α m} [_inst_2 : CompleteLattice.{u2} β] {f : α -> β}, (LE.le.{u1} (MeasureTheory.Measure.{u1} α m) (Preorder.toHasLe.{u1} (MeasureTheory.Measure.{u1} α m) (PartialOrder.toPreorder.{u1} (MeasureTheory.Measure.{u1} α m) (MeasureTheory.Measure.instPartialOrder.{u1} α m))) ν μ) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_2)))) (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_2) m f ν) (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_2) m f μ))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} {ν : MeasureTheory.Measure.{u2} α m} [_inst_2 : CompleteLattice.{u1} β] {f : α -> β}, (LE.le.{u2} (MeasureTheory.Measure.{u2} α m) (Preorder.toLE.{u2} (MeasureTheory.Measure.{u2} α m) (PartialOrder.toPreorder.{u2} (MeasureTheory.Measure.{u2} α m) (MeasureTheory.Measure.instPartialOrder.{u2} α m))) ν μ) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_2)))) (essSup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_2) m f ν) (essSup.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_2) m f μ))
+Case conversion may be inaccurate. Consider using '#align ess_sup_mono_measure' essSup_mono_measure'ₓ'. -/
 theorem essSup_mono_measure' {α : Type _} {β : Type _} {m : MeasurableSpace α}
     {μ ν : MeasureTheory.Measure α} [CompleteLattice β] {f : α → β} (hμν : ν ≤ μ) :
     essSup f ν ≤ essSup f μ :=
   essSup_mono_measure (Measure.absolutelyContinuous_of_le hμν)
 #align ess_sup_mono_measure' essSup_mono_measure'
 
+/- warning: ess_inf_antitone_measure -> essInf_antitone_measure is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {ν : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β] {f : α -> β}, (MeasureTheory.Measure.AbsolutelyContinuous.{u1} α m μ ν) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_1)))) (essInf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f ν) (essInf.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} {m : MeasurableSpace.{u2} α} {μ : MeasureTheory.Measure.{u2} α m} {ν : MeasureTheory.Measure.{u2} α m} [_inst_1 : CompleteLattice.{u1} β] {f : α -> β}, (MeasureTheory.Measure.AbsolutelyContinuous.{u2} α m μ ν) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) (essInf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m f ν) (essInf.{u2, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m f μ))
+Case conversion may be inaccurate. Consider using '#align ess_inf_antitone_measure essInf_antitone_measureₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem essInf_antitone_measure {f : α → β} (hμν : μ ≪ ν) : essInf f ν ≤ essInf f μ :=
   by
@@ -245,6 +411,12 @@ theorem essInf_antitone_measure {f : α → β} (hμν : μ ≪ ν) : essInf f 
       is_bounded_default
 #align ess_inf_antitone_measure essInf_antitone_measure
 
+/- warning: ess_sup_smul_measure -> essSup_smul_measure is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β] {f : α -> β} {c : ENNReal}, (Ne.{1} ENNReal c (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Eq.{succ u2} β (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f (SMul.smul.{0, u1} ENNReal (MeasureTheory.Measure.{u1} α m) (MeasureTheory.Measure.instSMul.{u1, 0} α 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)) (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β] {f : α -> β} {c : ENNReal}, (Ne.{1} ENNReal c (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Eq.{succ u2} β (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f (HSMul.hSMul.{0, u1, u1} ENNReal (MeasureTheory.Measure.{u1} α m) (MeasureTheory.Measure.{u1} α m) (instHSMul.{0, u1} ENNReal (MeasureTheory.Measure.{u1} α m) (MeasureTheory.Measure.instSMul.{u1, 0} α 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)) (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m f μ))
+Case conversion may be inaccurate. Consider using '#align ess_sup_smul_measure essSup_smul_measureₓ'. -/
 theorem essSup_smul_measure {f : α → β} {c : ℝ≥0∞} (hc : c ≠ 0) : essSup f (c • μ) = essSup f μ :=
   by
   simp_rw [essSup]
@@ -260,6 +432,12 @@ variable {γ : Type _} {mγ : MeasurableSpace γ} {f : α → γ} {g : γ → β
 
 include mγ
 
+/- warning: ess_sup_comp_le_ess_sup_map_measure -> essSup_comp_le_essSup_map_measure is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β] {γ : Type.{u3}} {mγ : MeasurableSpace.{u3} γ} {f : α -> γ} {g : γ -> β}, (AEMeasurable.{u1, u3} α γ mγ m f μ) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (CompleteSemilatticeInf.toPartialOrder.{u2} β (CompleteLattice.toCompleteSemilatticeInf.{u2} β _inst_1)))) (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m (Function.comp.{succ u1, succ u3, succ u2} α γ β g f) μ) (essSup.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) mγ g (MeasureTheory.Measure.map.{u1, u3} α γ mγ m f μ)))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u1}} {m : MeasurableSpace.{u3} α} {μ : MeasureTheory.Measure.{u3} α m} [_inst_1 : CompleteLattice.{u1} β] {γ : Type.{u2}} {mγ : MeasurableSpace.{u2} γ} {f : α -> γ} {g : γ -> β}, (AEMeasurable.{u3, u2} α γ mγ m f μ) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (OmegaCompletePartialOrder.toPartialOrder.{u1} β (CompleteLattice.instOmegaCompletePartialOrder.{u1} β _inst_1)))) (essSup.{u3, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m (Function.comp.{succ u3, succ u2, succ u1} α γ β g f) μ) (essSup.{u2, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) mγ g (MeasureTheory.Measure.map.{u3, u2} α γ mγ m f μ)))
+Case conversion may be inaccurate. Consider using '#align ess_sup_comp_le_ess_sup_map_measure essSup_comp_le_essSup_map_measureₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem essSup_comp_le_essSup_map_measure (hf : AEMeasurable f μ) :
@@ -281,6 +459,12 @@ theorem essSup_comp_le_essSup_map_measure (hf : AEMeasurable f μ) :
   exact fun h => mem_ae_of_mem_ae_map hf h
 #align ess_sup_comp_le_ess_sup_map_measure essSup_comp_le_essSup_map_measure
 
