probability.probability_mass_function.basic ⟷ Mathlib.Probability.ProbabilityMassFunction.Basic

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

@@ -3,7 +3,7 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 -/
-import Topology.Instances.Ennreal
+import Topology.Instances.ENNReal
 import MeasureTheory.Measure.MeasureSpace
 
 #align_import probability.probability_mass_function.basic from "leanprover-community/mathlib"@"a2706b55e8d7f7e9b1f93143f0b88f2e34a11eea"
@@ -262,7 +262,7 @@ theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p
 #align pmf.to_outer_measure_apply_eq_zero_iff PMF.toOuterMeasure_apply_eq_zero_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x «expr ∉ » s) -/
 #print PMF.toOuterMeasure_apply_eq_one_iff /-
 theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support ⊆ s :=
   by

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

@@ -51,12 +51,12 @@ def PMF.{u} (α : Type u) : Type u :=
 
 namespace PMF
 
-#print PMF.instDFunLike /-
-instance instDFunLike : DFunLike (PMF α) α fun p => ℝ≥0∞
+#print PMF.instFunLike /-
+instance instFunLike : DFunLike (PMF α) α fun p => ℝ≥0∞
     where
   coe p a := p.1 a
   coe_injective' p q h := Subtype.eq h
-#align pmf.fun_like PMF.instDFunLike
+#align pmf.fun_like PMF.instFunLike
 -/
 
 #print PMF.ext /-

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

@@ -51,24 +51,24 @@ def PMF.{u} (α : Type u) : Type u :=
 
 namespace PMF
 
-#print PMF.funLike /-
-instance funLike : FunLike (PMF α) α fun p => ℝ≥0∞
+#print PMF.instDFunLike /-
+instance instDFunLike : DFunLike (PMF α) α fun p => ℝ≥0∞
     where
   coe p a := p.1 a
   coe_injective' p q h := Subtype.eq h
-#align pmf.fun_like PMF.funLike
+#align pmf.fun_like PMF.instDFunLike
 -/
 
 #print PMF.ext /-
 @[ext]
 protected theorem ext {p q : PMF α} (h : ∀ x, p x = q x) : p = q :=
-  FunLike.ext p q h
+  DFunLike.ext p q h
 #align pmf.ext PMF.ext
 -/
 
 #print PMF.ext_iff /-
 theorem ext_iff {p q : PMF α} : p = q ↔ ∀ x, p x = q x :=
-  FunLike.ext_iff
+  DFunLike.ext_iff
 #align pmf.ext_iff PMF.ext_iff
 -/
 

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

@@ -41,108 +41,108 @@ variable {α β γ : Type _}
 
 open scoped Classical BigOperators NNReal ENNReal MeasureTheory
 
-#print Pmf /-
+#print PMF /-
 /-- A probability mass function, or discrete probability measures is a function `α → ℝ≥0∞` such
   that the values have (infinite) sum `1`. -/
-def Pmf.{u} (α : Type u) : Type u :=
+def PMF.{u} (α : Type u) : Type u :=
   { f : α → ℝ≥0∞ // HasSum f 1 }
-#align pmf Pmf
+#align pmf PMF
 -/
 
-namespace Pmf
+namespace PMF
 
-#print Pmf.funLike /-
-instance funLike : FunLike (Pmf α) α fun p => ℝ≥0∞
+#print PMF.funLike /-
+instance funLike : FunLike (PMF α) α fun p => ℝ≥0∞
     where
   coe p a := p.1 a
   coe_injective' p q h := Subtype.eq h
-#align pmf.fun_like Pmf.funLike
+#align pmf.fun_like PMF.funLike
 -/
 
-#print Pmf.ext /-
+#print PMF.ext /-
 @[ext]
-protected theorem ext {p q : Pmf α} (h : ∀ x, p x = q x) : p = q :=
+protected theorem ext {p q : PMF α} (h : ∀ x, p x = q x) : p = q :=
   FunLike.ext p q h
-#align pmf.ext Pmf.ext
+#align pmf.ext PMF.ext
 -/
 
-#print Pmf.ext_iff /-
-theorem ext_iff {p q : Pmf α} : p = q ↔ ∀ x, p x = q x :=
+#print PMF.ext_iff /-
+theorem ext_iff {p q : PMF α} : p = q ↔ ∀ x, p x = q x :=
   FunLike.ext_iff
-#align pmf.ext_iff Pmf.ext_iff
+#align pmf.ext_iff PMF.ext_iff
 -/
 
-#print Pmf.hasSum_coe_one /-
-theorem hasSum_coe_one (p : Pmf α) : HasSum p 1 :=
+#print PMF.hasSum_coe_one /-
+theorem hasSum_coe_one (p : PMF α) : HasSum p 1 :=
   p.2
-#align pmf.has_sum_coe_one Pmf.hasSum_coe_one
+#align pmf.has_sum_coe_one PMF.hasSum_coe_one
 -/
 
-#print Pmf.tsum_coe /-
+#print PMF.tsum_coe /-
 @[simp]
-theorem tsum_coe (p : Pmf α) : ∑' a, p a = 1 :=
+theorem tsum_coe (p : PMF α) : ∑' a, p a = 1 :=
   p.hasSum_coe_one.tsum_eq
-#align pmf.tsum_coe Pmf.tsum_coe
+#align pmf.tsum_coe PMF.tsum_coe
 -/
 
-#print Pmf.tsum_coe_ne_top /-
-theorem tsum_coe_ne_top (p : Pmf α) : ∑' a, p a ≠ ∞ :=
+#print PMF.tsum_coe_ne_top /-
+theorem tsum_coe_ne_top (p : PMF α) : ∑' a, p a ≠ ∞ :=
   p.tsum_coe.symm ▸ ENNReal.one_ne_top
-#align pmf.tsum_coe_ne_top Pmf.tsum_coe_ne_top
+#align pmf.tsum_coe_ne_top PMF.tsum_coe_ne_top
 -/
 
-#print Pmf.tsum_coe_indicator_ne_top /-
-theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : ∑' a, s.indicator p a ≠ ∞ :=
+#print PMF.tsum_coe_indicator_ne_top /-
+theorem tsum_coe_indicator_ne_top (p : PMF α) (s : Set α) : ∑' a, s.indicator p a ≠ ∞ :=
   ne_of_lt
     (lt_of_le_of_lt
       (tsum_le_tsum (fun a => Set.indicator_apply_le fun _ => le_rfl) ENNReal.summable
         ENNReal.summable)
       (lt_of_le_of_ne le_top p.tsum_coe_ne_top))
-#align pmf.tsum_coe_indicator_ne_top Pmf.tsum_coe_indicator_ne_top
+#align pmf.tsum_coe_indicator_ne_top PMF.tsum_coe_indicator_ne_top
 -/
 
-#print Pmf.coe_ne_zero /-
+#print PMF.coe_ne_zero /-
 @[simp]
-theorem coe_ne_zero (p : Pmf α) : ⇑p ≠ 0 := fun hp =>
+theorem coe_ne_zero (p : PMF α) : ⇑p ≠ 0 := fun hp =>
   zero_ne_one ((tsum_zero.symm.trans (tsum_congr fun x => symm (congr_fun hp x))).trans p.tsum_coe)
-#align pmf.coe_ne_zero Pmf.coe_ne_zero
+#align pmf.coe_ne_zero PMF.coe_ne_zero
 -/
 
-#print Pmf.support /-
+#print PMF.support /-
 /-- The support of a `pmf` is the set where it is nonzero. -/
-def support (p : Pmf α) : Set α :=
+def support (p : PMF α) : Set α :=
   Function.support p
-#align pmf.support Pmf.support
+#align pmf.support PMF.support
 -/
 
-#print Pmf.mem_support_iff /-
+#print PMF.mem_support_iff /-
 @[simp]
-theorem mem_support_iff (p : Pmf α) (a : α) : a ∈ p.support ↔ p a ≠ 0 :=
+theorem mem_support_iff (p : PMF α) (a : α) : a ∈ p.support ↔ p a ≠ 0 :=
   Iff.rfl
-#align pmf.mem_support_iff Pmf.mem_support_iff
+#align pmf.mem_support_iff PMF.mem_support_iff
 -/
 
-#print Pmf.support_nonempty /-
+#print PMF.support_nonempty /-
 @[simp]
-theorem support_nonempty (p : Pmf α) : p.support.Nonempty :=
+theorem support_nonempty (p : PMF α) : p.support.Nonempty :=
   Function.support_nonempty_iff.2 p.coe_ne_zero
-#align pmf.support_nonempty Pmf.support_nonempty
+#align pmf.support_nonempty PMF.support_nonempty
 -/
 
-#print Pmf.apply_eq_zero_iff /-
-theorem apply_eq_zero_iff (p : Pmf α) (a : α) : p a = 0 ↔ a ∉ p.support := by
+#print PMF.apply_eq_zero_iff /-
+theorem apply_eq_zero_iff (p : PMF α) (a : α) : p a = 0 ↔ a ∉ p.support := by
   rw [mem_support_iff, Classical.not_not]
-#align pmf.apply_eq_zero_iff Pmf.apply_eq_zero_iff
+#align pmf.apply_eq_zero_iff PMF.apply_eq_zero_iff
 -/
 
-#print Pmf.apply_pos_iff /-
-theorem apply_pos_iff (p : Pmf α) (a : α) : 0 < p a ↔ a ∈ p.support :=
+#print PMF.apply_pos_iff /-
+theorem apply_pos_iff (p : PMF α) (a : α) : 0 < p a ↔ a ∈ p.support :=
   pos_iff_ne_zero.trans (p.mem_support_iff a).symm
-#align pmf.apply_pos_iff Pmf.apply_pos_iff
+#align pmf.apply_pos_iff PMF.apply_pos_iff
 -/
 
-#print Pmf.apply_eq_one_iff /-
-theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
+#print PMF.apply_eq_one_iff /-
+theorem apply_eq_one_iff (p : PMF α) (a : α) : p a = 1 ↔ p.support = {a} :=
   by
   refine'
     ⟨fun h =>
@@ -166,49 +166,49 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
       exact symm (tsum_eq_single a fun b hb => if_neg hb)
     _ = ∑' b, (ite (b = a) (p b) 0 + ite (b = a) 0 (p b)) := ennreal.tsum_add.symm
     _ = ∑' b, p b := tsum_congr fun b => by split_ifs <;> simp only [zero_add, add_zero, le_rfl]
-#align pmf.apply_eq_one_iff Pmf.apply_eq_one_iff
+#align pmf.apply_eq_one_iff PMF.apply_eq_one_iff
 -/
 
-#print Pmf.coe_le_one /-
-theorem coe_le_one (p : Pmf α) (a : α) : p a ≤ 1 :=
+#print PMF.coe_le_one /-
+theorem coe_le_one (p : PMF α) (a : α) : p a ≤ 1 :=
   hasSum_le (by intro b; split_ifs <;> simp only [h, zero_le', le_rfl]) (hasSum_ite_eq a (p a))
     (hasSum_coe_one p)
-#align pmf.coe_le_one Pmf.coe_le_one
+#align pmf.coe_le_one PMF.coe_le_one
 -/
 
-#print Pmf.apply_ne_top /-
-theorem apply_ne_top (p : Pmf α) (a : α) : p a ≠ ∞ :=
+#print PMF.apply_ne_top /-
+theorem apply_ne_top (p : PMF α) (a : α) : p a ≠ ∞ :=
   ne_of_lt (lt_of_le_of_lt (p.coe_le_one a) ENNReal.one_lt_top)
-#align pmf.apply_ne_top Pmf.apply_ne_top
+#align pmf.apply_ne_top PMF.apply_ne_top
 -/
 
-#print Pmf.apply_lt_top /-
-theorem apply_lt_top (p : Pmf α) (a : α) : p a < ∞ :=
+#print PMF.apply_lt_top /-
+theorem apply_lt_top (p : PMF α) (a : α) : p a < ∞ :=
   lt_of_le_of_ne le_top (p.apply_ne_top a)
-#align pmf.apply_lt_top Pmf.apply_lt_top
+#align pmf.apply_lt_top PMF.apply_lt_top
 -/
 
 section OuterMeasure
 
 open MeasureTheory MeasureTheory.OuterMeasure
 
-#print Pmf.toOuterMeasure /-
+#print PMF.toOuterMeasure /-
 /-- Construct an `outer_measure` from a `pmf`, by assigning measure to each set `s : set α` equal
   to the sum of `p x` for for each `x ∈ α` -/
-def toOuterMeasure (p : Pmf α) : OuterMeasure α :=
+def toOuterMeasure (p : PMF α) : OuterMeasure α :=
   OuterMeasure.sum fun x : α => p x • dirac x
-#align pmf.to_outer_measure Pmf.toOuterMeasure
+#align pmf.to_outer_measure PMF.toOuterMeasure
 -/
 
-variable (p : Pmf α) (s t : Set α)
+variable (p : PMF α) (s t : Set α)
 
-#print Pmf.toOuterMeasure_apply /-
+#print PMF.toOuterMeasure_apply /-
 theorem toOuterMeasure_apply : p.toOuterMeasure s = ∑' x, s.indicator p x :=
   tsum_congr fun x => smul_dirac_apply (p x) x s
-#align pmf.to_outer_measure_apply Pmf.toOuterMeasure_apply
+#align pmf.to_outer_measure_apply PMF.toOuterMeasure_apply
 -/
 
-#print Pmf.toOuterMeasure_caratheodory /-
+#print PMF.toOuterMeasure_caratheodory /-
 @[simp]
 theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ :=
   by
@@ -216,54 +216,54 @@ theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ :=
   exact
     let ⟨y, hy⟩ := hx
     ((le_of_eq (dirac_caratheodory y).symm).trans (le_smul_caratheodory _ _)).trans (le_of_eq hy)
-#align pmf.to_outer_measure_caratheodory Pmf.toOuterMeasure_caratheodory
+#align pmf.to_outer_measure_caratheodory PMF.toOuterMeasure_caratheodory
 -/
 
-#print Pmf.toOuterMeasure_apply_finset /-
+#print PMF.toOuterMeasure_apply_finset /-
 @[simp]
 theorem toOuterMeasure_apply_finset (s : Finset α) : p.toOuterMeasure s = ∑ x in s, p x :=
   by
   refine' (to_outer_measure_apply p s).trans ((@tsum_eq_sum _ _ _ _ _ _ s _).trans _)
   · exact fun x hx => Set.indicator_of_not_mem hx _
   · exact Finset.sum_congr rfl fun x hx => Set.indicator_of_mem hx _
-#align pmf.to_outer_measure_apply_finset Pmf.toOuterMeasure_apply_finset
+#align pmf.to_outer_measure_apply_finset PMF.toOuterMeasure_apply_finset
 -/
 
-#print Pmf.toOuterMeasure_apply_singleton /-
+#print PMF.toOuterMeasure_apply_singleton /-
 theorem toOuterMeasure_apply_singleton (a : α) : p.toOuterMeasure {a} = p a :=
   by
   refine' (p.to_outer_measure_apply {a}).trans ((tsum_eq_single a fun b hb => _).trans _)
   · exact ite_eq_right_iff.2 fun hb' => False.elim <| hb hb'
   · exact ite_eq_left_iff.2 fun ha' => False.elim <| ha' rfl
-#align pmf.to_outer_measure_apply_singleton Pmf.toOuterMeasure_apply_singleton
+#align pmf.to_outer_measure_apply_singleton PMF.toOuterMeasure_apply_singleton
 -/
 
-#print Pmf.toOuterMeasure_injective /-
-theorem toOuterMeasure_injective : (toOuterMeasure : Pmf α → OuterMeasure α).Injective :=
+#print PMF.toOuterMeasure_injective /-
+theorem toOuterMeasure_injective : (toOuterMeasure : PMF α → OuterMeasure α).Injective :=
   fun p q h =>
-  Pmf.ext fun x =>
+  PMF.ext fun x =>
     (p.toOuterMeasure_apply_singleton x).symm.trans
       ((congr_fun (congr_arg _ h) _).trans <| q.toOuterMeasure_apply_singleton x)
-#align pmf.to_outer_measure_injective Pmf.toOuterMeasure_injective
+#align pmf.to_outer_measure_injective PMF.toOuterMeasure_injective
 -/
 
-#print Pmf.toOuterMeasure_inj /-
+#print PMF.toOuterMeasure_inj /-
 @[simp]
-theorem toOuterMeasure_inj {p q : Pmf α} : p.toOuterMeasure = q.toOuterMeasure ↔ p = q :=
+theorem toOuterMeasure_inj {p q : PMF α} : p.toOuterMeasure = q.toOuterMeasure ↔ p = q :=
   toOuterMeasure_injective.eq_iff
-#align pmf.to_outer_measure_inj Pmf.toOuterMeasure_inj
+#align pmf.to_outer_measure_inj PMF.toOuterMeasure_inj
 -/
 
-#print Pmf.toOuterMeasure_apply_eq_zero_iff /-
+#print PMF.toOuterMeasure_apply_eq_zero_iff /-
 theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p.support s :=
   by
   rw [to_outer_measure_apply, ENNReal.tsum_eq_zero]
   exact function.funext_iff.symm.trans Set.indicator_eq_zero'
-#align pmf.to_outer_measure_apply_eq_zero_iff Pmf.toOuterMeasure_apply_eq_zero_iff
+#align pmf.to_outer_measure_apply_eq_zero_iff PMF.toOuterMeasure_apply_eq_zero_iff
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ∉ » s) -/
-#print Pmf.toOuterMeasure_apply_eq_one_iff /-
+#print PMF.toOuterMeasure_apply_eq_one_iff /-
 theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support ⊆ s :=
   by
   refine' (p.to_outer_measure_apply s).symm ▸ ⟨fun h a hap => _, fun h => _⟩
@@ -279,38 +279,38 @@ theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support 
         (tsum_congr fun a => (Set.indicator_apply s p a).trans (ite_eq_left_iff.2 <| symm ∘ this a))
         p.tsum_coe
     exact fun a ha => (p.apply_eq_zero_iff a).2 <| Set.not_mem_subset h ha
-#align pmf.to_outer_measure_apply_eq_one_iff Pmf.toOuterMeasure_apply_eq_one_iff
+#align pmf.to_outer_measure_apply_eq_one_iff PMF.toOuterMeasure_apply_eq_one_iff
 -/
 
-#print Pmf.toOuterMeasure_apply_inter_support /-
+#print PMF.toOuterMeasure_apply_inter_support /-
 @[simp]
 theorem toOuterMeasure_apply_inter_support :
     p.toOuterMeasure (s ∩ p.support) = p.toOuterMeasure s := by
-  simp only [to_outer_measure_apply, Pmf.support, Set.indicator_inter_support]
-#align pmf.to_outer_measure_apply_inter_support Pmf.toOuterMeasure_apply_inter_support
+  simp only [to_outer_measure_apply, PMF.support, Set.indicator_inter_support]
+#align pmf.to_outer_measure_apply_inter_support PMF.toOuterMeasure_apply_inter_support
 -/
 
-#print Pmf.toOuterMeasure_mono /-
+#print PMF.toOuterMeasure_mono /-
 /-- Slightly stronger than `outer_measure.mono` having an intersection with `p.support` -/
 theorem toOuterMeasure_mono {s t : Set α} (h : s ∩ p.support ⊆ t) :
     p.toOuterMeasure s ≤ p.toOuterMeasure t :=
   le_trans (le_of_eq (toOuterMeasure_apply_inter_support p s).symm) (p.toOuterMeasure.mono h)
-#align pmf.to_outer_measure_mono Pmf.toOuterMeasure_mono
+#align pmf.to_outer_measure_mono PMF.toOuterMeasure_mono
 -/
 
-#print Pmf.toOuterMeasure_apply_eq_of_inter_support_eq /-
+#print PMF.toOuterMeasure_apply_eq_of_inter_support_eq /-
 theorem toOuterMeasure_apply_eq_of_inter_support_eq {s t : Set α}
     (h : s ∩ p.support = t ∩ p.support) : p.toOuterMeasure s = p.toOuterMeasure t :=
   le_antisymm (p.toOuterMeasure_mono (h.symm ▸ Set.inter_subset_left t p.support))
     (p.toOuterMeasure_mono (h ▸ Set.inter_subset_left s p.support))
-#align pmf.to_outer_measure_apply_eq_of_inter_support_eq Pmf.toOuterMeasure_apply_eq_of_inter_support_eq
+#align pmf.to_outer_measure_apply_eq_of_inter_support_eq PMF.toOuterMeasure_apply_eq_of_inter_support_eq
 -/
 
-#print Pmf.toOuterMeasure_apply_fintype /-
+#print PMF.toOuterMeasure_apply_fintype /-
 @[simp]
 theorem toOuterMeasure_apply_fintype [Fintype α] : p.toOuterMeasure s = ∑ x, s.indicator p x :=
   (p.toOuterMeasure_apply s).trans (tsum_eq_sum fun x h => absurd (Finset.mem_univ x) h)
-#align pmf.to_outer_measure_apply_fintype Pmf.toOuterMeasure_apply_fintype
+#align pmf.to_outer_measure_apply_fintype PMF.toOuterMeasure_apply_fintype
 -/
 
 end OuterMeasure
@@ -319,140 +319,140 @@ section Measure
 
 open MeasureTheory
 
-#print Pmf.toMeasure /-
+#print PMF.toMeasure /-
 /-- Since every set is Carathéodory-measurable under `pmf.to_outer_measure`,
   we can further extend this `outer_measure` to a `measure` on `α` -/
-def toMeasure [MeasurableSpace α] (p : Pmf α) : Measure α :=
+def toMeasure [MeasurableSpace α] (p : PMF α) : Measure α :=
   p.toOuterMeasure.toMeasure ((toOuterMeasure_caratheodory p).symm ▸ le_top)
-#align pmf.to_measure Pmf.toMeasure
+#align pmf.to_measure PMF.toMeasure
 -/
 
-variable [MeasurableSpace α] (p : Pmf α) (s t : Set α)
+variable [MeasurableSpace α] (p : PMF α) (s t : Set α)
 
-#print Pmf.toOuterMeasure_apply_le_toMeasure_apply /-
+#print PMF.toOuterMeasure_apply_le_toMeasure_apply /-
 theorem toOuterMeasure_apply_le_toMeasure_apply : p.toOuterMeasure s ≤ p.toMeasure s :=
   le_toMeasure_apply p.toOuterMeasure _ s
-#align pmf.to_outer_measure_apply_le_to_measure_apply Pmf.toOuterMeasure_apply_le_toMeasure_apply
+#align pmf.to_outer_measure_apply_le_to_measure_apply PMF.toOuterMeasure_apply_le_toMeasure_apply
 -/
 
-#print Pmf.toMeasure_apply_eq_toOuterMeasure_apply /-
+#print PMF.toMeasure_apply_eq_toOuterMeasure_apply /-
 theorem toMeasure_apply_eq_toOuterMeasure_apply (hs : MeasurableSet s) :
     p.toMeasure s = p.toOuterMeasure s :=
   toMeasure_apply p.toOuterMeasure _ hs
-#align pmf.to_measure_apply_eq_to_outer_measure_apply Pmf.toMeasure_apply_eq_toOuterMeasure_apply
+#align pmf.to_measure_apply_eq_to_outer_measure_apply PMF.toMeasure_apply_eq_toOuterMeasure_apply
 -/
 
-#print Pmf.toMeasure_apply /-
+#print PMF.toMeasure_apply /-
 theorem toMeasure_apply (hs : MeasurableSet s) : p.toMeasure s = ∑' x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs).trans (p.toOuterMeasure_apply s)
-#align pmf.to_measure_apply Pmf.toMeasure_apply
+#align pmf.to_measure_apply PMF.toMeasure_apply
 -/
 
-#print Pmf.toMeasure_apply_singleton /-
+#print PMF.toMeasure_apply_singleton /-
 theorem toMeasure_apply_singleton (a : α) (h : MeasurableSet ({a} : Set α)) :
     p.toMeasure {a} = p a := by
   simp [to_measure_apply_eq_to_outer_measure_apply _ _ h, to_outer_measure_apply_singleton]
-#align pmf.to_measure_apply_singleton Pmf.toMeasure_apply_singleton
+#align pmf.to_measure_apply_singleton PMF.toMeasure_apply_singleton
 -/
 
-#print Pmf.toMeasure_apply_eq_zero_iff /-
+#print PMF.toMeasure_apply_eq_zero_iff /-
 theorem toMeasure_apply_eq_zero_iff (hs : MeasurableSet s) :
     p.toMeasure s = 0 ↔ Disjoint p.support s := by
   rw [to_measure_apply_eq_to_outer_measure_apply p s hs, to_outer_measure_apply_eq_zero_iff]
-#align pmf.to_measure_apply_eq_zero_iff Pmf.toMeasure_apply_eq_zero_iff
+#align pmf.to_measure_apply_eq_zero_iff PMF.toMeasure_apply_eq_zero_iff
 -/
 
-#print Pmf.toMeasure_apply_eq_one_iff /-
+#print PMF.toMeasure_apply_eq_one_iff /-
 theorem toMeasure_apply_eq_one_iff (hs : MeasurableSet s) : p.toMeasure s = 1 ↔ p.support ⊆ s :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs : p.toMeasure s = p.toOuterMeasure s).symm ▸
     p.toOuterMeasure_apply_eq_one_iff s
-#align pmf.to_measure_apply_eq_one_iff Pmf.toMeasure_apply_eq_one_iff
+#align pmf.to_measure_apply_eq_one_iff PMF.toMeasure_apply_eq_one_iff
 -/
 
-#print Pmf.toMeasure_apply_inter_support /-
+#print PMF.toMeasure_apply_inter_support /-
 @[simp]
 theorem toMeasure_apply_inter_support (hs : MeasurableSet s) (hp : MeasurableSet p.support) :
     p.toMeasure (s ∩ p.support) = p.toMeasure s := by
   simp [p.to_measure_apply_eq_to_outer_measure_apply s hs,
     p.to_measure_apply_eq_to_outer_measure_apply _ (hs.inter hp)]
-#align pmf.to_measure_apply_inter_support Pmf.toMeasure_apply_inter_support
+#align pmf.to_measure_apply_inter_support PMF.toMeasure_apply_inter_support
 -/
 
-#print Pmf.toMeasure_mono /-
+#print PMF.toMeasure_mono /-
 theorem toMeasure_mono {s t : Set α} (hs : MeasurableSet s) (ht : MeasurableSet t)
     (h : s ∩ p.support ⊆ t) : p.toMeasure s ≤ p.toMeasure t := by
   simpa only [p.to_measure_apply_eq_to_outer_measure_apply, hs, ht] using to_outer_measure_mono p h
-#align pmf.to_measure_mono Pmf.toMeasure_mono
+#align pmf.to_measure_mono PMF.toMeasure_mono
 -/
 
-#print Pmf.toMeasure_apply_eq_of_inter_support_eq /-
+#print PMF.toMeasure_apply_eq_of_inter_support_eq /-
 theorem toMeasure_apply_eq_of_inter_support_eq {s t : Set α} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (h : s ∩ p.support = t ∩ p.support) : p.toMeasure s = p.toMeasure t := by
   simpa only [p.to_measure_apply_eq_to_outer_measure_apply, hs, ht] using
     to_outer_measure_apply_eq_of_inter_support_eq p h
-#align pmf.to_measure_apply_eq_of_inter_support_eq Pmf.toMeasure_apply_eq_of_inter_support_eq
+#align pmf.to_measure_apply_eq_of_inter_support_eq PMF.toMeasure_apply_eq_of_inter_support_eq
 -/
 
 section MeasurableSingletonClass
 
 variable [MeasurableSingletonClass α]
 
-#print Pmf.toMeasure_injective /-
-theorem toMeasure_injective : (toMeasure : Pmf α → Measure α).Injective := fun p q h =>
-  Pmf.ext fun x =>
+#print PMF.toMeasure_injective /-
+theorem toMeasure_injective : (toMeasure : PMF α → Measure α).Injective := fun p q h =>
+  PMF.ext fun x =>
     (p.toMeasure_apply_singleton x <| measurableSet_singleton x).symm.trans
       ((congr_fun (congr_arg _ h) _).trans <|
         q.toMeasure_apply_singleton x <| measurableSet_singleton x)
-#align pmf.to_measure_injective Pmf.toMeasure_injective
+#align pmf.to_measure_injective PMF.toMeasure_injective
 -/
 
-#print Pmf.toMeasure_inj /-
+#print PMF.toMeasure_inj /-
 @[simp]
-theorem toMeasure_inj {p q : Pmf α} : p.toMeasure = q.toMeasure ↔ p = q :=
+theorem toMeasure_inj {p q : PMF α} : p.toMeasure = q.toMeasure ↔ p = q :=
   toMeasure_injective.eq_iff
-#align pmf.to_measure_inj Pmf.toMeasure_inj
+#align pmf.to_measure_inj PMF.toMeasure_inj
 -/
 
-#print Pmf.toMeasure_apply_finset /-
+#print PMF.toMeasure_apply_finset /-
 @[simp]
 theorem toMeasure_apply_finset (s : Finset α) : p.toMeasure s = ∑ x in s, p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.MeasurableSet).trans
     (p.toOuterMeasure_apply_finset s)
-#align pmf.to_measure_apply_finset Pmf.toMeasure_apply_finset
+#align pmf.to_measure_apply_finset PMF.toMeasure_apply_finset
 -/
 
-#print Pmf.toMeasure_apply_of_finite /-
+#print PMF.toMeasure_apply_of_finite /-
 theorem toMeasure_apply_of_finite (hs : s.Finite) : p.toMeasure s = ∑' x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs.MeasurableSet).trans (p.toOuterMeasure_apply s)
-#align pmf.to_measure_apply_of_finite Pmf.toMeasure_apply_of_finite
+#align pmf.to_measure_apply_of_finite PMF.toMeasure_apply_of_finite
 -/
 
-#print Pmf.toMeasure_apply_fintype /-
+#print PMF.toMeasure_apply_fintype /-
 @[simp]
 theorem toMeasure_apply_fintype [Fintype α] : p.toMeasure s = ∑ x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.toFinite.MeasurableSet).trans
     (p.toOuterMeasure_apply_fintype s)
-#align pmf.to_measure_apply_fintype Pmf.toMeasure_apply_fintype
+#align pmf.to_measure_apply_fintype PMF.toMeasure_apply_fintype
 -/
 
 end MeasurableSingletonClass
 
 end Measure
 
-end Pmf
+end PMF
 
 namespace MeasureTheory
 
-open Pmf
+open PMF
 
 namespace Measure
 
-#print MeasureTheory.Measure.toPmf /-
+#print MeasureTheory.Measure.toPMF /-
 /-- Given that `α` is a countable, measurable space with all singleton sets measurable,
 we can convert any probability measure into a `pmf`, where the mass of a point
 is the measure of the singleton set under the original measure. -/
-def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
-    [h : IsProbabilityMeasure μ] : Pmf α :=
+def toPMF [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
+    [h : IsProbabilityMeasure μ] : PMF α :=
   ⟨fun x => μ ({x} : Set α),
     ENNReal.summable.hasSum_iff.2
       (trans
@@ -460,66 +460,66 @@ def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ
           (tsum_indicator_apply_singleton μ Set.univ MeasurableSet.univ).symm.trans
             (tsum_congr fun x => congr_fun (Set.indicator_univ _) x))
         h.measure_univ)⟩
-#align measure_theory.measure.to_pmf MeasureTheory.Measure.toPmf
+#align measure_theory.measure.to_pmf MeasureTheory.Measure.toPMF
 -/
 
 variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
   [IsProbabilityMeasure μ]
 
-#print MeasureTheory.Measure.toPmf_apply /-
-theorem toPmf_apply (x : α) : μ.toPmf x = μ {x} :=
+#print MeasureTheory.Measure.toPMF_apply /-
+theorem toPMF_apply (x : α) : μ.toPMF x = μ {x} :=
   rfl
-#align measure_theory.measure.to_pmf_apply MeasureTheory.Measure.toPmf_apply
+#align measure_theory.measure.to_pmf_apply MeasureTheory.Measure.toPMF_apply
 -/
 
-#print MeasureTheory.Measure.toPmf_toMeasure /-
+#print MeasureTheory.Measure.toPMF_toMeasure /-
 @[simp]
-theorem toPmf_toMeasure : μ.toPmf.toMeasure = μ :=
+theorem toPMF_toMeasure : μ.toPMF.toMeasure = μ :=
   Measure.ext fun s hs => by
     simpa only [μ.to_pmf.to_measure_apply s hs, ← μ.tsum_indicator_apply_singleton s hs]
-#align measure_theory.measure.to_pmf_to_measure MeasureTheory.Measure.toPmf_toMeasure
+#align measure_theory.measure.to_pmf_to_measure MeasureTheory.Measure.toPMF_toMeasure
 -/
 
 end Measure
 
 end MeasureTheory
 
-namespace Pmf
+namespace PMF
 
 open MeasureTheory
 
-#print Pmf.toMeasure.isProbabilityMeasure /-
+#print PMF.toMeasure.isProbabilityMeasure /-
 /-- The measure associated to a `pmf` by `to_measure` is a probability measure -/
-instance toMeasure.isProbabilityMeasure [MeasurableSpace α] (p : Pmf α) :
+instance toMeasure.isProbabilityMeasure [MeasurableSpace α] (p : PMF α) :
     IsProbabilityMeasure p.toMeasure :=
   ⟨by
     simpa only [MeasurableSet.univ, to_measure_apply_eq_to_outer_measure_apply, Set.indicator_univ,
       to_outer_measure_apply, ENNReal.coe_eq_one] using tsum_coe p⟩
-#align pmf.to_measure.is_probability_measure Pmf.toMeasure.isProbabilityMeasure
+#align pmf.to_measure.is_probability_measure PMF.toMeasure.isProbabilityMeasure
 -/
 
-variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (p : Pmf α) (μ : Measure α)
+variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (p : PMF α) (μ : Measure α)
   [IsProbabilityMeasure μ]
 
-#print Pmf.toMeasure_toPmf /-
+#print PMF.toMeasure_toPMF /-
 @[simp]
-theorem toMeasure_toPmf : p.toMeasure.toPmf = p :=
-  Pmf.ext fun x => by
+theorem toMeasure_toPMF : p.toMeasure.toPMF = p :=
+  PMF.ext fun x => by
     rw [← p.to_measure_apply_singleton x (measurable_set_singleton x), p.to_measure.to_pmf_apply]
-#align pmf.to_measure_to_pmf Pmf.toMeasure_toPmf
+#align pmf.to_measure_to_pmf PMF.toMeasure_toPMF
 -/
 