+/- warning: measurable_embedding.ess_sup_map_measure -> MeasurableEmbedding.essSup_map_measure is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} [_inst_1 : CompleteLattice.{u2} β] {γ : Type.{u3}} {mγ : MeasurableSpace.{u3} γ} {f : α -> γ} {g : γ -> β}, (MeasurableEmbedding.{u1, u3} α γ m mγ f) -> (Eq.{succ u2} β (essSup.{u3, u2} γ β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) mγ g (MeasureTheory.Measure.map.{u1, u3} α γ mγ m f μ)) (essSup.{u1, u2} α β (CompleteLattice.toConditionallyCompleteLattice.{u2} β _inst_1) m (Function.comp.{succ u1, succ u3, succ u2} α γ β g f) μ))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u1}} {m : MeasurableSpace.{u3} α} {μ : MeasureTheory.Measure.{u3} α m} [_inst_1 : CompleteLattice.{u1} β] {γ : Type.{u2}} {mγ : MeasurableSpace.{u2} γ} {f : α -> γ} {g : γ -> β}, (MeasurableEmbedding.{u3, u2} α γ m mγ f) -> (Eq.{succ u1} β (essSup.{u2, u1} γ β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) mγ g (MeasureTheory.Measure.map.{u3, u2} α γ mγ m f μ)) (essSup.{u3, u1} α β (CompleteLattice.toConditionallyCompleteLattice.{u1} β _inst_1) m (Function.comp.{succ u3, succ u2, succ u1} α γ β g f) μ))
+Case conversion may be inaccurate. Consider using '#align measurable_embedding.ess_sup_map_measure MeasurableEmbedding.essSup_map_measureₓ'. -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem MeasurableEmbedding.essSup_map_measure (hf : MeasurableEmbedding f) :
@@ -305,6 +489,7 @@ variable [MeasurableSpace β] [TopologicalSpace β] [SecondCountableTopology β]
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+#print essSup_map_measure_of_measurable /-
 theorem essSup_map_measure_of_measurable (hg : Measurable g) (hf : AEMeasurable f μ) :
     essSup g (Measure.map f μ) = essSup (g ∘ f) μ :=
   by
@@ -322,7 +507,9 @@ theorem essSup_map_measure_of_measurable (hg : Measurable g) (hf : AEMeasurable
   rw [ae_map_iff hf (measurableSet_le hg measurable_const)]
   exact h_le
 #align ess_sup_map_measure_of_measurable essSup_map_measure_of_measurable
+-/
 
+#print essSup_map_measure /-
 theorem essSup_map_measure (hg : AEMeasurable g (Measure.map f μ)) (hf : AEMeasurable f μ) :
     essSup g (Measure.map f μ) = essSup (g ∘ f) μ :=
   by
@@ -332,6 +519,7 @@ theorem essSup_map_measure (hg : AEMeasurable g (Measure.map f μ)) (hf : AEMeas
   rw [← eventually_eq] at h_eq
   exact h_eq.symm
 #align ess_sup_map_measure essSup_map_measure
+-/
 
 omit mγ
 
@@ -347,6 +535,7 @@ variable [CompleteLinearOrder β]
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+#print essSup_indicator_eq_essSup_restrict /-
 theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → β}
     (hf : 0 ≤ᵐ[μ.restrict s] f) (hs : MeasurableSet s) (hs_not_null : μ s ≠ 0) :
     essSup (s.indicator f) μ = essSup f (μ.restrict s) :=
@@ -390,6 +579,7 @@ theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → 
   · simpa [hxs] using hxc hxs
   · simpa [hxs] using hc
 #align ess_sup_indicator_eq_ess_sup_restrict essSup_indicator_eq_essSup_restrict
+-/
 
 end CompleteLinearOrder
 
@@ -397,27 +587,63 @@ namespace ENNReal
 
 variable {f : α → ℝ≥0∞}
 
+/- warning: ennreal.ae_le_ess_sup -> ENNReal.ae_le_essSup is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} (f : α -> ENNReal), Filter.Eventually.{u1} α (fun (y : α) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (f y) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m f μ)) (MeasureTheory.Measure.ae.{u1} α m μ)
+but is expected to have type
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} (f : α -> ENNReal), Filter.Eventually.{u1} α (fun (y : α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (f y) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m f μ)) (MeasureTheory.Measure.ae.{u1} α m μ)
+Case conversion may be inaccurate. Consider using '#align ennreal.ae_le_ess_sup ENNReal.ae_le_essSupₓ'. -/
 theorem ae_le_essSup (f : α → ℝ≥0∞) : ∀ᵐ y ∂μ, f y ≤ essSup f μ :=
   eventually_le_limsup f
 #align ennreal.ae_le_ess_sup ENNReal.ae_le_essSup
 
+/- warning: ennreal.ess_sup_eq_zero_iff -> ENNReal.essSup_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {f : α -> ENNReal}, Iff (Eq.{1} ENNReal (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m f μ) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Filter.EventuallyEq.{u1, 0} α ENNReal (MeasureTheory.Measure.ae.{u1} α m μ) f (OfNat.ofNat.{u1} (α -> ENNReal) 0 (OfNat.mk.{u1} (α -> ENNReal) 0 (Zero.zero.{u1} (α -> ENNReal) (Pi.instZero.{u1, 0} α (fun (ᾰ : α) => ENNReal) (fun (i : α) => ENNReal.hasZero))))))
+but is expected to have type
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {f : α -> ENNReal}, Iff (Eq.{1} ENNReal (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m f μ) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Filter.EventuallyEq.{u1, 0} α ENNReal (MeasureTheory.Measure.ae.{u1} α m μ) f (OfNat.ofNat.{u1} (α -> ENNReal) 0 (Zero.toOfNat0.{u1} (α -> ENNReal) (Pi.instZero.{u1, 0} α (fun (a._@.Mathlib.Order.Filter.Basic._hyg.19136 : α) => ENNReal) (fun (i : α) => instENNRealZero)))))
+Case conversion may be inaccurate. Consider using '#align ennreal.ess_sup_eq_zero_iff ENNReal.essSup_eq_zero_iffₓ'. -/
 @[simp]
 theorem essSup_eq_zero_iff : essSup f μ = 0 ↔ f =ᵐ[μ] 0 :=
   limsup_eq_zero_iff
 #align ennreal.ess_sup_eq_zero_iff ENNReal.essSup_eq_zero_iff
 
+/- warning: ennreal.ess_sup_const_mul -> ENNReal.essSup_const_mul is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {f : α -> ENNReal} {a : ENNReal}, Eq.{1} ENNReal (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m (fun (x : α) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) a (f x)) μ) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) a (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m f μ))
+but is expected to have type
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {f : α -> ENNReal} {a : ENNReal}, Eq.{1} ENNReal (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m (fun (x : α) => HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) a (f x)) μ) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) a (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m f μ))
+Case conversion may be inaccurate. Consider using '#align ennreal.ess_sup_const_mul ENNReal.essSup_const_mulₓ'. -/
 theorem essSup_const_mul {a : ℝ≥0∞} : essSup (fun x : α => a * f x) μ = a * essSup f μ :=
   limsup_const_mul
 #align ennreal.ess_sup_const_mul ENNReal.essSup_const_mul
 