-#print Pmf.toMeasure_eq_iff_eq_toPmf /-
-theorem toMeasure_eq_iff_eq_toPmf (μ : Measure α) [IsProbabilityMeasure μ] :
-    p.toMeasure = μ ↔ p = μ.toPmf := by rw [← to_measure_inj, measure.to_pmf_to_measure]
-#align pmf.to_measure_eq_iff_eq_to_pmf Pmf.toMeasure_eq_iff_eq_toPmf
+#print PMF.toMeasure_eq_iff_eq_toPMF /-
+theorem toMeasure_eq_iff_eq_toPMF (μ : Measure α) [IsProbabilityMeasure μ] :
+    p.toMeasure = μ ↔ p = μ.toPMF := by rw [← to_measure_inj, measure.to_pmf_to_measure]
+#align pmf.to_measure_eq_iff_eq_to_pmf PMF.toMeasure_eq_iff_eq_toPMF
 -/
 
-#print Pmf.toPmf_eq_iff_toMeasure_eq /-
-theorem toPmf_eq_iff_toMeasure_eq (μ : Measure α) [IsProbabilityMeasure μ] :
-    μ.toPmf = p ↔ μ = p.toMeasure := by rw [← to_measure_inj, measure.to_pmf_to_measure]
-#align pmf.to_pmf_eq_iff_to_measure_eq Pmf.toPmf_eq_iff_toMeasure_eq
+#print PMF.toPMF_eq_iff_toMeasure_eq /-
+theorem toPMF_eq_iff_toMeasure_eq (μ : Measure α) [IsProbabilityMeasure μ] :
+    μ.toPMF = p ↔ μ = p.toMeasure := by rw [← to_measure_inj, measure.to_pmf_to_measure]
+#align pmf.to_pmf_eq_iff_to_measure_eq PMF.toPMF_eq_iff_toMeasure_eq
 -/
 
-end Pmf
+end PMF
 

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

@@ -3,8 +3,8 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 -/
-import Mathbin.Topology.Instances.Ennreal
-import Mathbin.MeasureTheory.Measure.MeasureSpace
+import Topology.Instances.Ennreal
+import MeasureTheory.Measure.MeasureSpace
 
 #align_import probability.probability_mass_function.basic from "leanprover-community/mathlib"@"a2706b55e8d7f7e9b1f93143f0b88f2e34a11eea"
 
@@ -262,7 +262,7 @@ theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p
 #align pmf.to_outer_measure_apply_eq_zero_iff Pmf.toOuterMeasure_apply_eq_zero_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x «expr ∉ » s) -/
 #print Pmf.toOuterMeasure_apply_eq_one_iff /-
 theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support ⊆ s :=
   by

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

@@ -2,15 +2,12 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
-
-! This file was ported from Lean 3 source module probability.probability_mass_function.basic
-! leanprover-community/mathlib commit a2706b55e8d7f7e9b1f93143f0b88f2e34a11eea
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Instances.Ennreal
 import Mathbin.MeasureTheory.Measure.MeasureSpace
 
+#align_import probability.probability_mass_function.basic from "leanprover-community/mathlib"@"a2706b55e8d7f7e9b1f93143f0b88f2e34a11eea"
+
 /-!
 # Probability mass functions
 
@@ -265,7 +262,7 @@ theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p
 #align pmf.to_outer_measure_apply_eq_zero_iff Pmf.toOuterMeasure_apply_eq_zero_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
 #print Pmf.toOuterMeasure_apply_eq_one_iff /-
 theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support ⊆ s :=
   by

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

@@ -75,19 +75,26 @@ theorem ext_iff {p q : Pmf α} : p = q ↔ ∀ x, p x = q x :=
 #align pmf.ext_iff Pmf.ext_iff
 -/
 
+#print Pmf.hasSum_coe_one /-
 theorem hasSum_coe_one (p : Pmf α) : HasSum p 1 :=
   p.2
 #align pmf.has_sum_coe_one Pmf.hasSum_coe_one
+-/
 
+#print Pmf.tsum_coe /-
 @[simp]
 theorem tsum_coe (p : Pmf α) : ∑' a, p a = 1 :=
   p.hasSum_coe_one.tsum_eq
 #align pmf.tsum_coe Pmf.tsum_coe
+-/
 
+#print Pmf.tsum_coe_ne_top /-
 theorem tsum_coe_ne_top (p : Pmf α) : ∑' a, p a ≠ ∞ :=
   p.tsum_coe.symm ▸ ENNReal.one_ne_top
 #align pmf.tsum_coe_ne_top Pmf.tsum_coe_ne_top
+-/
 
+#print Pmf.tsum_coe_indicator_ne_top /-
 theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : ∑' a, s.indicator p a ≠ ∞ :=
   ne_of_lt
     (lt_of_le_of_lt
@@ -95,11 +102,14 @@ theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : ∑' a, s.indicato
         ENNReal.summable)
       (lt_of_le_of_ne le_top p.tsum_coe_ne_top))
 #align pmf.tsum_coe_indicator_ne_top Pmf.tsum_coe_indicator_ne_top
+-/
 
+#print Pmf.coe_ne_zero /-
 @[simp]
 theorem coe_ne_zero (p : Pmf α) : ⇑p ≠ 0 := fun hp =>
   zero_ne_one ((tsum_zero.symm.trans (tsum_congr fun x => symm (congr_fun hp x))).trans p.tsum_coe)
 #align pmf.coe_ne_zero Pmf.coe_ne_zero
+-/
 
 #print Pmf.support /-
 /-- The support of a `pmf` is the set where it is nonzero. -/
@@ -108,10 +118,12 @@ def support (p : Pmf α) : Set α :=
 #align pmf.support Pmf.support
 -/
 
+#print Pmf.mem_support_iff /-
 @[simp]
 theorem mem_support_iff (p : Pmf α) (a : α) : a ∈ p.support ↔ p a ≠ 0 :=
   Iff.rfl
 #align pmf.mem_support_iff Pmf.mem_support_iff
+-/
 
 #print Pmf.support_nonempty /-
 @[simp]
@@ -120,13 +132,17 @@ theorem support_nonempty (p : Pmf α) : p.support.Nonempty :=
 #align pmf.support_nonempty Pmf.support_nonempty
 -/
 
+#print Pmf.apply_eq_zero_iff /-
 theorem apply_eq_zero_iff (p : Pmf α) (a : α) : p a = 0 ↔ a ∉ p.support := by
   rw [mem_support_iff, Classical.not_not]
 #align pmf.apply_eq_zero_iff Pmf.apply_eq_zero_iff
+-/
 
+#print Pmf.apply_pos_iff /-
 theorem apply_pos_iff (p : Pmf α) (a : α) : 0 < p a ↔ a ∈ p.support :=
   pos_iff_ne_zero.trans (p.mem_support_iff a).symm
 #align pmf.apply_pos_iff Pmf.apply_pos_iff
+-/
 
 #print Pmf.apply_eq_one_iff /-
 theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
@@ -156,18 +172,24 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
 #align pmf.apply_eq_one_iff Pmf.apply_eq_one_iff
 -/
 
+#print Pmf.coe_le_one /-
 theorem coe_le_one (p : Pmf α) (a : α) : p a ≤ 1 :=
   hasSum_le (by intro b; split_ifs <;> simp only [h, zero_le', le_rfl]) (hasSum_ite_eq a (p a))
     (hasSum_coe_one p)
 #align pmf.coe_le_one Pmf.coe_le_one
+-/
 
+#print Pmf.apply_ne_top /-
 theorem apply_ne_top (p : Pmf α) (a : α) : p a ≠ ∞ :=
   ne_of_lt (lt_of_le_of_lt (p.coe_le_one a) ENNReal.one_lt_top)
 #align pmf.apply_ne_top Pmf.apply_ne_top
+-/
 
+#print Pmf.apply_lt_top /-
 theorem apply_lt_top (p : Pmf α) (a : α) : p a < ∞ :=
   lt_of_le_of_ne le_top (p.apply_ne_top a)
 #align pmf.apply_lt_top Pmf.apply_lt_top
+-/
 
 section OuterMeasure
 
@@ -183,10 +205,13 @@ def toOuterMeasure (p : Pmf α) : OuterMeasure α :=
 
 variable (p : Pmf α) (s t : Set α)
 
+#print Pmf.toOuterMeasure_apply /-
 theorem toOuterMeasure_apply : p.toOuterMeasure s = ∑' x, s.indicator p x :=
   tsum_congr fun x => smul_dirac_apply (p x) x s
 #align pmf.to_outer_measure_apply Pmf.toOuterMeasure_apply
+-/
 
+#print Pmf.toOuterMeasure_caratheodory /-
 @[simp]
 theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ :=
   by
@@ -195,7 +220,9 @@ theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ :=
     let ⟨y, hy⟩ := hx
     ((le_of_eq (dirac_caratheodory y).symm).trans (le_smul_caratheodory _ _)).trans (le_of_eq hy)
 #align pmf.to_outer_measure_caratheodory Pmf.toOuterMeasure_caratheodory
+-/
 
+#print Pmf.toOuterMeasure_apply_finset /-
 @[simp]
 theorem toOuterMeasure_apply_finset (s : Finset α) : p.toOuterMeasure s = ∑ x in s, p x :=
   by
@@ -203,6 +230,7 @@ theorem toOuterMeasure_apply_finset (s : Finset α) : p.toOuterMeasure s = ∑ x
   · exact fun x hx => Set.indicator_of_not_mem hx _
   · exact Finset.sum_congr rfl fun x hx => Set.indicator_of_mem hx _
 #align pmf.to_outer_measure_apply_finset Pmf.toOuterMeasure_apply_finset
+-/
 
 #print Pmf.toOuterMeasure_apply_singleton /-
 theorem toOuterMeasure_apply_singleton (a : α) : p.toOuterMeasure {a} = p a :=
@@ -229,11 +257,13 @@ theorem toOuterMeasure_inj {p q : Pmf α} : p.toOuterMeasure = q.toOuterMeasure
 #align pmf.to_outer_measure_inj Pmf.toOuterMeasure_inj
 -/
 
+#print Pmf.toOuterMeasure_apply_eq_zero_iff /-
 theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p.support s :=
   by
   rw [to_outer_measure_apply, ENNReal.tsum_eq_zero]
   exact function.funext_iff.symm.trans Set.indicator_eq_zero'
 #align pmf.to_outer_measure_apply_eq_zero_iff Pmf.toOuterMeasure_apply_eq_zero_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » s) -/
 #print Pmf.toOuterMeasure_apply_eq_one_iff /-
@@ -255,28 +285,36 @@ theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support 
 #align pmf.to_outer_measure_apply_eq_one_iff Pmf.toOuterMeasure_apply_eq_one_iff
 -/
 
+#print Pmf.toOuterMeasure_apply_inter_support /-
 @[simp]
 theorem toOuterMeasure_apply_inter_support :
     p.toOuterMeasure (s ∩ p.support) = p.toOuterMeasure s := by
   simp only [to_outer_measure_apply, Pmf.support, Set.indicator_inter_support]
 #align pmf.to_outer_measure_apply_inter_support Pmf.toOuterMeasure_apply_inter_support
+-/
 
+#print Pmf.toOuterMeasure_mono /-
 /-- Slightly stronger than `outer_measure.mono` having an intersection with `p.support` -/
 theorem toOuterMeasure_mono {s t : Set α} (h : s ∩ p.support ⊆ t) :
     p.toOuterMeasure s ≤ p.toOuterMeasure t :=
   le_trans (le_of_eq (toOuterMeasure_apply_inter_support p s).symm) (p.toOuterMeasure.mono h)
 #align pmf.to_outer_measure_mono Pmf.toOuterMeasure_mono
+-/
 
+#print Pmf.toOuterMeasure_apply_eq_of_inter_support_eq /-
 theorem toOuterMeasure_apply_eq_of_inter_support_eq {s t : Set α}
     (h : s ∩ p.support = t ∩ p.support) : p.toOuterMeasure s = p.toOuterMeasure t :=
   le_antisymm (p.toOuterMeasure_mono (h.symm ▸ Set.inter_subset_left t p.support))
     (p.toOuterMeasure_mono (h ▸ Set.inter_subset_left s p.support))
 #align pmf.to_outer_measure_apply_eq_of_inter_support_eq Pmf.toOuterMeasure_apply_eq_of_inter_support_eq
+-/
 
+#print Pmf.toOuterMeasure_apply_fintype /-
 @[simp]
 theorem toOuterMeasure_apply_fintype [Fintype α] : p.toOuterMeasure s = ∑ x, s.indicator p x :=
   (p.toOuterMeasure_apply s).trans (tsum_eq_sum fun x h => absurd (Finset.mem_univ x) h)
 #align pmf.to_outer_measure_apply_fintype Pmf.toOuterMeasure_apply_fintype
+-/
 
 end OuterMeasure
 
@@ -294,9 +332,11 @@ def toMeasure [MeasurableSpace α] (p : Pmf α) : Measure α :=
 
 variable [MeasurableSpace α] (p : Pmf α) (s t : Set α)
 
+#print Pmf.toOuterMeasure_apply_le_toMeasure_apply /-
 theorem toOuterMeasure_apply_le_toMeasure_apply : p.toOuterMeasure s ≤ p.toMeasure s :=
   le_toMeasure_apply p.toOuterMeasure _ s
 #align pmf.to_outer_measure_apply_le_to_measure_apply Pmf.toOuterMeasure_apply_le_toMeasure_apply
+-/
 
 #print Pmf.toMeasure_apply_eq_toOuterMeasure_apply /-
 theorem toMeasure_apply_eq_toOuterMeasure_apply (hs : MeasurableSet s) :
@@ -305,9 +345,11 @@ theorem toMeasure_apply_eq_toOuterMeasure_apply (hs : MeasurableSet s) :
 #align pmf.to_measure_apply_eq_to_outer_measure_apply Pmf.toMeasure_apply_eq_toOuterMeasure_apply
 -/
 
+#print Pmf.toMeasure_apply /-
 theorem toMeasure_apply (hs : MeasurableSet s) : p.toMeasure s = ∑' x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs).trans (p.toOuterMeasure_apply s)
 #align pmf.to_measure_apply Pmf.toMeasure_apply
+-/
 
 #print Pmf.toMeasure_apply_singleton /-
 theorem toMeasure_apply_singleton (a : α) (h : MeasurableSet ({a} : Set α)) :
@@ -316,10 +358,12 @@ theorem toMeasure_apply_singleton (a : α) (h : MeasurableSet ({a} : Set α)) :
 #align pmf.to_measure_apply_singleton Pmf.toMeasure_apply_singleton
 -/
 
+#print Pmf.toMeasure_apply_eq_zero_iff /-
 theorem toMeasure_apply_eq_zero_iff (hs : MeasurableSet s) :
     p.toMeasure s = 0 ↔ Disjoint p.support s := by
   rw [to_measure_apply_eq_to_outer_measure_apply p s hs, to_outer_measure_apply_eq_zero_iff]
 #align pmf.to_measure_apply_eq_zero_iff Pmf.toMeasure_apply_eq_zero_iff
+-/
 
 #print Pmf.toMeasure_apply_eq_one_iff /-
 theorem toMeasure_apply_eq_one_iff (hs : MeasurableSet s) : p.toMeasure s = 1 ↔ p.support ⊆ s :=
@@ -328,23 +372,29 @@ theorem toMeasure_apply_eq_one_iff (hs : MeasurableSet s) : p.toMeasure s = 1 
 #align pmf.to_measure_apply_eq_one_iff Pmf.toMeasure_apply_eq_one_iff
 -/
 
+#print Pmf.toMeasure_apply_inter_support /-
 @[simp]
 theorem toMeasure_apply_inter_support (hs : MeasurableSet s) (hp : MeasurableSet p.support) :
     p.toMeasure (s ∩ p.support) = p.toMeasure s := by
   simp [p.to_measure_apply_eq_to_outer_measure_apply s hs,
     p.to_measure_apply_eq_to_outer_measure_apply _ (hs.inter hp)]
 #align pmf.to_measure_apply_inter_support Pmf.toMeasure_apply_inter_support
+-/
 
+#print Pmf.toMeasure_mono /-
 theorem toMeasure_mono {s t : Set α} (hs : MeasurableSet s) (ht : MeasurableSet t)
     (h : s ∩ p.support ⊆ t) : p.toMeasure s ≤ p.toMeasure t := by
   simpa only [p.to_measure_apply_eq_to_outer_measure_apply, hs, ht] using to_outer_measure_mono p h
 #align pmf.to_measure_mono Pmf.toMeasure_mono
+-/
 