+/- warning: ennreal.ess_sup_mul_le -> ENNReal.essSup_mul_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} (f : α -> ENNReal) (g : α -> ENNReal), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m (HMul.hMul.{u1, u1, u1} (α -> ENNReal) (α -> ENNReal) (α -> ENNReal) (instHMul.{u1} (α -> ENNReal) (Pi.instMul.{u1, 0} α (fun (ᾰ : α) => ENNReal) (fun (i : α) => Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) f g) μ) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m f μ) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m g μ))
+but is expected to have type
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} (f : α -> ENNReal) (g : α -> ENNReal), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m (HMul.hMul.{u1, u1, u1} (α -> ENNReal) (α -> ENNReal) (α -> ENNReal) (instHMul.{u1} (α -> ENNReal) (Pi.instMul.{u1, 0} α (fun (ᾰ : α) => ENNReal) (fun (i : α) => CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))) f g) μ) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m f μ) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m g μ))
+Case conversion may be inaccurate. Consider using '#align ennreal.ess_sup_mul_le ENNReal.essSup_mul_leₓ'. -/
 theorem essSup_mul_le (f g : α → ℝ≥0∞) : essSup (f * g) μ ≤ essSup f μ * essSup g μ :=
   limsup_mul_le f g
 #align ennreal.ess_sup_mul_le ENNReal.essSup_mul_le
 
+/- warning: ennreal.ess_sup_add_le -> ENNReal.essSup_add_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} (f : α -> ENNReal) (g : α -> ENNReal), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m (HAdd.hAdd.{u1, u1, u1} (α -> ENNReal) (α -> ENNReal) (α -> ENNReal) (instHAdd.{u1} (α -> ENNReal) (Pi.instAdd.{u1, 0} α (fun (ᾰ : α) => ENNReal) (fun (i : α) => Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))))) f g) μ) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m f μ) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m g μ))
+but is expected to have type
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} (f : α -> ENNReal) (g : α -> ENNReal), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m (HAdd.hAdd.{u1, u1, u1} (α -> ENNReal) (α -> ENNReal) (α -> ENNReal) (instHAdd.{u1} (α -> ENNReal) (Pi.instAdd.{u1, 0} α (fun (ᾰ : α) => ENNReal) (fun (i : α) => Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))))) f g) μ) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m f μ) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m g μ))
+Case conversion may be inaccurate. Consider using '#align ennreal.ess_sup_add_le ENNReal.essSup_add_leₓ'. -/
 theorem essSup_add_le (f g : α → ℝ≥0∞) : essSup (f + g) μ ≤ essSup f μ + essSup g μ :=
   limsup_add_le f g
 #align ennreal.ess_sup_add_le ENNReal.essSup_add_le
 
+/- warning: ennreal.ess_sup_liminf_le -> ENNReal.essSup_liminf_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {ι : Type.{u2}} [_inst_1 : Countable.{succ u2} ι] [_inst_2 : LinearOrder.{u2} ι] (f : ι -> α -> ENNReal), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m (fun (x : α) => Filter.liminf.{0, u2} ENNReal ι (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) (fun (n : ι) => f n x) (Filter.atTop.{u2} ι (PartialOrder.toPreorder.{u2} ι (SemilatticeInf.toPartialOrder.{u2} ι (Lattice.toSemilatticeInf.{u2} ι (LinearOrder.toLattice.{u2} ι _inst_2)))))) μ) (Filter.liminf.{0, u2} ENNReal ι (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) (fun (n : ι) => essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m (fun (x : α) => f n x) μ) (Filter.atTop.{u2} ι (PartialOrder.toPreorder.{u2} ι (SemilatticeInf.toPartialOrder.{u2} ι (Lattice.toSemilatticeInf.{u2} ι (LinearOrder.toLattice.{u2} ι _inst_2))))))
+but is expected to have type
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {ι : Type.{u2}} [_inst_1 : Countable.{succ u2} ι] [_inst_2 : LinearOrder.{u2} ι] (f : ι -> α -> ENNReal), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m (fun (x : α) => Filter.liminf.{0, u2} ENNReal ι (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) (fun (n : ι) => f n x) (Filter.atTop.{u2} ι (PartialOrder.toPreorder.{u2} ι (SemilatticeInf.toPartialOrder.{u2} ι (Lattice.toSemilatticeInf.{u2} ι (DistribLattice.toLattice.{u2} ι (instDistribLattice.{u2} ι _inst_2))))))) μ) (Filter.liminf.{0, u2} ENNReal ι (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) (fun (n : ι) => essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m (fun (x : α) => f n x) μ) (Filter.atTop.{u2} ι (PartialOrder.toPreorder.{u2} ι (SemilatticeInf.toPartialOrder.{u2} ι (Lattice.toSemilatticeInf.{u2} ι (DistribLattice.toLattice.{u2} ι (instDistribLattice.{u2} ι _inst_2)))))))
+Case conversion may be inaccurate. Consider using '#align ennreal.ess_sup_liminf_le ENNReal.essSup_liminf_leₓ'. -/
 theorem essSup_liminf_le {ι} [Countable ι] [LinearOrder ι] (f : ι → α → ℝ≥0∞) :
     essSup (fun x => atTop.liminf fun n => f n x) μ ≤
       atTop.liminf fun n => essSup (fun x => f n x) μ :=
@@ -426,6 +652,12 @@ theorem essSup_liminf_le {ι} [Countable ι] [LinearOrder ι] (f : ι → α →
   exact ENNReal.limsup_liminf_le_liminf_limsup fun a b => f b a
 #align ennreal.ess_sup_liminf_le ENNReal.essSup_liminf_le
 
+/- warning: ennreal.coe_ess_sup -> ENNReal.coe_essSup is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {f : α -> NNReal}, (Filter.IsBoundedUnder.{0, u1} NNReal α (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring))))) (MeasureTheory.Measure.ae.{u1} α m μ) f) -> (Eq.{1} ENNReal ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (essSup.{u1, 0} α NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) m f μ)) (essSup.{u1, 0} α ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)) m (fun (x : α) => (fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) (f x)) μ))
+but is expected to have type
+  forall {α : Type.{u1}} {m : MeasurableSpace.{u1} α} {μ : MeasureTheory.Measure.{u1} α m} {f : α -> NNReal}, (Filter.IsBoundedUnder.{0, u1} NNReal α (fun (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.3950 : NNReal) (x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.3952 : NNReal) => LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.3950 x._@.Mathlib.MeasureTheory.Function.EssSup._hyg.3952) (MeasureTheory.Measure.ae.{u1} α m μ) f) -> (Eq.{1} ENNReal (ENNReal.some (essSup.{u1, 0} α NNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.instConditionallyCompleteLinearOrderBotNNReal)) m f μ)) (essSup.{u1, 0} α ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))) m (fun (x : α) => ENNReal.some (f x)) μ))
+Case conversion may be inaccurate. Consider using '#align ennreal.coe_ess_sup ENNReal.coe_essSupₓ'. -/
 theorem coe_essSup {f : α → ℝ≥0} (hf : IsBoundedUnder (· ≤ ·) μ.ae f) :
     (↑(essSup f μ) : ℝ≥0∞) = essSup (fun x => f x) μ :=
   (ENNReal.coe_sInf <| hf).trans <|