+#print Pmf.toMeasure_apply_eq_of_inter_support_eq /-
 theorem toMeasure_apply_eq_of_inter_support_eq {s t : Set α} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (h : s ∩ p.support = t ∩ p.support) : p.toMeasure s = p.toMeasure t := by
   simpa only [p.to_measure_apply_eq_to_outer_measure_apply, hs, ht] using
     to_outer_measure_apply_eq_of_inter_support_eq p h
 #align pmf.to_measure_apply_eq_of_inter_support_eq Pmf.toMeasure_apply_eq_of_inter_support_eq
+-/
 
 section MeasurableSingletonClass
 
@@ -366,21 +416,27 @@ theorem toMeasure_inj {p q : Pmf α} : p.toMeasure = q.toMeasure ↔ p = q :=
 #align pmf.to_measure_inj Pmf.toMeasure_inj
 -/
 
+#print Pmf.toMeasure_apply_finset /-
 @[simp]
 theorem toMeasure_apply_finset (s : Finset α) : p.toMeasure s = ∑ x in s, p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.MeasurableSet).trans
     (p.toOuterMeasure_apply_finset s)
 #align pmf.to_measure_apply_finset Pmf.toMeasure_apply_finset
+-/
 
+#print Pmf.toMeasure_apply_of_finite /-
 theorem toMeasure_apply_of_finite (hs : s.Finite) : p.toMeasure s = ∑' x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs.MeasurableSet).trans (p.toOuterMeasure_apply s)
 #align pmf.to_measure_apply_of_finite Pmf.toMeasure_apply_of_finite
+-/
 
+#print Pmf.toMeasure_apply_fintype /-
 @[simp]
 theorem toMeasure_apply_fintype [Fintype α] : p.toMeasure s = ∑ x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.toFinite.MeasurableSet).trans
     (p.toOuterMeasure_apply_fintype s)
 #align pmf.to_measure_apply_fintype Pmf.toMeasure_apply_fintype
+-/
 
 end MeasurableSingletonClass
 

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

@@ -80,15 +80,15 @@ theorem hasSum_coe_one (p : Pmf α) : HasSum p 1 :=
 #align pmf.has_sum_coe_one Pmf.hasSum_coe_one
 
 @[simp]
-theorem tsum_coe (p : Pmf α) : (∑' a, p a) = 1 :=
+theorem tsum_coe (p : Pmf α) : ∑' a, p a = 1 :=
   p.hasSum_coe_one.tsum_eq
 #align pmf.tsum_coe Pmf.tsum_coe
 
-theorem tsum_coe_ne_top (p : Pmf α) : (∑' a, p a) ≠ ∞ :=
+theorem tsum_coe_ne_top (p : Pmf α) : ∑' a, p a ≠ ∞ :=
   p.tsum_coe.symm ▸ ENNReal.one_ne_top
 #align pmf.tsum_coe_ne_top Pmf.tsum_coe_ne_top
 
-theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : (∑' a, s.indicator p a) ≠ ∞ :=
+theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : ∑' a, s.indicator p a ≠ ∞ :=
   ne_of_lt
     (lt_of_le_of_lt
       (tsum_le_tsum (fun a => Set.indicator_apply_le fun _ => le_rfl) ENNReal.summable
@@ -149,9 +149,9 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
     _ < p a + ∑' b, ite (b = a) 0 (p b) :=
       (ENNReal.add_lt_add_of_le_of_lt ENNReal.one_ne_top (le_of_eq h.symm) this)
     _ = ite (a = a) (p a) 0 + ∑' b, ite (b = a) 0 (p b) := by rw [eq_self_iff_true, if_true]
-    _ = (∑' b, ite (b = a) (p b) 0) + ∑' b, ite (b = a) 0 (p b) := by congr;
+    _ = ∑' b, ite (b = a) (p b) 0 + ∑' b, ite (b = a) 0 (p b) := by congr;
       exact symm (tsum_eq_single a fun b hb => if_neg hb)
-    _ = ∑' b, ite (b = a) (p b) 0 + ite (b = a) 0 (p b) := ennreal.tsum_add.symm
+    _ = ∑' b, (ite (b = a) (p b) 0 + ite (b = a) 0 (p b)) := ennreal.tsum_add.symm
     _ = ∑' b, p b := tsum_congr fun b => by split_ifs <;> simp only [zero_add, add_zero, le_rfl]
 #align pmf.apply_eq_one_iff Pmf.apply_eq_one_iff
 -/

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

@@ -153,7 +153,6 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
       exact symm (tsum_eq_single a fun b hb => if_neg hb)
     _ = ∑' b, ite (b = a) (p b) 0 + ite (b = a) 0 (p b) := ennreal.tsum_add.symm
     _ = ∑' b, p b := tsum_congr fun b => by split_ifs <;> simp only [zero_add, add_zero, le_rfl]
-    
 #align pmf.apply_eq_one_iff Pmf.apply_eq_one_iff
 -/
 

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

@@ -236,7 +236,7 @@ theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p
   exact function.funext_iff.symm.trans Set.indicator_eq_zero'
 #align pmf.to_outer_measure_apply_eq_zero_iff Pmf.toOuterMeasure_apply_eq_zero_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x «expr ∉ » s) -/
 #print Pmf.toOuterMeasure_apply_eq_one_iff /-
 theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support ⊆ s :=
   by

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

@@ -400,7 +400,7 @@ namespace Measure
 we can convert any probability measure into a `pmf`, where the mass of a point
 is the measure of the singleton set under the original measure. -/
 def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
-    [h : ProbabilityMeasure μ] : Pmf α :=
+    [h : IsProbabilityMeasure μ] : Pmf α :=
   ⟨fun x => μ ({x} : Set α),
     ENNReal.summable.hasSum_iff.2
       (trans
@@ -412,7 +412,7 @@ def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ
 -/
 
 variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
-  [ProbabilityMeasure μ]
+  [IsProbabilityMeasure μ]
 
 #print MeasureTheory.Measure.toPmf_apply /-
 theorem toPmf_apply (x : α) : μ.toPmf x = μ {x} :=
@@ -436,18 +436,18 @@ namespace Pmf
 
 open MeasureTheory
 
-#print Pmf.toMeasure.probabilityMeasure /-
+#print Pmf.toMeasure.isProbabilityMeasure /-
 /-- The measure associated to a `pmf` by `to_measure` is a probability measure -/
-instance toMeasure.probabilityMeasure [MeasurableSpace α] (p : Pmf α) :
-    ProbabilityMeasure p.toMeasure :=
+instance toMeasure.isProbabilityMeasure [MeasurableSpace α] (p : Pmf α) :
+    IsProbabilityMeasure p.toMeasure :=
   ⟨by
     simpa only [MeasurableSet.univ, to_measure_apply_eq_to_outer_measure_apply, Set.indicator_univ,
       to_outer_measure_apply, ENNReal.coe_eq_one] using tsum_coe p⟩
-#align pmf.to_measure.is_probability_measure Pmf.toMeasure.probabilityMeasure
+#align pmf.to_measure.is_probability_measure Pmf.toMeasure.isProbabilityMeasure
 -/
 
 variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (p : Pmf α) (μ : Measure α)
-  [ProbabilityMeasure μ]
+  [IsProbabilityMeasure μ]
 
 #print Pmf.toMeasure_toPmf /-
 @[simp]
@@ -458,13 +458,13 @@ theorem toMeasure_toPmf : p.toMeasure.toPmf = p :=
 -/
 
 #print Pmf.toMeasure_eq_iff_eq_toPmf /-
-theorem toMeasure_eq_iff_eq_toPmf (μ : Measure α) [ProbabilityMeasure μ] :
+theorem toMeasure_eq_iff_eq_toPmf (μ : Measure α) [IsProbabilityMeasure μ] :
     p.toMeasure = μ ↔ p = μ.toPmf := by rw [← to_measure_inj, measure.to_pmf_to_measure]
 #align pmf.to_measure_eq_iff_eq_to_pmf Pmf.toMeasure_eq_iff_eq_toPmf
 -/
 
 #print Pmf.toPmf_eq_iff_toMeasure_eq /-
-theorem toPmf_eq_iff_toMeasure_eq (μ : Measure α) [ProbabilityMeasure μ] :
+theorem toPmf_eq_iff_toMeasure_eq (μ : Measure α) [IsProbabilityMeasure μ] :
     μ.toPmf = p ↔ μ = p.toMeasure := by rw [← to_measure_inj, measure.to_pmf_to_measure]
 #align pmf.to_pmf_eq_iff_to_measure_eq Pmf.toPmf_eq_iff_toMeasure_eq
 -/

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

@@ -149,7 +149,7 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
     _ < p a + ∑' b, ite (b = a) 0 (p b) :=
       (ENNReal.add_lt_add_of_le_of_lt ENNReal.one_ne_top (le_of_eq h.symm) this)
     _ = ite (a = a) (p a) 0 + ∑' b, ite (b = a) 0 (p b) := by rw [eq_self_iff_true, if_true]
-    _ = (∑' b, ite (b = a) (p b) 0) + ∑' b, ite (b = a) 0 (p b) := by congr ;
+    _ = (∑' b, ite (b = a) (p b) 0) + ∑' b, ite (b = a) 0 (p b) := by congr;
       exact symm (tsum_eq_single a fun b hb => if_neg hb)
     _ = ∑' b, ite (b = a) (p b) 0 + ite (b = a) 0 (p b) := ennreal.tsum_add.symm
     _ = ∑' b, p b := tsum_congr fun b => by split_ifs <;> simp only [zero_add, add_zero, le_rfl]

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

@@ -276,7 +276,7 @@ theorem toOuterMeasure_apply_eq_of_inter_support_eq {s t : Set α}
 
 @[simp]
 theorem toOuterMeasure_apply_fintype [Fintype α] : p.toOuterMeasure s = ∑ x, s.indicator p x :=
-  (p.to_outer_measure_apply s).trans (tsum_eq_sum fun x h => absurd (Finset.mem_univ x) h)
+  (p.toOuterMeasure_apply s).trans (tsum_eq_sum fun x h => absurd (Finset.mem_univ x) h)
 #align pmf.to_outer_measure_apply_fintype Pmf.toOuterMeasure_apply_fintype
 
 end OuterMeasure
@@ -307,7 +307,7 @@ theorem toMeasure_apply_eq_toOuterMeasure_apply (hs : MeasurableSet s) :
 -/
 
 theorem toMeasure_apply (hs : MeasurableSet s) : p.toMeasure s = ∑' x, s.indicator p x :=
-  (p.toMeasure_apply_eq_toOuterMeasure_apply s hs).trans (p.to_outer_measure_apply s)
+  (p.toMeasure_apply_eq_toOuterMeasure_apply s hs).trans (p.toOuterMeasure_apply s)
 #align pmf.to_measure_apply Pmf.toMeasure_apply
 
 #print Pmf.toMeasure_apply_singleton /-
@@ -374,7 +374,7 @@ theorem toMeasure_apply_finset (s : Finset α) : p.toMeasure s = ∑ x in s, p x
 #align pmf.to_measure_apply_finset Pmf.toMeasure_apply_finset
 
 theorem toMeasure_apply_of_finite (hs : s.Finite) : p.toMeasure s = ∑' x, s.indicator p x :=
-  (p.toMeasure_apply_eq_toOuterMeasure_apply s hs.MeasurableSet).trans (p.to_outer_measure_apply s)
+  (p.toMeasure_apply_eq_toOuterMeasure_apply s hs.MeasurableSet).trans (p.toOuterMeasure_apply s)
 #align pmf.to_measure_apply_of_finite Pmf.toMeasure_apply_of_finite
 
 @[simp]

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

@@ -42,7 +42,7 @@ noncomputable section
 
 variable {α β γ : Type _}
 
-open Classical BigOperators NNReal ENNReal MeasureTheory
+open scoped Classical BigOperators NNReal ENNReal MeasureTheory
 
 #print Pmf /-
 /-- A probability mass function, or discrete probability measures is a function `α → ℝ≥0∞` such

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

@@ -75,43 +75,19 @@ theorem ext_iff {p q : Pmf α} : p = q ↔ ∀ x, p x = q x :=
 #align pmf.ext_iff Pmf.ext_iff
 -/
 
-/- warning: pmf.has_sum_coe_one -> Pmf.hasSum_coe_one is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (p : Pmf.{u1} α), HasSum.{0, u1} ENNReal α (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))
-but is expected to have type
-  forall {α : Type.{u1}} (p : Pmf.{u1} α), HasSum.{0, u1} ENNReal α (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))
-Case conversion may be inaccurate. Consider using '#align pmf.has_sum_coe_one Pmf.hasSum_coe_oneₓ'. -/
 theorem hasSum_coe_one (p : Pmf α) : HasSum p 1 :=
   p.2
 #align pmf.has_sum_coe_one Pmf.hasSum_coe_one
 
-/- warning: pmf.tsum_coe -> Pmf.tsum_coe is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (p : Pmf.{u1} α), Eq.{1} ENNReal (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a)) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))
-but is expected to have type
-  forall {α : Type.{u1}} (p : Pmf.{u1} α), Eq.{1} ENNReal (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a)) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))
-Case conversion may be inaccurate. Consider using '#align pmf.tsum_coe Pmf.tsum_coeₓ'. -/
 @[simp]
 theorem tsum_coe (p : Pmf α) : (∑' a, p a) = 1 :=
   p.hasSum_coe_one.tsum_eq
 #align pmf.tsum_coe Pmf.tsum_coe
 
-/- warning: pmf.tsum_coe_ne_top -> Pmf.tsum_coe_ne_top is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (p : Pmf.{u1} α), Ne.{1} ENNReal (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
-but is expected to have type
-  forall {α : Type.{u1}} (p : Pmf.{u1} α), Ne.{1} ENNReal (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
-Case conversion may be inaccurate. Consider using '#align pmf.tsum_coe_ne_top Pmf.tsum_coe_ne_topₓ'. -/
 theorem tsum_coe_ne_top (p : Pmf α) : (∑' a, p a) ≠ ∞ :=
   p.tsum_coe.symm ▸ ENNReal.one_ne_top
 #align pmf.tsum_coe_ne_top Pmf.tsum_coe_ne_top
 
-/- warning: pmf.tsum_coe_indicator_ne_top -> Pmf.tsum_coe_indicator_ne_top is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Set.{u1} α), Ne.{1} ENNReal (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => Set.indicator.{u1, 0} α ENNReal ENNReal.hasZero s (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p) a)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
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-Case conversion may be inaccurate. Consider using '#align pmf.tsum_coe_indicator_ne_top Pmf.tsum_coe_indicator_ne_topₓ'. -/
 theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : (∑' a, s.indicator p a) ≠ ∞ :=
   ne_of_lt
     (lt_of_le_of_lt
@@ -120,12 +96,6 @@ theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : (∑' a, s.indicat
       (lt_of_le_of_ne le_top p.tsum_coe_ne_top))
 #align pmf.tsum_coe_indicator_ne_top Pmf.tsum_coe_indicator_ne_top
 
-/- warning: pmf.coe_ne_zero -> Pmf.coe_ne_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align pmf.coe_ne_zero Pmf.coe_ne_zeroₓ'. -/
 @[simp]
 theorem coe_ne_zero (p : Pmf α) : ⇑p ≠ 0 := fun hp =>
   zero_ne_one ((tsum_zero.symm.trans (tsum_congr fun x => symm (congr_fun hp x))).trans p.tsum_coe)
@@ -138,12 +108,6 @@ def support (p : Pmf α) : Set α :=
 #align pmf.support Pmf.support
 -/
 
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-Case conversion may be inaccurate. Consider using '#align pmf.mem_support_iff Pmf.mem_support_iffₓ'. -/
 @[simp]
 theorem mem_support_iff (p : Pmf α) (a : α) : a ∈ p.support ↔ p a ≠ 0 :=
   Iff.rfl
@@ -156,22 +120,10 @@ theorem support_nonempty (p : Pmf α) : p.support.Nonempty :=
 #align pmf.support_nonempty Pmf.support_nonempty
 -/
 
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-Case conversion may be inaccurate. Consider using '#align pmf.apply_eq_zero_iff Pmf.apply_eq_zero_iffₓ'. -/
 theorem apply_eq_zero_iff (p : Pmf α) (a : α) : p a = 0 ↔ a ∉ p.support := by
   rw [mem_support_iff, Classical.not_not]
 #align pmf.apply_eq_zero_iff Pmf.apply_eq_zero_iff
 
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-Case conversion may be inaccurate. Consider using '#align pmf.apply_pos_iff Pmf.apply_pos_iffₓ'. -/
 theorem apply_pos_iff (p : Pmf α) (a : α) : 0 < p a ↔ a ∈ p.support :=
   pos_iff_ne_zero.trans (p.mem_support_iff a).symm
 #align pmf.apply_pos_iff Pmf.apply_pos_iff
@@ -205,33 +157,15 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
 #align pmf.apply_eq_one_iff Pmf.apply_eq_one_iff
 -/
 
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-Case conversion may be inaccurate. Consider using '#align pmf.coe_le_one Pmf.coe_le_oneₓ'. -/
 theorem coe_le_one (p : Pmf α) (a : α) : p a ≤ 1 :=
   hasSum_le (by intro b; split_ifs <;> simp only [h, zero_le', le_rfl]) (hasSum_ite_eq a (p a))
     (hasSum_coe_one p)
 #align pmf.coe_le_one Pmf.coe_le_one
 
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 theorem apply_ne_top (p : Pmf α) (a : α) : p a ≠ ∞ :=
   ne_of_lt (lt_of_le_of_lt (p.coe_le_one a) ENNReal.one_lt_top)
 #align pmf.apply_ne_top Pmf.apply_ne_top
 
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-Case conversion may be inaccurate. Consider using '#align pmf.apply_lt_top Pmf.apply_lt_topₓ'. -/
 theorem apply_lt_top (p : Pmf α) (a : α) : p a < ∞ :=
   lt_of_le_of_ne le_top (p.apply_ne_top a)
 #align pmf.apply_lt_top Pmf.apply_lt_top
@@ -250,22 +184,10 @@ def toOuterMeasure (p : Pmf α) : OuterMeasure α :=
 
 variable (p : Pmf α) (s t : Set α)
 
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-Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_apply Pmf.toOuterMeasure_applyₓ'. -/
 theorem toOuterMeasure_apply : p.toOuterMeasure s = ∑' x, s.indicator p x :=
   tsum_congr fun x => smul_dirac_apply (p x) x s
 #align pmf.to_outer_measure_apply Pmf.toOuterMeasure_apply
 
-/- warning: pmf.to_outer_measure_caratheodory -> Pmf.toOuterMeasure_caratheodory is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_caratheodory Pmf.toOuterMeasure_caratheodoryₓ'. -/
 @[simp]
 theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ :=
   by
@@ -275,12 +197,6 @@ theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ :=
     ((le_of_eq (dirac_caratheodory y).symm).trans (le_smul_caratheodory _ _)).trans (le_of_eq hy)
 #align pmf.to_outer_measure_caratheodory Pmf.toOuterMeasure_caratheodory
 
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 @[simp]
 theorem toOuterMeasure_apply_finset (s : Finset α) : p.toOuterMeasure s = ∑ x in s, p x :=
   by
@@ -314,12 +230,6 @@ theorem toOuterMeasure_inj {p q : Pmf α} : p.toOuterMeasure = q.toOuterMeasure
 #align pmf.to_outer_measure_inj Pmf.toOuterMeasure_inj
 -/
 
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-Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_apply_eq_zero_iff Pmf.toOuterMeasure_apply_eq_zero_iffₓ'. -/
 theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p.support s :=
   by
   rw [to_outer_measure_apply, ENNReal.tsum_eq_zero]
@@ -346,48 +256,24 @@ theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support 
 #align pmf.to_outer_measure_apply_eq_one_iff Pmf.toOuterMeasure_apply_eq_one_iff
 -/
 
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 @[simp]
 theorem toOuterMeasure_apply_inter_support :
     p.toOuterMeasure (s ∩ p.support) = p.toOuterMeasure s := by
   simp only [to_outer_measure_apply, Pmf.support, Set.indicator_inter_support]
 #align pmf.to_outer_measure_apply_inter_support Pmf.toOuterMeasure_apply_inter_support
 
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 /-- Slightly stronger than `outer_measure.mono` having an intersection with `p.support` -/
 theorem toOuterMeasure_mono {s t : Set α} (h : s ∩ p.support ⊆ t) :
     p.toOuterMeasure s ≤ p.toOuterMeasure t :=
   le_trans (le_of_eq (toOuterMeasure_apply_inter_support p s).symm) (p.toOuterMeasure.mono h)
 #align pmf.to_outer_measure_mono Pmf.toOuterMeasure_mono
 
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 theorem toOuterMeasure_apply_eq_of_inter_support_eq {s t : Set α}
     (h : s ∩ p.support = t ∩ p.support) : p.toOuterMeasure s = p.toOuterMeasure t :=
   le_antisymm (p.toOuterMeasure_mono (h.symm ▸ Set.inter_subset_left t p.support))
     (p.toOuterMeasure_mono (h ▸ Set.inter_subset_left s p.support))
 #align pmf.to_outer_measure_apply_eq_of_inter_support_eq Pmf.toOuterMeasure_apply_eq_of_inter_support_eq
 
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 @[simp]
 theorem toOuterMeasure_apply_fintype [Fintype α] : p.toOuterMeasure s = ∑ x, s.indicator p x :=
   (p.to_outer_measure_apply s).trans (tsum_eq_sum fun x h => absurd (Finset.mem_univ x) h)
@@ -409,12 +295,6 @@ def toMeasure [MeasurableSpace α] (p : Pmf α) : Measure α :=
 
 variable [MeasurableSpace α] (p : Pmf α) (s t : Set α)
 
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 theorem toOuterMeasure_apply_le_toMeasure_apply : p.toOuterMeasure s ≤ p.toMeasure s :=
   le_toMeasure_apply p.toOuterMeasure _ s
 #align pmf.to_outer_measure_apply_le_to_measure_apply Pmf.toOuterMeasure_apply_le_toMeasure_apply
@@ -426,12 +306,6 @@ theorem toMeasure_apply_eq_toOuterMeasure_apply (hs : MeasurableSet s) :
 #align pmf.to_measure_apply_eq_to_outer_measure_apply Pmf.toMeasure_apply_eq_toOuterMeasure_apply
 -/
 
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-Case conversion may be inaccurate. Consider using '#align pmf.to_measure_apply Pmf.toMeasure_applyₓ'. -/
 theorem toMeasure_apply (hs : MeasurableSet s) : p.toMeasure s = ∑' x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs).trans (p.to_outer_measure_apply s)
 #align pmf.to_measure_apply Pmf.toMeasure_apply
@@ -443,12 +317,6 @@ theorem toMeasure_apply_singleton (a : α) (h : MeasurableSet ({a} : Set α)) :
 #align pmf.to_measure_apply_singleton Pmf.toMeasure_apply_singleton
 -/
 
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 theorem toMeasure_apply_eq_zero_iff (hs : MeasurableSet s) :
     p.toMeasure s = 0 ↔ Disjoint p.support s := by
   rw [to_measure_apply_eq_to_outer_measure_apply p s hs, to_outer_measure_apply_eq_zero_iff]
@@ -461,12 +329,6 @@ theorem toMeasure_apply_eq_one_iff (hs : MeasurableSet s) : p.toMeasure s = 1 
 #align pmf.to_measure_apply_eq_one_iff Pmf.toMeasure_apply_eq_one_iff
 -/
 
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 @[simp]
 theorem toMeasure_apply_inter_support (hs : MeasurableSet s) (hp : MeasurableSet p.support) :
     p.toMeasure (s ∩ p.support) = p.toMeasure s := by
@@ -474,23 +336,11 @@ theorem toMeasure_apply_inter_support (hs : MeasurableSet s) (hp : MeasurableSet
     p.to_measure_apply_eq_to_outer_measure_apply _ (hs.inter hp)]
 #align pmf.to_measure_apply_inter_support Pmf.toMeasure_apply_inter_support
 
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 theorem toMeasure_mono {s t : Set α} (hs : MeasurableSet s) (ht : MeasurableSet t)
     (h : s ∩ p.support ⊆ t) : p.toMeasure s ≤ p.toMeasure t := by
   simpa only [p.to_measure_apply_eq_to_outer_measure_apply, hs, ht] using to_outer_measure_mono p h
 #align pmf.to_measure_mono Pmf.toMeasure_mono
 
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 theorem toMeasure_apply_eq_of_inter_support_eq {s t : Set α} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (h : s ∩ p.support = t ∩ p.support) : p.toMeasure s = p.toMeasure t := by
   simpa only [p.to_measure_apply_eq_to_outer_measure_apply, hs, ht] using
@@ -517,34 +367,16 @@ theorem toMeasure_inj {p q : Pmf α} : p.toMeasure = q.toMeasure ↔ p = q :=
 #align pmf.to_measure_inj Pmf.toMeasure_inj
 -/
 
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 @[simp]
 theorem toMeasure_apply_finset (s : Finset α) : p.toMeasure s = ∑ x in s, p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.MeasurableSet).trans
     (p.toOuterMeasure_apply_finset s)
 #align pmf.to_measure_apply_finset Pmf.toMeasure_apply_finset
 
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 theorem toMeasure_apply_of_finite (hs : s.Finite) : p.toMeasure s = ∑' x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs.MeasurableSet).trans (p.to_outer_measure_apply s)
 #align pmf.to_measure_apply_of_finite Pmf.toMeasure_apply_of_finite
 
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 @[simp]
 theorem toMeasure_apply_fintype [Fintype α] : p.toMeasure s = ∑ x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.toFinite.MeasurableSet).trans

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

@@ -197,9 +197,7 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
     _ < p a + ∑' b, ite (b = a) 0 (p b) :=
       (ENNReal.add_lt_add_of_le_of_lt ENNReal.one_ne_top (le_of_eq h.symm) this)
     _ = ite (a = a) (p a) 0 + ∑' b, ite (b = a) 0 (p b) := by rw [eq_self_iff_true, if_true]
-    _ = (∑' b, ite (b = a) (p b) 0) + ∑' b, ite (b = a) 0 (p b) :=
-      by
-      congr
+    _ = (∑' b, ite (b = a) (p b) 0) + ∑' b, ite (b = a) 0 (p b) := by congr ;
       exact symm (tsum_eq_single a fun b hb => if_neg hb)
     _ = ∑' b, ite (b = a) (p b) 0 + ite (b = a) 0 (p b) := ennreal.tsum_add.symm
     _ = ∑' b, p b := tsum_congr fun b => by split_ifs <;> simp only [zero_add, add_zero, le_rfl]
@@ -214,11 +212,8 @@ but is expected to have type
   forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), LE.le.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (Preorder.toLE.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (PartialOrder.toPreorder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (OmegaCompletePartialOrder.toPartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLattice.instOmegaCompletePartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLinearOrder.toCompleteLattice.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCompleteLinearOrderENNReal))))) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CanonicallyOrderedCommSemiring.toOne.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCanonicallyOrderedCommSemiringENNReal)))
 Case conversion may be inaccurate. Consider using '#align pmf.coe_le_one Pmf.coe_le_oneₓ'. -/
 theorem coe_le_one (p : Pmf α) (a : α) : p a ≤ 1 :=
-  hasSum_le
-    (by
-      intro b
-      split_ifs <;> simp only [h, zero_le', le_rfl])
-    (hasSum_ite_eq a (p a)) (hasSum_coe_one p)
+  hasSum_le (by intro b; split_ifs <;> simp only [h, zero_le', le_rfl]) (hasSum_ite_eq a (p a))
+    (hasSum_coe_one p)
 #align pmf.coe_le_one Pmf.coe_le_one
 
 /- warning: pmf.apply_ne_top -> Pmf.apply_ne_top is a dubious translation:

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

@@ -168,7 +168,7 @@ theorem apply_eq_zero_iff (p : Pmf α) (a : α) : p a = 0 ↔ a ∉ p.support :=
 
 /- warning: pmf.apply_pos_iff -> Pmf.apply_pos_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p))
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), Iff (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p))
 but is expected to have type
   forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), Iff (LT.lt.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (Preorder.toLT.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (PartialOrder.toPreorder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (OmegaCompletePartialOrder.toPartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLattice.instOmegaCompletePartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLinearOrder.toCompleteLattice.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero)) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Pmf.support.{u1} α p))
 Case conversion may be inaccurate. Consider using '#align pmf.apply_pos_iff Pmf.apply_pos_iffₓ'. -/
@@ -209,7 +209,7 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
 
 /- warning: pmf.coe_le_one -> Pmf.coe_le_one is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : 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))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))
 but is expected to have type
   forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), LE.le.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (Preorder.toLE.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (PartialOrder.toPreorder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (OmegaCompletePartialOrder.toPartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLattice.instOmegaCompletePartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLinearOrder.toCompleteLattice.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCompleteLinearOrderENNReal))))) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CanonicallyOrderedCommSemiring.toOne.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCanonicallyOrderedCommSemiringENNReal)))
 Case conversion may be inaccurate. Consider using '#align pmf.coe_le_one Pmf.coe_le_oneₓ'. -/
@@ -233,7 +233,7 @@ theorem apply_ne_top (p : Pmf α) (a : α) : p a ≠ ∞ :=
 
 /- warning: pmf.apply_lt_top -> Pmf.apply_lt_top is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
 but is expected to have type
   forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), LT.lt.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (Preorder.toLT.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (PartialOrder.toPreorder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (OmegaCompletePartialOrder.toPartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLattice.instOmegaCompletePartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLinearOrder.toCompleteLattice.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCompleteLinearOrderENNReal))))) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
 Case conversion may be inaccurate. Consider using '#align pmf.apply_lt_top Pmf.apply_lt_topₓ'. -/
@@ -365,7 +365,7 @@ theorem toOuterMeasure_apply_inter_support :
 
 /- warning: pmf.to_outer_measure_mono -> Pmf.toOuterMeasure_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Pmf.support.{u1} α p)) t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) s) (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) t))
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Pmf.support.{u1} α p)) t) -> (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))))) (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) s) (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) t))
 but is expected to have type
   forall {α : Type.{u1}} (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Pmf.support.{u1} α p)) t) -> (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))))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) s) (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) t))
 Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_mono Pmf.toOuterMeasure_monoₓ'. -/
@@ -416,7 +416,7 @@ variable [MeasurableSpace α] (p : Pmf α) (s t : Set α)
 
 /- warning: pmf.to_outer_measure_apply_le_to_measure_apply -> Pmf.toOuterMeasure_apply_le_toMeasure_apply is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) s) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s)
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} 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))))) (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) s) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} 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))))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) s) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) s)
 Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_apply_le_to_measure_apply Pmf.toOuterMeasure_apply_le_toMeasure_applyₓ'. -/
@@ -481,7 +481,7 @@ theorem toMeasure_apply_inter_support (hs : MeasurableSet s) (hp : MeasurableSet
 
 /- warning: pmf.to_measure_mono -> Pmf.toMeasure_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (MeasurableSet.{u1} α _inst_1 s) -> (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Pmf.support.{u1} α p)) t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) t))
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (MeasurableSet.{u1} α _inst_1 s) -> (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Pmf.support.{u1} α p)) t) -> (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))))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (MeasurableSet.{u1} α _inst_1 s) -> (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Pmf.support.{u1} α p)) t) -> (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))))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) s) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) t))
 Case conversion may be inaccurate. Consider using '#align pmf.to_measure_mono Pmf.toMeasure_monoₓ'. -/

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

@@ -274,7 +274,7 @@ Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_c
 @[simp]
 theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ :=
   by
-  refine' eq_top_iff.2 <| le_trans (le_infₛ fun x hx => _) (le_sum_caratheodory _)
+  refine' eq_top_iff.2 <| le_trans (le_sInf fun x hx => _) (le_sum_caratheodory _)
   exact
     let ⟨y, hy⟩ := hx
     ((le_of_eq (dirac_caratheodory y).symm).trans (le_smul_caratheodory _ _)).trans (le_of_eq hy)

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 
 ! This file was ported from Lean 3 source module probability.probability_mass_function.basic
-! leanprover-community/mathlib commit 4ac69b290818724c159de091daa3acd31da0ee6d
+! leanprover-community/mathlib commit a2706b55e8d7f7e9b1f93143f0b88f2e34a11eea
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.MeasureTheory.Measure.MeasureSpace
 /-!
 # Probability mass functions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file is about probability mass functions or discrete probability measures:
 a function `α → ℝ≥0∞` such that the values have (infinite) sum `1`.
 