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

@@ -4,11 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 
 ! This file was ported from Lean 3 source module measure_theory.function.ess_sup
-! leanprover-community/mathlib commit 52932b3a083d4142e78a15dc928084a22fea9ba0
+! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
-import Mathbin.MeasureTheory.Constructions.BorelSpace
+import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
 import Mathbin.Order.Filter.Ennreal
 
 /-!

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

@@ -90,19 +90,19 @@ section ConditionallyCompleteLinearOrder
 
 variable [ConditionallyCompleteLinearOrder β] {x : β} {f : α → β}
 
-theorem essSup_eq_infₛ {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
-    essSup f μ = infₛ { a | μ { x | a < f x } = 0 } :=
+theorem essSup_eq_sInf {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
+    essSup f μ = sInf { a | μ { x | a < f x } = 0 } :=
   by
   dsimp [essSup, limsup, Limsup]
   simp only [ae_iff, not_le]
-#align ess_sup_eq_Inf essSup_eq_infₛ
+#align ess_sup_eq_Inf essSup_eq_sInf
 
-theorem essInf_eq_supₛ {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
-    essInf f μ = supₛ { a | μ { x | f x < a } = 0 } :=
+theorem essInf_eq_sSup {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
+    essInf f μ = sSup { a | μ { x | f x < a } = 0 } :=
   by
   dsimp [essInf, liminf, Liminf]
   simp only [ae_iff, not_le]
-#align ess_inf_eq_Sup essInf_eq_supₛ
+#align ess_inf_eq_Sup essInf_eq_sSup
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
 theorem ae_lt_of_essSup_lt (hx : essSup f μ < x)
@@ -170,7 +170,7 @@ variable [CompleteLattice β]
 
 @[simp]
 theorem essSup_measure_zero {m : MeasurableSpace α} {f : α → β} : essSup f (0 : Measure α) = ⊥ :=
-  le_bot_iff.mp (infₛ_le (by simp [Set.mem_setOf_eq, eventually_le, ae_iff]))
+  le_bot_iff.mp (sInf_le (by simp [Set.mem_setOf_eq, eventually_le, ae_iff]))
 #align ess_sup_measure_zero essSup_measure_zero
 
 @[simp]
@@ -428,7 +428,7 @@ theorem essSup_liminf_le {ι} [Countable ι] [LinearOrder ι] (f : ι → α →
 
 theorem coe_essSup {f : α → ℝ≥0} (hf : IsBoundedUnder (· ≤ ·) μ.ae f) :
     (↑(essSup f μ) : ℝ≥0∞) = essSup (fun x => f x) μ :=
-  (ENNReal.coe_infₛ <| hf).trans <|
+  (ENNReal.coe_sInf <| hf).trans <|
     eq_of_forall_le_iff fun r => by
       simp [essSup, limsup, Limsup, eventually_map, ENNReal.forall_ennreal]
 #align ennreal.coe_ess_sup ENNReal.coe_essSup

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

@@ -233,7 +233,7 @@ theorem essSup_mono_measure {f : α → β} (hμν : ν ≪ μ) : essSup f ν 
 theorem essSup_mono_measure' {α : Type _} {β : Type _} {m : MeasurableSpace α}
     {μ ν : MeasureTheory.Measure α} [CompleteLattice β] {f : α → β} (hμν : ν ≤ μ) :
     essSup f ν ≤ essSup f μ :=
-  essSup_mono_measure (Measure.absolutelyContinuousOfLe hμν)
+  essSup_mono_measure (Measure.absolutelyContinuous_of_le hμν)
 #align ess_sup_mono_measure' essSup_mono_measure'
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
@@ -262,7 +262,7 @@ include mγ
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
-theorem essSup_comp_le_essSup_map_measure (hf : AeMeasurable f μ) :
+theorem essSup_comp_le_essSup_map_measure (hf : AEMeasurable f μ) :
     essSup (g ∘ f) μ ≤ essSup g (Measure.map f μ) :=
   by
   refine'
@@ -305,7 +305,7 @@ variable [MeasurableSpace β] [TopologicalSpace β] [SecondCountableTopology β]
 
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
-theorem essSup_map_measure_of_measurable (hg : Measurable g) (hf : AeMeasurable f μ) :
+theorem essSup_map_measure_of_measurable (hg : Measurable g) (hf : AEMeasurable f μ) :
     essSup g (Measure.map f μ) = essSup (g ∘ f) μ :=
   by
   refine' le_antisymm _ (essSup_comp_le_essSup_map_measure hf)
@@ -323,7 +323,7 @@ theorem essSup_map_measure_of_measurable (hg : Measurable g) (hf : AeMeasurable
   exact h_le
 #align ess_sup_map_measure_of_measurable essSup_map_measure_of_measurable
 
-theorem essSup_map_measure (hg : AeMeasurable g (Measure.map f μ)) (hf : AeMeasurable f μ) :
+theorem essSup_map_measure (hg : AEMeasurable g (Measure.map f μ)) (hf : AEMeasurable f μ) :
     essSup g (Measure.map f μ) = essSup (g ∘ f) μ :=
   by
   rw [essSup_congr_ae hg.ae_eq_mk, essSup_map_measure_of_measurable hg.measurable_mk hf]

mathlib commit https://github.com/leanprover-community/mathlib/commit/52932b3a083d4142e78a15dc928084a22fea9ba0

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
 
 ! This file was ported from Lean 3 source module measure_theory.function.ess_sup
-! leanprover-community/mathlib commit 394f6e63f63ebc49b2b723e62f89f1604aa4b87d
+! leanprover-community/mathlib commit 52932b3a083d4142e78a15dc928084a22fea9ba0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -32,9 +32,9 @@ sense). We do not define that quantity here, which is simply the supremum of a m
 -/
 
 
-open MeasureTheory Filter TopologicalSpace
+open MeasureTheory Filter Set TopologicalSpace
 