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

@@ -41,42 +41,74 @@ variable {α β γ : Type _}
 
 open Classical BigOperators NNReal ENNReal MeasureTheory
 
+#print Pmf /-
 /-- A probability mass function, or discrete probability measures is a function `α → ℝ≥0∞` such
   that the values have (infinite) sum `1`. -/
 def Pmf.{u} (α : Type u) : Type u :=
   { f : α → ℝ≥0∞ // HasSum f 1 }
 #align pmf Pmf
+-/
 
 namespace Pmf
 
+#print Pmf.funLike /-
 instance funLike : FunLike (Pmf α) α fun p => ℝ≥0∞
     where
   coe p a := p.1 a
   coe_injective' p q h := Subtype.eq h
 #align pmf.fun_like Pmf.funLike
+-/
 
+#print Pmf.ext /-
 @[ext]
 protected theorem ext {p q : Pmf α} (h : ∀ x, p x = q x) : p = q :=
   FunLike.ext p q h
 #align pmf.ext Pmf.ext
+-/
 
+#print Pmf.ext_iff /-
 theorem ext_iff {p q : Pmf α} : p = q ↔ ∀ x, p x = q x :=
   FunLike.ext_iff
 #align pmf.ext_iff Pmf.ext_iff
+-/
 
+/- warning: pmf.has_sum_coe_one -> Pmf.hasSum_coe_one is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α), HasSum.{0, u1} ENNReal α (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α), HasSum.{0, u1} ENNReal α (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))
+Case conversion may be inaccurate. Consider using '#align pmf.has_sum_coe_one Pmf.hasSum_coe_oneₓ'. -/
 theorem hasSum_coe_one (p : Pmf α) : HasSum p 1 :=
   p.2
 #align pmf.has_sum_coe_one Pmf.hasSum_coe_one
 
+/- warning: pmf.tsum_coe -> Pmf.tsum_coe is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α), Eq.{1} ENNReal (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a)) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α), Eq.{1} ENNReal (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a)) (OfNat.ofNat.{0} ENNReal 1 (One.toOfNat1.{0} ENNReal (CanonicallyOrderedCommSemiring.toOne.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))
+Case conversion may be inaccurate. Consider using '#align pmf.tsum_coe Pmf.tsum_coeₓ'. -/
 @[simp]
 theorem tsum_coe (p : Pmf α) : (∑' a, p a) = 1 :=
   p.hasSum_coe_one.tsum_eq
 #align pmf.tsum_coe Pmf.tsum_coe
 
+/- warning: pmf.tsum_coe_ne_top -> Pmf.tsum_coe_ne_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α), Ne.{1} ENNReal (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α), Ne.{1} ENNReal (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
+Case conversion may be inaccurate. Consider using '#align pmf.tsum_coe_ne_top Pmf.tsum_coe_ne_topₓ'. -/
 theorem tsum_coe_ne_top (p : Pmf α) : (∑' a, p a) ≠ ∞ :=
   p.tsum_coe.symm ▸ ENNReal.one_ne_top
 #align pmf.tsum_coe_ne_top Pmf.tsum_coe_ne_top
 
+/- warning: pmf.tsum_coe_indicator_ne_top -> Pmf.tsum_coe_indicator_ne_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Set.{u1} α), Ne.{1} ENNReal (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (a : α) => Set.indicator.{u1, 0} α ENNReal ENNReal.hasZero s (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p) a)) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Set.{u1} α), Ne.{1} ENNReal (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (a : α) => Set.indicator.{u1, 0} α ENNReal instENNRealZero s (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p) a)) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
+Case conversion may be inaccurate. Consider using '#align pmf.tsum_coe_indicator_ne_top Pmf.tsum_coe_indicator_ne_topₓ'. -/
 theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : (∑' a, s.indicator p a) ≠ ∞ :=
   ne_of_lt
     (lt_of_le_of_lt
@@ -85,34 +117,63 @@ theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : (∑' a, s.indicat
       (lt_of_le_of_ne le_top p.tsum_coe_ne_top))
 #align pmf.tsum_coe_indicator_ne_top Pmf.tsum_coe_indicator_ne_top
 
+/- warning: pmf.coe_ne_zero -> Pmf.coe_ne_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α), Ne.{succ u1} (α -> ENNReal) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p) (OfNat.ofNat.{u1} (α -> ENNReal) 0 (OfNat.mk.{u1} (α -> ENNReal) 0 (Zero.zero.{u1} (α -> ENNReal) (Pi.instZero.{u1, 0} α (fun (a : α) => ENNReal) (fun (i : α) => ENNReal.hasZero)))))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α), Ne.{succ u1} (forall (a : α), (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p) (OfNat.ofNat.{u1} (forall (a : α), (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{u1} (forall (a : α), (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (Pi.instZero.{u1, 0} α (fun (a : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (fun (i : α) => instENNRealZero))))
+Case conversion may be inaccurate. Consider using '#align pmf.coe_ne_zero Pmf.coe_ne_zeroₓ'. -/
 @[simp]
 theorem coe_ne_zero (p : Pmf α) : ⇑p ≠ 0 := fun hp =>
   zero_ne_one ((tsum_zero.symm.trans (tsum_congr fun x => symm (congr_fun hp x))).trans p.tsum_coe)
 #align pmf.coe_ne_zero Pmf.coe_ne_zero
 
+#print Pmf.support /-
 /-- The support of a `pmf` is the set where it is nonzero. -/
 def support (p : Pmf α) : Set α :=
   Function.support p
 #align pmf.support Pmf.support
+-/
 
+/- warning: pmf.mem_support_iff -> Pmf.mem_support_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)) (Ne.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p 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.{u1}} (p : Pmf.{u1} α) (a : α), Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Pmf.support.{u1} α p)) (Ne.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align pmf.mem_support_iff Pmf.mem_support_iffₓ'. -/
 @[simp]
 theorem mem_support_iff (p : Pmf α) (a : α) : a ∈ p.support ↔ p a ≠ 0 :=
   Iff.rfl
 #align pmf.mem_support_iff Pmf.mem_support_iff
 
+#print Pmf.support_nonempty /-
 @[simp]
 theorem support_nonempty (p : Pmf α) : p.support.Nonempty :=
   Function.support_nonempty_iff.2 p.coe_ne_zero
 #align pmf.support_nonempty Pmf.support_nonempty
+-/
 
+/- warning: pmf.apply_eq_zero_iff -> Pmf.apply_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), Iff (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Not (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p)))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), Iff (Eq.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero))) (Not (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Pmf.support.{u1} α p)))
+Case conversion may be inaccurate. Consider using '#align pmf.apply_eq_zero_iff Pmf.apply_eq_zero_iffₓ'. -/
 theorem apply_eq_zero_iff (p : Pmf α) (a : α) : p a = 0 ↔ a ∉ p.support := by
   rw [mem_support_iff, Classical.not_not]
 #align pmf.apply_eq_zero_iff Pmf.apply_eq_zero_iff
 
+/- warning: pmf.apply_pos_iff -> Pmf.apply_pos_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a)) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a (Pmf.support.{u1} α p))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), Iff (LT.lt.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (Preorder.toLT.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (PartialOrder.toPreorder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (OmegaCompletePartialOrder.toPartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLattice.instOmegaCompletePartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLinearOrder.toCompleteLattice.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 0 (Zero.toOfNat0.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) instENNRealZero)) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a)) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a (Pmf.support.{u1} α p))
+Case conversion may be inaccurate. Consider using '#align pmf.apply_pos_iff Pmf.apply_pos_iffₓ'. -/
 theorem apply_pos_iff (p : Pmf α) (a : α) : 0 < p a ↔ a ∈ p.support :=
   pos_iff_ne_zero.trans (p.mem_support_iff a).symm
 #align pmf.apply_pos_iff Pmf.apply_pos_iff
 
+#print Pmf.apply_eq_one_iff /-
 theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
   by
   refine'
@@ -141,7 +202,14 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
     _ = ∑' b, p b := tsum_congr fun b => by split_ifs <;> simp only [zero_add, add_zero, le_rfl]
     
 #align pmf.apply_eq_one_iff Pmf.apply_eq_one_iff
+-/
 
+/- warning: pmf.coe_le_one -> Pmf.coe_le_one is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (OfNat.ofNat.{0} ENNReal 1 (OfNat.mk.{0} ENNReal 1 (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), LE.le.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (Preorder.toLE.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (PartialOrder.toPreorder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (OmegaCompletePartialOrder.toPartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLattice.instOmegaCompletePartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLinearOrder.toCompleteLattice.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCompleteLinearOrderENNReal))))) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (OfNat.ofNat.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) 1 (One.toOfNat1.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CanonicallyOrderedCommSemiring.toOne.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCanonicallyOrderedCommSemiringENNReal)))
+Case conversion may be inaccurate. Consider using '#align pmf.coe_le_one Pmf.coe_le_oneₓ'. -/
 theorem coe_le_one (p : Pmf α) (a : α) : p a ≤ 1 :=
   hasSum_le
     (by
@@ -150,10 +218,22 @@ theorem coe_le_one (p : Pmf α) (a : α) : p a ≤ 1 :=
     (hasSum_ite_eq a (p a)) (hasSum_coe_one p)
 #align pmf.coe_le_one Pmf.coe_le_one
 
+/- warning: pmf.apply_ne_top -> Pmf.apply_ne_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), Ne.{1} ENNReal (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), Ne.{1} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
+Case conversion may be inaccurate. Consider using '#align pmf.apply_ne_top Pmf.apply_ne_topₓ'. -/
 theorem apply_ne_top (p : Pmf α) (a : α) : p a ≠ ∞ :=
   ne_of_lt (lt_of_le_of_lt (p.coe_le_one a) ENNReal.one_lt_top)
 #align pmf.apply_ne_top Pmf.apply_ne_top
 
+/- warning: pmf.apply_lt_top -> Pmf.apply_lt_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p a) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (a : α), LT.lt.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (Preorder.toLT.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (PartialOrder.toPreorder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (OmegaCompletePartialOrder.toPartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLattice.instOmegaCompletePartialOrder.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) (CompleteLinearOrder.toCompleteLattice.{0} ((fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) a) ENNReal.instCompleteLinearOrderENNReal))))) (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p a) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))
+Case conversion may be inaccurate. Consider using '#align pmf.apply_lt_top Pmf.apply_lt_topₓ'. -/
 theorem apply_lt_top (p : Pmf α) (a : α) : p a < ∞ :=
   lt_of_le_of_ne le_top (p.apply_ne_top a)
 #align pmf.apply_lt_top Pmf.apply_lt_top
@@ -162,18 +242,32 @@ section OuterMeasure
 
 open MeasureTheory MeasureTheory.OuterMeasure
 
+#print Pmf.toOuterMeasure /-
 /-- Construct an `outer_measure` from a `pmf`, by assigning measure to each set `s : set α` equal
   to the sum of `p x` for for each `x ∈ α` -/
 def toOuterMeasure (p : Pmf α) : OuterMeasure α :=
   OuterMeasure.sum fun x : α => p x • dirac x
 #align pmf.to_outer_measure Pmf.toOuterMeasure
+-/
 
 variable (p : Pmf α) (s t : Set α)
 
+/- warning: pmf.to_outer_measure_apply -> Pmf.toOuterMeasure_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Set.{u1} α), Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) s) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (x : α) => Set.indicator.{u1, 0} α ENNReal ENNReal.hasZero s (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p) x))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Set.{u1} α), Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) s) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (x : α) => Set.indicator.{u1, 0} α ENNReal instENNRealZero s (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p) x))
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_apply Pmf.toOuterMeasure_applyₓ'. -/
 theorem toOuterMeasure_apply : p.toOuterMeasure s = ∑' x, s.indicator p x :=
   tsum_congr fun x => smul_dirac_apply (p x) x s
 #align pmf.to_outer_measure_apply Pmf.toOuterMeasure_apply
 
+/- warning: pmf.to_outer_measure_caratheodory -> Pmf.toOuterMeasure_caratheodory is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α), Eq.{succ u1} (MeasurableSpace.{u1} α) (MeasureTheory.OuterMeasure.caratheodory.{u1} α (Pmf.toOuterMeasure.{u1} α p)) (Top.top.{u1} (MeasurableSpace.{u1} α) (CompleteLattice.toHasTop.{u1} (MeasurableSpace.{u1} α) (MeasurableSpace.completeLattice.{u1} α)))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α), Eq.{succ u1} (MeasurableSpace.{u1} α) (MeasureTheory.OuterMeasure.caratheodory.{u1} α (Pmf.toOuterMeasure.{u1} α p)) (Top.top.{u1} (MeasurableSpace.{u1} α) (CompleteLattice.toTop.{u1} (MeasurableSpace.{u1} α) (MeasurableSpace.instCompleteLatticeMeasurableSpace.{u1} α)))
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_caratheodory Pmf.toOuterMeasure_caratheodoryₓ'. -/
 @[simp]
 theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ :=
   by
@@ -183,6 +277,12 @@ theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ :=
     ((le_of_eq (dirac_caratheodory y).symm).trans (le_smul_caratheodory _ _)).trans (le_of_eq hy)
 #align pmf.to_outer_measure_caratheodory Pmf.toOuterMeasure_caratheodory
 
+/- warning: pmf.to_outer_measure_apply_finset -> Pmf.toOuterMeasure_apply_finset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Finset.{u1} α), Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (Finset.sum.{0, u1} ENNReal α (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) s (fun (x : α) => coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p x))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Finset.{u1} α), Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) (Finset.toSet.{u1} α s)) (Finset.sum.{0, u1} ENNReal α (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (x : α) => FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p x))
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_apply_finset Pmf.toOuterMeasure_apply_finsetₓ'. -/
 @[simp]
 theorem toOuterMeasure_apply_finset (s : Finset α) : p.toOuterMeasure s = ∑ x in s, p x :=
   by
@@ -191,25 +291,37 @@ theorem toOuterMeasure_apply_finset (s : Finset α) : p.toOuterMeasure s = ∑ x
   · exact Finset.sum_congr rfl fun x hx => Set.indicator_of_mem hx _
 #align pmf.to_outer_measure_apply_finset Pmf.toOuterMeasure_apply_finset
 
+#print Pmf.toOuterMeasure_apply_singleton /-
 theorem toOuterMeasure_apply_singleton (a : α) : p.toOuterMeasure {a} = p a :=
   by
   refine' (p.to_outer_measure_apply {a}).trans ((tsum_eq_single a fun b hb => _).trans _)
   · exact ite_eq_right_iff.2 fun hb' => False.elim <| hb hb'
   · exact ite_eq_left_iff.2 fun ha' => False.elim <| ha' rfl
 #align pmf.to_outer_measure_apply_singleton Pmf.toOuterMeasure_apply_singleton
+-/
 
+#print Pmf.toOuterMeasure_injective /-
 theorem toOuterMeasure_injective : (toOuterMeasure : Pmf α → OuterMeasure α).Injective :=
   fun p q h =>
   Pmf.ext fun x =>
     (p.toOuterMeasure_apply_singleton x).symm.trans
       ((congr_fun (congr_arg _ h) _).trans <| q.toOuterMeasure_apply_singleton x)
 #align pmf.to_outer_measure_injective Pmf.toOuterMeasure_injective
+-/
 
+#print Pmf.toOuterMeasure_inj /-
 @[simp]
 theorem toOuterMeasure_inj {p q : Pmf α} : p.toOuterMeasure = q.toOuterMeasure ↔ p = q :=
   toOuterMeasure_injective.eq_iff
 #align pmf.to_outer_measure_inj Pmf.toOuterMeasure_inj
+-/
 
+/- warning: pmf.to_outer_measure_apply_eq_zero_iff -> Pmf.toOuterMeasure_apply_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Set.{u1} α), Iff (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) (Pmf.support.{u1} α p) s)
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Set.{u1} α), Iff (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Disjoint.{u1} (Set.{u1} α) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (Pmf.support.{u1} α p) s)
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_apply_eq_zero_iff Pmf.toOuterMeasure_apply_eq_zero_iffₓ'. -/
 theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p.support s :=
   by
   rw [to_outer_measure_apply, ENNReal.tsum_eq_zero]
@@ -217,6 +329,7 @@ theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p
 #align pmf.to_outer_measure_apply_eq_zero_iff Pmf.toOuterMeasure_apply_eq_zero_iff
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
+#print Pmf.toOuterMeasure_apply_eq_one_iff /-
 theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support ⊆ s :=
   by
   refine' (p.to_outer_measure_apply s).symm ▸ ⟨fun h a hap => _, fun h => _⟩
@@ -233,25 +346,50 @@ theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support 
         p.tsum_coe
     exact fun a ha => (p.apply_eq_zero_iff a).2 <| Set.not_mem_subset h ha
 #align pmf.to_outer_measure_apply_eq_one_iff Pmf.toOuterMeasure_apply_eq_one_iff
+-/
 
+/- warning: pmf.to_outer_measure_apply_inter_support -> Pmf.toOuterMeasure_apply_inter_support is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Set.{u1} α), Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Pmf.support.{u1} α p))) (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) s)
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Set.{u1} α), Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Pmf.support.{u1} α p))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) s)
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_apply_inter_support Pmf.toOuterMeasure_apply_inter_supportₓ'. -/
 @[simp]
 theorem toOuterMeasure_apply_inter_support :
     p.toOuterMeasure (s ∩ p.support) = p.toOuterMeasure s := by
   simp only [to_outer_measure_apply, Pmf.support, Set.indicator_inter_support]
 #align pmf.to_outer_measure_apply_inter_support Pmf.toOuterMeasure_apply_inter_support
 
+/- warning: pmf.to_outer_measure_mono -> Pmf.toOuterMeasure_mono is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Pmf.support.{u1} α p)) t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) s) (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) t))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Pmf.support.{u1} α p)) t) -> (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))))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) s) (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) t))
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_mono Pmf.toOuterMeasure_monoₓ'. -/
 /-- Slightly stronger than `outer_measure.mono` having an intersection with `p.support` -/
 theorem toOuterMeasure_mono {s t : Set α} (h : s ∩ p.support ⊆ t) :
     p.toOuterMeasure s ≤ p.toOuterMeasure t :=
   le_trans (le_of_eq (toOuterMeasure_apply_inter_support p s).symm) (p.toOuterMeasure.mono h)
 #align pmf.to_outer_measure_mono Pmf.toOuterMeasure_mono
 
+/- warning: pmf.to_outer_measure_apply_eq_of_inter_support_eq -> Pmf.toOuterMeasure_apply_eq_of_inter_support_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Pmf.support.{u1} α p)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) t (Pmf.support.{u1} α p))) -> (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) s) (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) t))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Pmf.support.{u1} α p)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) t (Pmf.support.{u1} α p))) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) s) (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) t))
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_apply_eq_of_inter_support_eq Pmf.toOuterMeasure_apply_eq_of_inter_support_eqₓ'. -/
 theorem toOuterMeasure_apply_eq_of_inter_support_eq {s t : Set α}
     (h : s ∩ p.support = t ∩ p.support) : p.toOuterMeasure s = p.toOuterMeasure t :=
   le_antisymm (p.toOuterMeasure_mono (h.symm ▸ Set.inter_subset_left t p.support))
     (p.toOuterMeasure_mono (h ▸ Set.inter_subset_left s p.support))
 #align pmf.to_outer_measure_apply_eq_of_inter_support_eq Pmf.toOuterMeasure_apply_eq_of_inter_support_eq
 