-open ENNReal MeasureTheory
+open ENNReal MeasureTheory NNReal
 
 variable {α β : Type _} {m : MeasurableSpace α} {μ ν : Measure α}
 
@@ -62,21 +62,106 @@ theorem essInf_congr_ae {f g : α → β} (hfg : f =ᵐ[μ] g) : essInf f μ = e
   @essSup_congr_ae α βᵒᵈ _ _ _ _ _ hfg
 #align ess_inf_congr_ae essInf_congr_ae
 
+@[simp]
+theorem essSup_const' [μ.ae.ne_bot] (c : β) : essSup (fun x : α => c) μ = c :=
+  limsup_const _
+#align ess_sup_const' essSup_const'
+
+@[simp]
+theorem essInf_const' [μ.ae.ne_bot] (c : β) : essInf (fun x : α => c) μ = c :=
+  liminf_const _
+#align ess_inf_const' essInf_const'
+
+theorem essSup_const (c : β) (hμ : μ ≠ 0) : essSup (fun x : α => c) μ = c :=
+  by
+  rw [← ae_ne_bot] at hμ
+  exact essSup_const' _
+#align ess_sup_const essSup_const
+
+theorem essInf_const (c : β) (hμ : μ ≠ 0) : essInf (fun x : α => c) μ = c :=
+  by
+  rw [← ae_ne_bot] at hμ
+  exact essInf_const' _
+#align ess_inf_const essInf_const
+
 end ConditionallyCompleteLattice
 
 section ConditionallyCompleteLinearOrder
 
-variable [ConditionallyCompleteLinearOrder β]
+variable [ConditionallyCompleteLinearOrder β] {x : β} {f : α → β}
 
 theorem essSup_eq_infₛ {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
     essSup f μ = infₛ { a | μ { x | a < f x } = 0 } :=
   by
   dsimp [essSup, limsup, Limsup]
-  congr
-  ext a
-  simp [eventually_map, ae_iff]
+  simp only [ae_iff, not_le]
 #align ess_sup_eq_Inf essSup_eq_infₛ
 
+theorem essInf_eq_supₛ {m : MeasurableSpace α} (μ : Measure α) (f : α → β) :
+    essInf f μ = supₛ { a | μ { x | f x < a } = 0 } :=
+  by
+  dsimp [essInf, liminf, Liminf]
+  simp only [ae_iff, not_le]
+#align ess_inf_eq_Sup essInf_eq_supₛ
+
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+theorem ae_lt_of_essSup_lt (hx : essSup f μ < x)
+    (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
+      run_tac
+        is_bounded_default) :
+    ∀ᵐ y ∂μ, f y < x :=
+  eventually_lt_of_limsup_lt hx hf
+#align ae_lt_of_ess_sup_lt ae_lt_of_essSup_lt
+
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+theorem ae_lt_of_lt_essInf (hx : x < essInf f μ)
+    (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
+      run_tac
+        is_bounded_default) :
+    ∀ᵐ y ∂μ, x < f y :=
+  eventually_lt_of_lt_liminf hx hf
+#align ae_lt_of_lt_ess_inf ae_lt_of_lt_essInf
+
+variable [TopologicalSpace β] [FirstCountableTopology β] [OrderTopology β]
+
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+theorem ae_le_essSup
+    (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
+      run_tac
+        is_bounded_default) :
+    ∀ᵐ y ∂μ, f y ≤ essSup f μ :=
+  eventually_le_limsup hf
+#align ae_le_ess_sup ae_le_essSup
+
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+theorem ae_essInf_le
+    (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
+      run_tac
+        is_bounded_default) :
+    ∀ᵐ y ∂μ, essInf f μ ≤ f y :=
+  eventually_liminf_le hf
+#align ae_ess_inf_le ae_essInf_le
+
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+theorem meas_essSup_lt
+    (hf : IsBoundedUnder (· ≤ ·) μ.ae f := by
+      run_tac
+        is_bounded_default) :
+    μ { y | essSup f μ < f y } = 0 := by
+  simp_rw [← not_le]
+  exact ae_le_essSup hf
+#align meas_ess_sup_lt meas_essSup_lt
+
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic is_bounded_default -/
+theorem meas_lt_essInf
+    (hf : IsBoundedUnder (· ≥ ·) μ.ae f := by
+      run_tac
+        is_bounded_default) :
+    μ { y | f y < essInf f μ } = 0 := by
+  simp_rw [← not_le]
+  exact ae_essInf_le hf
+#align meas_lt_ess_inf meas_lt_essInf
+
 end ConditionallyCompleteLinearOrder
 
 section CompleteLattice
@@ -101,11 +186,6 @@ theorem essInf_mono_ae {f g : α → β} (hfg : f ≤ᵐ[μ] g) : essInf f μ 
   liminf_le_liminf hfg
 #align ess_inf_mono_ae essInf_mono_ae
 
-theorem essSup_const (c : β) (hμ : μ ≠ 0) : essSup (fun x : α => c) μ = c :=
-  haveI hμ_ne_bot : μ.ae.ne_bot := by rwa [ne_bot_iff, Ne.def, ae_eq_bot]
-  limsup_const c
-#align ess_sup_const essSup_const
-
 theorem essSup_le_of_ae_le {f : α → β} (c : β) (hf : f ≤ᵐ[μ] fun _ => c) : essSup f μ ≤ c :=
   by
   refine' (essSup_mono_ae hf).trans _
@@ -114,10 +194,6 @@ theorem essSup_le_of_ae_le {f : α → β} (c : β) (hf : f ≤ᵐ[μ] fun _ =>
   · rwa [essSup_const]
 #align ess_sup_le_of_ae_le essSup_le_of_ae_le
 
-theorem essInf_const (c : β) (hμ : μ ≠ 0) : essInf (fun x : α => c) μ = c :=
-  @essSup_const α βᵒᵈ _ _ _ _ hμ
-#align ess_inf_const essInf_const
-
 theorem le_essInf_of_ae_le {f : α → β} (c : β) (hf : (fun _ => c) ≤ᵐ[μ] f) : c ≤ essInf f μ :=
   @essSup_le_of_ae_le α βᵒᵈ _ _ _ _ c hf
 #align le_ess_inf_of_ae_le le_essInf_of_ae_le
@@ -267,14 +343,6 @@ section CompleteLinearOrder
 
 variable [CompleteLinearOrder β]
 
-theorem ae_lt_of_essSup_lt {f : α → β} {x : β} (hf : essSup f μ < x) : ∀ᵐ y ∂μ, f y < x :=
-  Filter.eventually_lt_of_limsup_lt hf
-#align ae_lt_of_ess_sup_lt ae_lt_of_essSup_lt
-
-theorem ae_lt_of_lt_essInf {f : α → β} {x : β} (hf : x < essInf f μ) : ∀ᵐ y ∂μ, x < f y :=
-  @ae_lt_of_essSup_lt α βᵒᵈ _ _ _ _ _ hf
-#align ae_lt_of_lt_ess_inf ae_lt_of_lt_essInf
-
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 /- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
@@ -358,5 +426,12 @@ theorem essSup_liminf_le {ι} [Countable ι] [LinearOrder ι] (f : ι → α →
   exact ENNReal.limsup_liminf_le_liminf_limsup fun a b => f b a
 #align ennreal.ess_sup_liminf_le ENNReal.essSup_liminf_le
 
+theorem coe_essSup {f : α → ℝ≥0} (hf : IsBoundedUnder (· ≤ ·) μ.ae f) :
+    (↑(essSup f μ) : ℝ≥0∞) = essSup (fun x => f x) μ :=
+  (ENNReal.coe_infₛ <| hf).trans <|
+    eq_of_forall_le_iff fun r => by
+      simp [essSup, limsup, Limsup, eventually_map, ENNReal.forall_ennreal]
+#align ennreal.coe_ess_sup ENNReal.coe_essSup
+
 end ENNReal
 

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

@@ -130,7 +130,7 @@ theorem essInf_const_top : essInf (fun x : α => (⊤ : β)) μ = (⊤ : β) :=
   liminf_const_top
 #align ess_inf_const_top essInf_const_top
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem OrderIso.essSup_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ] (f : α → β)
     (μ : Measure α) (g : β ≃o γ) : g (essSup f μ) = essSup (fun x => g (f x)) μ :=
   by
@@ -145,7 +145,7 @@ theorem OrderIso.essInf_apply {m : MeasurableSpace α} {γ} [CompleteLattice γ]
   @OrderIso.essSup_apply α βᵒᵈ _ _ γᵒᵈ _ _ _ g.dual
 #align order_iso.ess_inf_apply OrderIso.essInf_apply
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem essSup_mono_measure {f : α → β} (hμν : ν ≪ μ) : essSup f ν ≤ essSup f μ :=
   by
   refine' limsup_le_limsup_of_le (measure.ae_le_iff_absolutely_continuous.mpr hμν) _ _
@@ -160,7 +160,7 @@ theorem essSup_mono_measure' {α : Type _} {β : Type _} {m : MeasurableSpace α
   essSup_mono_measure (Measure.absolutelyContinuousOfLe hμν)
 #align ess_sup_mono_measure' essSup_mono_measure'
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem essInf_antitone_measure {f : α → β} (hμν : μ ≪ ν) : essInf f ν ≤ essInf f μ :=
   by
   refine' liminf_le_liminf_of_le (measure.ae_le_iff_absolutely_continuous.mpr hμν) _ _
@@ -184,8 +184,8 @@ variable {γ : Type _} {mγ : MeasurableSpace γ} {f : α → γ} {g : γ → β
 
 include mγ
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem essSup_comp_le_essSup_map_measure (hf : AeMeasurable f μ) :
     essSup (g ∘ f) μ ≤ essSup g (Measure.map f μ) :=
   by
@@ -205,8 +205,8 @@ theorem essSup_comp_le_essSup_map_measure (hf : AeMeasurable f μ) :
   exact fun h => mem_ae_of_mem_ae_map hf h
 #align ess_sup_comp_le_ess_sup_map_measure essSup_comp_le_essSup_map_measure
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem MeasurableEmbedding.essSup_map_measure (hf : MeasurableEmbedding f) :
     essSup g (Measure.map f μ) = essSup (g ∘ f) μ :=
   by
@@ -227,8 +227,8 @@ theorem MeasurableEmbedding.essSup_map_measure (hf : MeasurableEmbedding f) :
 variable [MeasurableSpace β] [TopologicalSpace β] [SecondCountableTopology β]
   [OrderClosedTopology β] [OpensMeasurableSpace β]
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem essSup_map_measure_of_measurable (hg : Measurable g) (hf : AeMeasurable f μ) :
     essSup g (Measure.map f μ) = essSup (g ∘ f) μ :=
   by
@@ -275,10 +275,10 @@ theorem ae_lt_of_lt_essInf {f : α → β} {x : β} (hf : x < essInf f μ) : ∀
   @ae_lt_of_essSup_lt α βᵒᵈ _ _ _ _ _ hf
 #align ae_lt_of_lt_ess_inf ae_lt_of_lt_essInf
 
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
-/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:72:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
+/- ./././Mathport/Syntax/Translate/Tactic/Builtin.lean:69:18: unsupported non-interactive tactic filter.is_bounded_default -/
 theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → β}
     (hf : 0 ≤ᵐ[μ.restrict s] f) (hs : MeasurableSet s) (hs_not_null : μ s ≠ 0) :
     essSup (s.indicator f) μ = essSup f (μ.restrict s) :=

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

@@ -34,7 +34,7 @@ sense). We do not define that quantity here, which is simply the supremum of a m
 
 open MeasureTheory Filter TopologicalSpace
 
-open Ennreal MeasureTheory
+open ENNReal MeasureTheory
 
 variable {α β : Type _} {m : MeasurableSpace α} {μ ν : Measure α}
 
@@ -325,38 +325,38 @@ theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → 
 
 end CompleteLinearOrder
 
-namespace Ennreal
+namespace ENNReal
 
 variable {f : α → ℝ≥0∞}
 
 theorem ae_le_essSup (f : α → ℝ≥0∞) : ∀ᵐ y ∂μ, f y ≤ essSup f μ :=
   eventually_le_limsup f
-#align ennreal.ae_le_ess_sup Ennreal.ae_le_essSup
+#align ennreal.ae_le_ess_sup ENNReal.ae_le_essSup
 
 @[simp]
 theorem essSup_eq_zero_iff : essSup f μ = 0 ↔ f =ᵐ[μ] 0 :=
   limsup_eq_zero_iff
-#align ennreal.ess_sup_eq_zero_iff Ennreal.essSup_eq_zero_iff
+#align ennreal.ess_sup_eq_zero_iff ENNReal.essSup_eq_zero_iff
 
 theorem essSup_const_mul {a : ℝ≥0∞} : essSup (fun x : α => a * f x) μ = a * essSup f μ :=
   limsup_const_mul
-#align ennreal.ess_sup_const_mul Ennreal.essSup_const_mul
+#align ennreal.ess_sup_const_mul ENNReal.essSup_const_mul
 
 theorem essSup_mul_le (f g : α → ℝ≥0∞) : essSup (f * g) μ ≤ essSup f μ * essSup g μ :=
   limsup_mul_le f g
-#align ennreal.ess_sup_mul_le Ennreal.essSup_mul_le
+#align ennreal.ess_sup_mul_le ENNReal.essSup_mul_le
 