+/- warning: pmf.to_outer_measure_apply_fintype -> Pmf.toOuterMeasure_apply_fintype is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Set.{u1} α) [_inst_1 : Fintype.{u1} α], Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) s) (Finset.sum.{0, u1} ENNReal α (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.univ.{u1} α _inst_1) (fun (x : α) => Set.indicator.{u1, 0} α ENNReal ENNReal.hasZero s (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p) x))
+but is expected to have type
+  forall {α : Type.{u1}} (p : Pmf.{u1} α) (s : Set.{u1} α) [_inst_1 : Fintype.{u1} α], Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) s) (Finset.sum.{0, u1} ENNReal α (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) (Finset.univ.{u1} α _inst_1) (fun (x : α) => Set.indicator.{u1, 0} α ENNReal instENNRealZero s (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p) x))
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_apply_fintype Pmf.toOuterMeasure_apply_fintypeₓ'. -/
 @[simp]
 theorem toOuterMeasure_apply_fintype [Fintype α] : p.toOuterMeasure s = ∑ x, s.indicator p x :=
   (p.to_outer_measure_apply s).trans (tsum_eq_sum fun x h => absurd (Finset.mem_univ x) h)
@@ -263,42 +401,74 @@ section Measure
 
 open MeasureTheory
 
+#print Pmf.toMeasure /-
 /-- Since every set is Carathéodory-measurable under `pmf.to_outer_measure`,
   we can further extend this `outer_measure` to a `measure` on `α` -/
 def toMeasure [MeasurableSpace α] (p : Pmf α) : Measure α :=
   p.toOuterMeasure.toMeasure ((toOuterMeasure_caratheodory p).symm ▸ le_top)
 #align pmf.to_measure Pmf.toMeasure
+-/
 
 variable [MeasurableSpace α] (p : Pmf α) (s t : Set α)
 
+/- warning: pmf.to_outer_measure_apply_le_to_measure_apply -> Pmf.toOuterMeasure_apply_le_toMeasure_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (MeasureTheory.OuterMeasure.{u1} α) (fun (_x : MeasureTheory.OuterMeasure.{u1} α) => (Set.{u1} α) -> ENNReal) (MeasureTheory.OuterMeasure.instCoeFun.{u1} α) (Pmf.toOuterMeasure.{u1} α p) s) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} 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))))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (Pmf.toOuterMeasure.{u1} α p) s) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) s)
+Case conversion may be inaccurate. Consider using '#align pmf.to_outer_measure_apply_le_to_measure_apply Pmf.toOuterMeasure_apply_le_toMeasure_applyₓ'. -/
 theorem toOuterMeasure_apply_le_toMeasure_apply : p.toOuterMeasure s ≤ p.toMeasure s :=
   le_toMeasure_apply p.toOuterMeasure _ s
 #align pmf.to_outer_measure_apply_le_to_measure_apply Pmf.toOuterMeasure_apply_le_toMeasure_apply
 
+#print Pmf.toMeasure_apply_eq_toOuterMeasure_apply /-
 theorem toMeasure_apply_eq_toOuterMeasure_apply (hs : MeasurableSet s) :
     p.toMeasure s = p.toOuterMeasure s :=
   toMeasure_apply p.toOuterMeasure _ hs
 #align pmf.to_measure_apply_eq_to_outer_measure_apply Pmf.toMeasure_apply_eq_toOuterMeasure_apply
+-/
 
+/- warning: pmf.to_measure_apply -> Pmf.toMeasure_apply is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 s) -> (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (x : α) => Set.indicator.{u1, 0} α ENNReal ENNReal.hasZero s (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p) x)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 s) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) s) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (x : α) => Set.indicator.{u1, 0} α ENNReal instENNRealZero s (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p) x)))
+Case conversion may be inaccurate. Consider using '#align pmf.to_measure_apply Pmf.toMeasure_applyₓ'. -/
 theorem toMeasure_apply (hs : MeasurableSet s) : p.toMeasure s = ∑' x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs).trans (p.to_outer_measure_apply s)
 #align pmf.to_measure_apply Pmf.toMeasure_apply
 
+#print Pmf.toMeasure_apply_singleton /-
 theorem toMeasure_apply_singleton (a : α) (h : MeasurableSet ({a} : Set α)) :
     p.toMeasure {a} = p a := by
   simp [to_measure_apply_eq_to_outer_measure_apply _ _ h, to_outer_measure_apply_singleton]
 #align pmf.to_measure_apply_singleton Pmf.toMeasure_apply_singleton
+-/
 
+/- warning: pmf.to_measure_apply_eq_zero_iff -> Pmf.toMeasure_apply_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 s) -> (Iff (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) (Pmf.support.{u1} α p) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 s) -> (Iff (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Disjoint.{u1} (Set.{u1} α) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (OmegaCompletePartialOrder.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.instOmegaCompletePartialOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (Pmf.support.{u1} α p) s))
+Case conversion may be inaccurate. Consider using '#align pmf.to_measure_apply_eq_zero_iff Pmf.toMeasure_apply_eq_zero_iffₓ'. -/
 theorem toMeasure_apply_eq_zero_iff (hs : MeasurableSet s) :
     p.toMeasure s = 0 ↔ Disjoint p.support s := by
   rw [to_measure_apply_eq_to_outer_measure_apply p s hs, to_outer_measure_apply_eq_zero_iff]
 #align pmf.to_measure_apply_eq_zero_iff Pmf.toMeasure_apply_eq_zero_iff
 
+#print Pmf.toMeasure_apply_eq_one_iff /-
 theorem toMeasure_apply_eq_one_iff (hs : MeasurableSet s) : p.toMeasure s = 1 ↔ p.support ⊆ s :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs : p.toMeasure s = p.toOuterMeasure s).symm ▸
     p.toOuterMeasure_apply_eq_one_iff s
 #align pmf.to_measure_apply_eq_one_iff Pmf.toMeasure_apply_eq_one_iff
+-/
 
+/- warning: pmf.to_measure_apply_inter_support -> Pmf.toMeasure_apply_inter_support is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 s) -> (MeasurableSet.{u1} α _inst_1 (Pmf.support.{u1} α p)) -> (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Pmf.support.{u1} α p))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 s) -> (MeasurableSet.{u1} α _inst_1 (Pmf.support.{u1} α p)) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Pmf.support.{u1} α p))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) s))
+Case conversion may be inaccurate. Consider using '#align pmf.to_measure_apply_inter_support Pmf.toMeasure_apply_inter_supportₓ'. -/
 @[simp]
 theorem toMeasure_apply_inter_support (hs : MeasurableSet s) (hp : MeasurableSet p.support) :
     p.toMeasure (s ∩ p.support) = p.toMeasure s := by
@@ -306,11 +476,23 @@ theorem toMeasure_apply_inter_support (hs : MeasurableSet s) (hp : MeasurableSet
     p.to_measure_apply_eq_to_outer_measure_apply _ (hs.inter hp)]
 #align pmf.to_measure_apply_inter_support Pmf.toMeasure_apply_inter_support
 
+/- warning: pmf.to_measure_mono -> Pmf.toMeasure_mono is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (MeasurableSet.{u1} α _inst_1 s) -> (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Pmf.support.{u1} α p)) t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) t))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (MeasurableSet.{u1} α _inst_1 s) -> (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Pmf.support.{u1} α p)) t) -> (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))))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) s) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) t))
+Case conversion may be inaccurate. Consider using '#align pmf.to_measure_mono Pmf.toMeasure_monoₓ'. -/
 theorem toMeasure_mono {s t : Set α} (hs : MeasurableSet s) (ht : MeasurableSet t)
     (h : s ∩ p.support ⊆ t) : p.toMeasure s ≤ p.toMeasure t := by
   simpa only [p.to_measure_apply_eq_to_outer_measure_apply, hs, ht] using to_outer_measure_mono p h
 #align pmf.to_measure_mono Pmf.toMeasure_mono
 
+/- warning: pmf.to_measure_apply_eq_of_inter_support_eq -> Pmf.toMeasure_apply_eq_of_inter_support_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (MeasurableSet.{u1} α _inst_1 s) -> (MeasurableSet.{u1} α _inst_1 t) -> (Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s (Pmf.support.{u1} α p)) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) t (Pmf.support.{u1} α p))) -> (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) t))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) {s : Set.{u1} α} {t : Set.{u1} α}, (MeasurableSet.{u1} α _inst_1 s) -> (MeasurableSet.{u1} α _inst_1 t) -> (Eq.{succ u1} (Set.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s (Pmf.support.{u1} α p)) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) t (Pmf.support.{u1} α p))) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) s) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) t))
+Case conversion may be inaccurate. Consider using '#align pmf.to_measure_apply_eq_of_inter_support_eq Pmf.toMeasure_apply_eq_of_inter_support_eqₓ'. -/
 theorem toMeasure_apply_eq_of_inter_support_eq {s t : Set α} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (h : s ∩ p.support = t ∩ p.support) : p.toMeasure s = p.toMeasure t := by
   simpa only [p.to_measure_apply_eq_to_outer_measure_apply, hs, ht] using
@@ -321,28 +503,50 @@ section MeasurableSingletonClass
 
 variable [MeasurableSingletonClass α]
 
+#print Pmf.toMeasure_injective /-
 theorem toMeasure_injective : (toMeasure : Pmf α → Measure α).Injective := fun p q h =>
   Pmf.ext fun x =>
     (p.toMeasure_apply_singleton x <| measurableSet_singleton x).symm.trans
       ((congr_fun (congr_arg _ h) _).trans <|
         q.toMeasure_apply_singleton x <| measurableSet_singleton x)
 #align pmf.to_measure_injective Pmf.toMeasure_injective
+-/
 
+#print Pmf.toMeasure_inj /-
 @[simp]
 theorem toMeasure_inj {p q : Pmf α} : p.toMeasure = q.toMeasure ↔ p = q :=
   toMeasure_injective.eq_iff
 #align pmf.to_measure_inj Pmf.toMeasure_inj
+-/
 
+/- warning: pmf.to_measure_apply_finset -> Pmf.toMeasure_apply_finset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) [_inst_2 : MeasurableSingletonClass.{u1} α _inst_1] (s : Finset.{u1} α), Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} α) (Set.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} α) (Set.{u1} α) (Finset.Set.hasCoeT.{u1} α))) s)) (Finset.sum.{0, u1} ENNReal α (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) s (fun (x : α) => coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p x))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) [_inst_2 : MeasurableSingletonClass.{u1} α _inst_1] (s : Finset.{u1} α), Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) (Finset.toSet.{u1} α s)) (Finset.sum.{0, u1} ENNReal α (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) s (fun (x : α) => FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p x))
+Case conversion may be inaccurate. Consider using '#align pmf.to_measure_apply_finset Pmf.toMeasure_apply_finsetₓ'. -/
 @[simp]
 theorem toMeasure_apply_finset (s : Finset α) : p.toMeasure s = ∑ x in s, p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.MeasurableSet).trans
     (p.toOuterMeasure_apply_finset s)
 #align pmf.to_measure_apply_finset Pmf.toMeasure_apply_finset
 
+/- warning: pmf.to_measure_apply_of_finite -> Pmf.toMeasure_apply_of_finite is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α) [_inst_2 : MeasurableSingletonClass.{u1} α _inst_1], (Set.Finite.{u1} α s) -> (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s) (tsum.{0, u1} ENNReal (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) ENNReal.topologicalSpace α (fun (x : α) => Set.indicator.{u1, 0} α ENNReal ENNReal.hasZero s (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p) x)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α) [_inst_2 : MeasurableSingletonClass.{u1} α _inst_1], (Set.Finite.{u1} α s) -> (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) s) (tsum.{0, u1} ENNReal (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) ENNReal.instTopologicalSpaceENNReal α (fun (x : α) => Set.indicator.{u1, 0} α ENNReal instENNRealZero s (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p) x)))
+Case conversion may be inaccurate. Consider using '#align pmf.to_measure_apply_of_finite Pmf.toMeasure_apply_of_finiteₓ'. -/
 theorem toMeasure_apply_of_finite (hs : s.Finite) : p.toMeasure s = ∑' x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs.MeasurableSet).trans (p.to_outer_measure_apply s)
 #align pmf.to_measure_apply_of_finite Pmf.toMeasure_apply_of_finite
 
+/- warning: pmf.to_measure_apply_fintype -> Pmf.toMeasure_apply_fintype is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α) [_inst_2 : MeasurableSingletonClass.{u1} α _inst_1] [_inst_3 : Fintype.{u1} α], Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) (Pmf.toMeasure.{u1} α _inst_1 p) s) (Finset.sum.{0, u1} ENNReal α (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.univ.{u1} α _inst_3) (fun (x : α) => Set.indicator.{u1, 0} α ENNReal ENNReal.hasZero s (coeFn.{succ u1, succ u1} (Pmf.{u1} α) (fun (_x : Pmf.{u1} α) => α -> ENNReal) (FunLike.hasCoeToFun.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (p : α) => ENNReal) (Pmf.funLike.{u1} α)) p) x))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] (p : Pmf.{u1} α) (s : Set.{u1} α) [_inst_2 : MeasurableSingletonClass.{u1} α _inst_1] [_inst_3 : Fintype.{u1} α], Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 (Pmf.toMeasure.{u1} α _inst_1 p)) s) (Finset.sum.{0, u1} ENNReal α (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) (Finset.univ.{u1} α _inst_3) (fun (x : α) => Set.indicator.{u1, 0} α ENNReal instENNRealZero s (FunLike.coe.{succ u1, succ u1, 1} (Pmf.{u1} α) α (fun (_x : α) => (fun (x._@.Mathlib.Probability.ProbabilityMassFunction.Basic._hyg.47 : α) => ENNReal) _x) (Pmf.funLike.{u1} α) p) x))
+Case conversion may be inaccurate. Consider using '#align pmf.to_measure_apply_fintype Pmf.toMeasure_apply_fintypeₓ'. -/
 @[simp]
 theorem toMeasure_apply_fintype [Fintype α] : p.toMeasure s = ∑ x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.toFinite.MeasurableSet).trans
@@ -361,6 +565,7 @@ open Pmf
 
 namespace Measure
 
+#print MeasureTheory.Measure.toPmf /-
 /-- Given that `α` is a countable, measurable space with all singleton sets measurable,
 we can convert any probability measure into a `pmf`, where the mass of a point
 is the measure of the singleton set under the original measure. -/
@@ -374,19 +579,24 @@ def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ
             (tsum_congr fun x => congr_fun (Set.indicator_univ _) x))
         h.measure_univ)⟩
 #align measure_theory.measure.to_pmf MeasureTheory.Measure.toPmf
+-/
 
 variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
   [ProbabilityMeasure μ]
 
+#print MeasureTheory.Measure.toPmf_apply /-
 theorem toPmf_apply (x : α) : μ.toPmf x = μ {x} :=
   rfl
 #align measure_theory.measure.to_pmf_apply MeasureTheory.Measure.toPmf_apply
+-/
 
+#print MeasureTheory.Measure.toPmf_toMeasure /-
 @[simp]
 theorem toPmf_toMeasure : μ.toPmf.toMeasure = μ :=
   Measure.ext fun s hs => by
     simpa only [μ.to_pmf.to_measure_apply s hs, ← μ.tsum_indicator_apply_singleton s hs]
 #align measure_theory.measure.to_pmf_to_measure MeasureTheory.Measure.toPmf_toMeasure
+-/
 
 end Measure
 
@@ -396,6 +606,7 @@ namespace Pmf
 
 open MeasureTheory
 
+#print Pmf.toMeasure.probabilityMeasure /-
 /-- The measure associated to a `pmf` by `to_measure` is a probability measure -/
 instance toMeasure.probabilityMeasure [MeasurableSpace α] (p : Pmf α) :
     ProbabilityMeasure p.toMeasure :=
@@ -403,23 +614,30 @@ instance toMeasure.probabilityMeasure [MeasurableSpace α] (p : Pmf α) :
     simpa only [MeasurableSet.univ, to_measure_apply_eq_to_outer_measure_apply, Set.indicator_univ,
       to_outer_measure_apply, ENNReal.coe_eq_one] using tsum_coe p⟩
 #align pmf.to_measure.is_probability_measure Pmf.toMeasure.probabilityMeasure
+-/
 
 variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (p : Pmf α) (μ : Measure α)
   [ProbabilityMeasure μ]
 
+#print Pmf.toMeasure_toPmf /-
 @[simp]
 theorem toMeasure_toPmf : p.toMeasure.toPmf = p :=
   Pmf.ext fun x => by
     rw [← p.to_measure_apply_singleton x (measurable_set_singleton x), p.to_measure.to_pmf_apply]
 #align pmf.to_measure_to_pmf Pmf.toMeasure_toPmf
+-/
 
+#print Pmf.toMeasure_eq_iff_eq_toPmf /-
 theorem toMeasure_eq_iff_eq_toPmf (μ : Measure α) [ProbabilityMeasure μ] :
     p.toMeasure = μ ↔ p = μ.toPmf := by rw [← to_measure_inj, measure.to_pmf_to_measure]
 #align pmf.to_measure_eq_iff_eq_to_pmf Pmf.toMeasure_eq_iff_eq_toPmf
+-/
 