 theorem essSup_add_le (f g : α → ℝ≥0∞) : essSup (f + g) μ ≤ essSup f μ + essSup g μ :=
   limsup_add_le f g
-#align ennreal.ess_sup_add_le Ennreal.essSup_add_le
+#align ennreal.ess_sup_add_le ENNReal.essSup_add_le
 
 theorem essSup_liminf_le {ι} [Countable ι] [LinearOrder ι] (f : ι → α → ℝ≥0∞) :
     essSup (fun x => atTop.liminf fun n => f n x) μ ≤
       atTop.liminf fun n => essSup (fun x => f n x) μ :=
   by
   simp_rw [essSup]
-  exact Ennreal.limsup_liminf_le_liminf_limsup fun a b => f b a
-#align ennreal.ess_sup_liminf_le Ennreal.essSup_liminf_le
+  exact ENNReal.limsup_liminf_le_liminf_limsup fun a b => f b a
+#align ennreal.ess_sup_liminf_le ENNReal.essSup_liminf_le
 
-end Ennreal
+end ENNReal
 

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

@@ -15,12 +15,12 @@ We define the essential supremum and infimum of a function `f : α → β` with
 almost everywhere.
 
 TODO: The essential supremum of functions `α → ℝ≥0∞` is used in particular to define the norm in
-the `L∞` space (see `MeasureTheory.Function.LpSpace`).
+the `L∞` space (see `Mathlib.MeasureTheory.Function.LpSpace`).
 
 There is a different quantity which is sometimes also called essential supremum: the least
 upper-bound among measurable functions of a family of measurable functions (in an almost-everywhere
 sense). We do not define that quantity here, which is simply the supremum of a map with values in
-`α →ₘ[μ] β` (see `MeasureTheory.Function.AEEqFun`).
+`α →ₘ[μ] β` (see `Mathlib.MeasureTheory.Function.AEEqFun`).
 
 ## Main definitions
 

@@ -15,12 +15,12 @@ We define the essential supremum and infimum of a function `f : α → β` with
 almost everywhere.
 
 TODO: The essential supremum of functions `α → ℝ≥0∞` is used in particular to define the norm in
-the `L∞` space (see MeasureTheory/LpSpace.lean).
+the `L∞` space (see `MeasureTheory.Function.LpSpace`).
 
 There is a different quantity which is sometimes also called essential supremum: the least
 upper-bound among measurable functions of a family of measurable functions (in an almost-everywhere
 sense). We do not define that quantity here, which is simply the supremum of a map with values in
-`α →ₘ[μ] β` (see MeasureTheory/AEEqFun.lean).
+`α →ₘ[μ] β` (see `MeasureTheory.Function.AEEqFun`).
 
 ## Main definitions
 

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -205,7 +205,7 @@ theorem essInf_antitone_measure {f : α → β} (hμν : μ ≪ ν) : essInf f 
 theorem essSup_smul_measure {f : α → β} {c : ℝ≥0∞} (hc : c ≠ 0) :
     essSup f (c • μ) = essSup f μ := by
   simp_rw [essSup]
-  suffices h_smul : (c • μ).ae = μ.ae; · rw [h_smul]
+  suffices h_smul : (c • μ).ae = μ.ae by rw [h_smul]
   ext1
   simp_rw [mem_ae_iff]
   simp [hc]

• Add blimsup_eq_limsup and bliminf_eq_liminf
• Generalize limsup_nat_add and liminf_nat_add to a ConditionallyCompleteLattice.
• Add Filter.HasBasis.blimsup_eq_iInf_iSup.
• Add limsup_sup_filter, liminf_sup_filter, blimsup_sup_not, bliminf_inf_not, blimsup_not_sup, bliminf_not_inf, limsup_piecewise, and liminf_piecewise.
• Add essSup_piecewise.
• Assume that the codomain is ℝ≥0∞ in essSup_indicator_eq_essSup_restrict. This allows us to drop assumptions 0 ≤ᵐ[_] f and μ s ≠ 0.
• Upgrade inequality to an equality in snormEssSup_piecewise_le (now snormEssSup_piecewise) and snorm_top_piecewise_le (now snorm_top_piecewise).
• Use new lemmas to golf some proofs.

@@ -159,11 +159,8 @@ theorem essInf_mono_ae {f g : α → β} (hfg : f ≤ᵐ[μ] g) : essInf f μ 
   liminf_le_liminf hfg
 #align ess_inf_mono_ae essInf_mono_ae
 
-theorem essSup_le_of_ae_le {f : α → β} (c : β) (hf : f ≤ᵐ[μ] fun _ => c) : essSup f μ ≤ c := by
-  refine' (essSup_mono_ae hf).trans _
-  by_cases hμ : μ = 0
-  · simp [hμ]
-  · rwa [essSup_const]
+theorem essSup_le_of_ae_le {f : α → β} (c : β) (hf : f ≤ᵐ[μ] fun _ => c) : essSup f μ ≤ c :=
+  limsup_le_of_le (by isBoundedDefault) hf
 #align ess_sup_le_of_ae_le essSup_le_of_ae_le
 
 theorem le_essInf_of_ae_le {f : α → β} (c : β) (hf : (fun _ => c) ≤ᵐ[μ] f) : c ≤ essInf f μ :=
@@ -262,45 +259,20 @@ end TopologicalSpace
 
 end CompleteLattice
 
-section CompleteLinearOrder
-
-variable [CompleteLinearOrder β]
-theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → β}
-    (hf : 0 ≤ᵐ[μ.restrict s] f) (hs : MeasurableSet s) (hs_not_null : μ s ≠ 0) :
-    essSup (s.indicator f) μ = essSup f (μ.restrict s) := by
-  refine'
-    le_antisymm _
-      (limsSup_le_limsSup_of_le (map_restrict_ae_le_map_indicator_ae hs)
-        (by isBoundedDefault) (by isBoundedDefault) )
-  refine' limsSup_le_limsSup (by isBoundedDefault) (by isBoundedDefault) (fun c h_restrict_le => _)
-  rw [eventually_map] at h_restrict_le ⊢
-  rw [ae_restrict_iff' hs] at h_restrict_le
-  have hc : 0 ≤ c := by
-    rsuffices ⟨x, hx⟩ : ∃ x, 0 ≤ f x ∧ f x ≤ c
-    exact hx.1.trans hx.2
-    refine' Frequently.exists _
-    · exact μ.ae
-    rw [EventuallyLE, ae_restrict_iff' hs] at hf
-    have hs' : ∃ᵐ x ∂μ, x ∈ s := by
-      contrapose! hs_not_null
-      rw [not_frequently, ae_iff] at hs_not_null
-      suffices { a : α | ¬a ∉ s } = s by rwa [← this]
-      simp
-    refine' hs'.mp (hf.mp (h_restrict_le.mono fun x hxs_imp_c hxf_nonneg hxs => _))
-    rw [Pi.zero_apply] at hxf_nonneg
-    exact ⟨hxf_nonneg hxs, hxs_imp_c hxs⟩
-  refine' h_restrict_le.mono fun x hxc => _
-  by_cases hxs : x ∈ s
-  · simpa [hxs] using hxc hxs
-  · simpa [hxs] using hc
-#align ess_sup_indicator_eq_ess_sup_restrict essSup_indicator_eq_essSup_restrict
-
-end CompleteLinearOrder
-
 namespace ENNReal
 
 variable {f : α → ℝ≥0∞}
 
+lemma essSup_piecewise {s : Set α} [DecidablePred (· ∈ s)] {g} (hs : MeasurableSet s) :
+    essSup (s.piecewise f g) μ = max (essSup f (μ.restrict s)) (essSup g (μ.restrict sᶜ)) := by
+  simp only [essSup, limsup_piecewise, blimsup_eq_limsup, ae_restrict_eq, hs, hs.compl]; rfl
+
+theorem essSup_indicator_eq_essSup_restrict {s : Set α} {f : α → ℝ≥0∞} (hs : MeasurableSet s) :
+    essSup (s.indicator f) μ = essSup f (μ.restrict s) := by
+  classical
+  simp only [← piecewise_eq_indicator, essSup_piecewise hs, max_eq_left_iff]
+  exact limsup_const_bot.trans_le (zero_le _)
+
 theorem ae_le_essSup (f : α → ℝ≥0∞) : ∀ᵐ y ∂μ, f y ≤ essSup f μ :=
   eventually_le_limsup f
 #align ennreal.ae_le_ess_sup ENNReal.ae_le_essSup

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

This has nice performance benefits.

@@ -33,7 +33,7 @@ open MeasureTheory Filter Set TopologicalSpace
 
 open ENNReal MeasureTheory NNReal
 
-variable {α β : Type _} {m : MeasurableSpace α} {μ ν : Measure α}
+variable {α β : Type*} {m : MeasurableSpace α} {μ ν : Measure α}
 
 section ConditionallyCompleteLattice
 
@@ -194,7 +194,7 @@ theorem essSup_mono_measure {f : α → β} (hμν : ν ≪ μ) : essSup f ν 
   all_goals isBoundedDefault
 #align ess_sup_mono_measure essSup_mono_measure
 
-theorem essSup_mono_measure' {α : Type _} {β : Type _} {_ : MeasurableSpace α}
+theorem essSup_mono_measure' {α : Type*} {β : Type*} {_ : MeasurableSpace α}
     {μ ν : MeasureTheory.Measure α} [CompleteLattice β] {f : α → β} (hμν : ν ≤ μ) :
     essSup f ν ≤ essSup f μ :=
   essSup_mono_measure (Measure.absolutelyContinuous_of_le hμν)
@@ -216,7 +216,7 @@ theorem essSup_smul_measure {f : α → β} {c : ℝ≥0∞} (hc : c ≠ 0) :
 
 section TopologicalSpace
 
-variable {γ : Type _} {mγ : MeasurableSpace γ} {f : α → γ} {g : γ → β}
+variable {γ : Type*} {mγ : MeasurableSpace γ} {f : α → γ} {g : γ → β}
 
 theorem essSup_comp_le_essSup_map_measure (hf : AEMeasurable f μ) :
     essSup (g ∘ f) μ ≤ essSup g (Measure.map f μ) := by

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;

@@ -60,23 +60,21 @@ theorem essInf_congr_ae {f g : α → β} (hfg : f =ᵐ[μ] g) : essInf f μ = e
 #align ess_inf_congr_ae essInf_congr_ae
 
 @[simp]
-theorem essSup_const' [μ.ae.NeBot] (c : β) : essSup (fun _ : α => c) μ = c :=
+theorem essSup_const' [NeZero μ] (c : β) : essSup (fun _ : α => c) μ = c :=
   limsup_const _
 #align ess_sup_const' essSup_const'
 
 @[simp]
-theorem essInf_const' [μ.ae.NeBot] (c : β) : essInf (fun _ : α => c) μ = c :=
+theorem essInf_const' [NeZero μ] (c : β) : essInf (fun _ : α => c) μ = c :=
   liminf_const _
 #align ess_inf_const' essInf_const'
 
-theorem essSup_const (c : β) (hμ : μ ≠ 0) : essSup (fun _ : α => c) μ = c := by
-  rw [← ae_neBot] at hμ
-  exact essSup_const' _
+theorem essSup_const (c : β) (hμ : μ ≠ 0) : essSup (fun _ : α => c) μ = c :=
+  have := NeZero.mk hμ; essSup_const' _
 #align ess_sup_const essSup_const
 
-theorem essInf_const (c : β) (hμ : μ ≠ 0) : essInf (fun _ : α => c) μ = c := by
-  rw [← ae_neBot] at hμ
-  exact essInf_const' _
+theorem essInf_const (c : β) (hμ : μ ≠ 0) : essInf (fun _ : α => c) μ = c :=
+  have := NeZero.mk hμ; essInf_const' _
 #align ess_inf_const essInf_const
 
 end ConditionallyCompleteLattice

• 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) 2021 Rémy Degenne. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Rémy Degenne
-
-! This file was ported from Lean 3 source module measure_theory.function.ess_sup
-! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
 import Mathlib.Order.Filter.ENNReal
 
+#align_import measure_theory.function.ess_sup from "leanprover-community/mathlib"@"bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf"
+
 /-!
 # Essential supremum and infimum
 We define the essential supremum and infimum of a function `f : α → β` with respect to a measure

Changes are of the form

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

@@ -278,7 +278,7 @@ theorem essSup_indicator_eq_essSup_restrict [Zero β] {s : Set α} {f : α → 
       (limsSup_le_limsSup_of_le (map_restrict_ae_le_map_indicator_ae hs)
         (by isBoundedDefault) (by isBoundedDefault) )
   refine' limsSup_le_limsSup (by isBoundedDefault) (by isBoundedDefault) (fun c h_restrict_le => _)
-  rw [eventually_map] at h_restrict_le⊢
+  rw [eventually_map] at h_restrict_le ⊢
   rw [ae_restrict_iff' hs] at h_restrict_le
   have hc : 0 ≤ c := by
     rsuffices ⟨x, hx⟩ : ∃ x, 0 ≤ f x ∧ f x ≤ c

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name> Co-authored-by: ChrisHughes24 <chrishughes24@gmail.com>