+#print Pmf.toPmf_eq_iff_toMeasure_eq /-
 theorem toPmf_eq_iff_toMeasure_eq (μ : Measure α) [ProbabilityMeasure μ] :
     μ.toPmf = p ↔ μ = p.toMeasure := by rw [← to_measure_inj, measure.to_pmf_to_measure]
 #align pmf.to_pmf_eq_iff_to_measure_eq Pmf.toPmf_eq_iff_toMeasure_eq
+-/
 
 end Pmf
 

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

@@ -365,7 +365,7 @@ namespace Measure
 we can convert any probability measure into a `pmf`, where the mass of a point
 is the measure of the singleton set under the original measure. -/
 def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
-    [h : IsProbabilityMeasure μ] : Pmf α :=
+    [h : ProbabilityMeasure μ] : Pmf α :=
   ⟨fun x => μ ({x} : Set α),
     ENNReal.summable.hasSum_iff.2
       (trans
@@ -376,7 +376,7 @@ def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ
 #align measure_theory.measure.to_pmf MeasureTheory.Measure.toPmf
 
 variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
-  [IsProbabilityMeasure μ]
+  [ProbabilityMeasure μ]
 
 theorem toPmf_apply (x : α) : μ.toPmf x = μ {x} :=
   rfl
@@ -397,15 +397,15 @@ namespace Pmf
 open MeasureTheory
 
 /-- The measure associated to a `pmf` by `to_measure` is a probability measure -/
-instance toMeasure.isProbabilityMeasure [MeasurableSpace α] (p : Pmf α) :
-    IsProbabilityMeasure p.toMeasure :=
+instance toMeasure.probabilityMeasure [MeasurableSpace α] (p : Pmf α) :
+    ProbabilityMeasure p.toMeasure :=
   ⟨by
     simpa only [MeasurableSet.univ, to_measure_apply_eq_to_outer_measure_apply, Set.indicator_univ,
       to_outer_measure_apply, ENNReal.coe_eq_one] using tsum_coe p⟩
-#align pmf.to_measure.is_probability_measure Pmf.toMeasure.isProbabilityMeasure
+#align pmf.to_measure.is_probability_measure Pmf.toMeasure.probabilityMeasure
 
 variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (p : Pmf α) (μ : Measure α)
-  [IsProbabilityMeasure μ]
+  [ProbabilityMeasure μ]
 
 @[simp]
 theorem toMeasure_toPmf : p.toMeasure.toPmf = p :=
@@ -413,11 +413,11 @@ theorem toMeasure_toPmf : p.toMeasure.toPmf = p :=
     rw [← p.to_measure_apply_singleton x (measurable_set_singleton x), p.to_measure.to_pmf_apply]
 #align pmf.to_measure_to_pmf Pmf.toMeasure_toPmf
 
-theorem toMeasure_eq_iff_eq_toPmf (μ : Measure α) [IsProbabilityMeasure μ] :
+theorem toMeasure_eq_iff_eq_toPmf (μ : Measure α) [ProbabilityMeasure μ] :
     p.toMeasure = μ ↔ p = μ.toPmf := by rw [← to_measure_inj, measure.to_pmf_to_measure]
 #align pmf.to_measure_eq_iff_eq_to_pmf Pmf.toMeasure_eq_iff_eq_toPmf
 
-theorem toPmf_eq_iff_toMeasure_eq (μ : Measure α) [IsProbabilityMeasure μ] :
+theorem toPmf_eq_iff_toMeasure_eq (μ : Measure α) [ProbabilityMeasure μ] :
     μ.toPmf = p ↔ μ = p.toMeasure := by rw [← to_measure_inj, measure.to_pmf_to_measure]
 #align pmf.to_pmf_eq_iff_to_measure_eq Pmf.toPmf_eq_iff_toMeasure_eq
 

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

@@ -254,7 +254,7 @@ theorem toOuterMeasure_apply_eq_of_inter_support_eq {s t : Set α}
 
 @[simp]
 theorem toOuterMeasure_apply_fintype [Fintype α] : p.toOuterMeasure s = ∑ x, s.indicator p x :=
-  (p.toOuterMeasure_apply s).trans (tsum_eq_sum fun x h => absurd (Finset.mem_univ x) h)
+  (p.to_outer_measure_apply s).trans (tsum_eq_sum fun x h => absurd (Finset.mem_univ x) h)
 #align pmf.to_outer_measure_apply_fintype Pmf.toOuterMeasure_apply_fintype
 
 end OuterMeasure
@@ -281,7 +281,7 @@ theorem toMeasure_apply_eq_toOuterMeasure_apply (hs : MeasurableSet s) :
 #align pmf.to_measure_apply_eq_to_outer_measure_apply Pmf.toMeasure_apply_eq_toOuterMeasure_apply
 
 theorem toMeasure_apply (hs : MeasurableSet s) : p.toMeasure s = ∑' x, s.indicator p x :=
-  (p.toMeasure_apply_eq_toOuterMeasure_apply s hs).trans (p.toOuterMeasure_apply s)
+  (p.toMeasure_apply_eq_toOuterMeasure_apply s hs).trans (p.to_outer_measure_apply s)
 #align pmf.to_measure_apply Pmf.toMeasure_apply
 
 theorem toMeasure_apply_singleton (a : α) (h : MeasurableSet ({a} : Set α)) :
@@ -340,7 +340,7 @@ theorem toMeasure_apply_finset (s : Finset α) : p.toMeasure s = ∑ x in s, p x
 #align pmf.to_measure_apply_finset Pmf.toMeasure_apply_finset
 
 theorem toMeasure_apply_of_finite (hs : s.Finite) : p.toMeasure s = ∑' x, s.indicator p x :=
-  (p.toMeasure_apply_eq_toOuterMeasure_apply s hs.MeasurableSet).trans (p.toOuterMeasure_apply s)
+  (p.toMeasure_apply_eq_toOuterMeasure_apply s hs.MeasurableSet).trans (p.to_outer_measure_apply s)
 #align pmf.to_measure_apply_of_finite Pmf.toMeasure_apply_of_finite
 
 @[simp]

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 
 ! This file was ported from Lean 3 source module probability.probability_mass_function.basic
-! leanprover-community/mathlib commit 3f5c9d30716c775bda043456728a1a3ee31412e7
+! leanprover-community/mathlib commit 4ac69b290818724c159de091daa3acd31da0ee6d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -49,14 +49,21 @@ def Pmf.{u} (α : Type u) : Type u :=
 
 namespace Pmf
 
-instance : CoeFun (Pmf α) fun p => α → ℝ≥0∞ :=
-  ⟨fun p a => p.1 a⟩
+instance funLike : FunLike (Pmf α) α fun p => ℝ≥0∞
+    where
+  coe p a := p.1 a
+  coe_injective' p q h := Subtype.eq h
+#align pmf.fun_like Pmf.funLike
 
 @[ext]
-protected theorem ext : ∀ {p q : Pmf α}, (∀ a, p a = q a) → p = q
-  | ⟨f, hf⟩, ⟨g, hg⟩, Eq => Subtype.eq <| funext Eq
+protected theorem ext {p q : Pmf α} (h : ∀ x, p x = q x) : p = q :=
+  FunLike.ext p q h
 #align pmf.ext Pmf.ext
 
+theorem ext_iff {p q : Pmf α} : p = q ↔ ∀ x, p x = q x :=
+  FunLike.ext_iff
+#align pmf.ext_iff Pmf.ext_iff
+
 theorem hasSum_coe_one (p : Pmf α) : HasSum p 1 :=
   p.2
 #align pmf.has_sum_coe_one Pmf.hasSum_coe_one
@@ -78,6 +85,11 @@ theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : (∑' a, s.indicat
       (lt_of_le_of_ne le_top p.tsum_coe_ne_top))
 #align pmf.tsum_coe_indicator_ne_top Pmf.tsum_coe_indicator_ne_top
 
+@[simp]
+theorem coe_ne_zero (p : Pmf α) : ⇑p ≠ 0 := fun hp =>
+  zero_ne_one ((tsum_zero.symm.trans (tsum_congr fun x => symm (congr_fun hp x))).trans p.tsum_coe)
+#align pmf.coe_ne_zero Pmf.coe_ne_zero
+
 /-- The support of a `pmf` is the set where it is nonzero. -/
 def support (p : Pmf α) : Set α :=
   Function.support p
@@ -88,6 +100,11 @@ theorem mem_support_iff (p : Pmf α) (a : α) : a ∈ p.support ↔ p a ≠ 0 :=
   Iff.rfl
 #align pmf.mem_support_iff Pmf.mem_support_iff
 
+@[simp]
+theorem support_nonempty (p : Pmf α) : p.support.Nonempty :=
+  Function.support_nonempty_iff.2 p.coe_ne_zero
+#align pmf.support_nonempty Pmf.support_nonempty
+
 theorem apply_eq_zero_iff (p : Pmf α) (a : α) : p a = 0 ↔ a ∉ p.support := by
   rw [mem_support_iff, Classical.not_not]
 #align pmf.apply_eq_zero_iff Pmf.apply_eq_zero_iff

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

@@ -114,7 +114,7 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
   calc
     1 = 1 + 0 := (add_zero 1).symm
     _ < p a + ∑' b, ite (b = a) 0 (p b) :=
-      ENNReal.add_lt_add_of_le_of_lt ENNReal.one_ne_top (le_of_eq h.symm) this
+      (ENNReal.add_lt_add_of_le_of_lt ENNReal.one_ne_top (le_of_eq h.symm) this)
     _ = ite (a = a) (p a) 0 + ∑' b, ite (b = a) 0 (p b) := by rw [eq_self_iff_true, if_true]
     _ = (∑' b, ite (b = a) (p b) 0) + ∑' b, ite (b = a) 0 (p b) :=
       by
@@ -199,7 +199,7 @@ theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p
   exact function.funext_iff.symm.trans Set.indicator_eq_zero'
 #align pmf.to_outer_measure_apply_eq_zero_iff Pmf.toOuterMeasure_apply_eq_zero_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x «expr ∉ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x «expr ∉ » s) -/
 theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support ⊆ s :=
   by
   refine' (p.to_outer_measure_apply s).symm ▸ ⟨fun h a hap => _, fun h => _⟩

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

@@ -39,7 +39,7 @@ noncomputable section
 
 variable {α β γ : Type _}
 
-open Classical BigOperators NNReal Ennreal MeasureTheory
+open Classical BigOperators NNReal ENNReal MeasureTheory
 
 /-- A probability mass function, or discrete probability measures is a function `α → ℝ≥0∞` such
   that the values have (infinite) sum `1`. -/
@@ -67,14 +67,14 @@ theorem tsum_coe (p : Pmf α) : (∑' a, p a) = 1 :=
 #align pmf.tsum_coe Pmf.tsum_coe
 
 theorem tsum_coe_ne_top (p : Pmf α) : (∑' a, p a) ≠ ∞ :=
-  p.tsum_coe.symm ▸ Ennreal.one_ne_top
+  p.tsum_coe.symm ▸ ENNReal.one_ne_top
 #align pmf.tsum_coe_ne_top Pmf.tsum_coe_ne_top
 
 theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : (∑' a, s.indicator p a) ≠ ∞ :=
   ne_of_lt
     (lt_of_le_of_lt
-      (tsum_le_tsum (fun a => Set.indicator_apply_le fun _ => le_rfl) Ennreal.summable
-        Ennreal.summable)
+      (tsum_le_tsum (fun a => Set.indicator_apply_le fun _ => le_rfl) ENNReal.summable
+        ENNReal.summable)
       (lt_of_le_of_ne le_top p.tsum_coe_ne_top))
 #align pmf.tsum_coe_indicator_ne_top Pmf.tsum_coe_indicator_ne_top
 
@@ -109,12 +109,12 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
   exact ne_of_lt this p.tsum_coe.symm
   have : 0 < ∑' b, ite (b = a) 0 (p b) :=
     lt_of_le_of_ne' zero_le'
-      ((tsum_ne_zero_iff Ennreal.summable).2
+      ((tsum_ne_zero_iff ENNReal.summable).2
         ⟨a', ite_ne_left_iff.2 ⟨ha, Ne.symm <| (p.mem_support_iff a').2 ha'⟩⟩)
   calc
     1 = 1 + 0 := (add_zero 1).symm
     _ < p a + ∑' b, ite (b = a) 0 (p b) :=
-      Ennreal.add_lt_add_of_le_of_lt Ennreal.one_ne_top (le_of_eq h.symm) this
+      ENNReal.add_lt_add_of_le_of_lt ENNReal.one_ne_top (le_of_eq h.symm) this
     _ = ite (a = a) (p a) 0 + ∑' b, ite (b = a) 0 (p b) := by rw [eq_self_iff_true, if_true]
     _ = (∑' b, ite (b = a) (p b) 0) + ∑' b, ite (b = a) 0 (p b) :=
       by
@@ -134,7 +134,7 @@ theorem coe_le_one (p : Pmf α) (a : α) : p a ≤ 1 :=
 #align pmf.coe_le_one Pmf.coe_le_one
 
 theorem apply_ne_top (p : Pmf α) (a : α) : p a ≠ ∞ :=
-  ne_of_lt (lt_of_le_of_lt (p.coe_le_one a) Ennreal.one_lt_top)
+  ne_of_lt (lt_of_le_of_lt (p.coe_le_one a) ENNReal.one_lt_top)
 #align pmf.apply_ne_top Pmf.apply_ne_top
 
 theorem apply_lt_top (p : Pmf α) (a : α) : p a < ∞ :=
@@ -195,7 +195,7 @@ theorem toOuterMeasure_inj {p q : Pmf α} : p.toOuterMeasure = q.toOuterMeasure
 
 theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p.support s :=
   by
-  rw [to_outer_measure_apply, Ennreal.tsum_eq_zero]
+  rw [to_outer_measure_apply, ENNReal.tsum_eq_zero]
   exact function.funext_iff.symm.trans Set.indicator_eq_zero'
 #align pmf.to_outer_measure_apply_eq_zero_iff Pmf.toOuterMeasure_apply_eq_zero_iff
 
@@ -207,7 +207,7 @@ theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support 
     have hs' : s.indicator p a = 0 := Set.indicator_apply_eq_zero.2 fun hs' => False.elim <| hs hs'
     have hsa : s.indicator p a < p a := hs'.symm ▸ (p.apply_pos_iff a).2 hap
     exact
-      Ennreal.tsum_lt_tsum (p.tsum_coe_indicator_ne_top s)
+      ENNReal.tsum_lt_tsum (p.tsum_coe_indicator_ne_top s)
         (fun x => Set.indicator_apply_le fun _ => le_rfl) hsa
   · suffices : ∀ (x) (_ : x ∉ s), p x = 0
     exact
@@ -350,7 +350,7 @@ is the measure of the singleton set under the original measure. -/
 def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
     [h : IsProbabilityMeasure μ] : Pmf α :=
   ⟨fun x => μ ({x} : Set α),
-    Ennreal.summable.hasSum_iff.2
+    ENNReal.summable.hasSum_iff.2
       (trans
         (symm <|
           (tsum_indicator_apply_singleton μ Set.univ MeasurableSet.univ).symm.trans
@@ -384,7 +384,7 @@ instance toMeasure.isProbabilityMeasure [MeasurableSpace α] (p : Pmf α) :
     IsProbabilityMeasure p.toMeasure :=
   ⟨by
     simpa only [MeasurableSet.univ, to_measure_apply_eq_to_outer_measure_apply, Set.indicator_univ,
-      to_outer_measure_apply, Ennreal.coe_eq_one] using tsum_coe p⟩
+      to_outer_measure_apply, ENNReal.coe_eq_one] using tsum_coe p⟩
 #align pmf.to_measure.is_probability_measure Pmf.toMeasure.isProbabilityMeasure
 
 variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (p : Pmf α) (μ : Measure α)

mathlib commit https://github.com/leanprover-community/mathlib/commit/c23aca359d4be6975b2a577d5cdb9d77b82c7407

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 
 ! This file was ported from Lean 3 source module probability.probability_mass_function.basic
-! leanprover-community/mathlib commit e50b8c261b0a000b806ec0e1356b41945eda61f7
+! leanprover-community/mathlib commit 3f5c9d30716c775bda043456728a1a3ee31412e7
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -25,6 +25,9 @@ by assigning each set the sum of the probabilities of each of its elements.
 Under this outer measure, every set is Carathéodory-measurable,
 so we can further extend this to a `measure` on `α`, see `pmf.to_measure`.
 `pmf.to_measure.is_probability_measure` shows this associated measure is a probability measure.
+Conversely, given a probability measure `μ` on a measurable space `α` with all singleton sets
+measurable, `μ.to_pmf` constructs a `pmf` on `α`, setting the probability mass of a point `x`
+to be the measure of the singleton set `{x}`.
 
 ## Tags
 
@@ -36,7 +39,7 @@ noncomputable section
 
 variable {α β γ : Type _}
 
-open Classical BigOperators NNReal Ennreal
+open Classical BigOperators NNReal Ennreal MeasureTheory
 
 /-- A probability mass function, or discrete probability measures is a function `α → ℝ≥0∞` such
   that the values have (infinite) sum `1`. -/
@@ -154,6 +157,15 @@ theorem toOuterMeasure_apply : p.toOuterMeasure s = ∑' x, s.indicator p x :=
   tsum_congr fun x => smul_dirac_apply (p x) x s
 #align pmf.to_outer_measure_apply Pmf.toOuterMeasure_apply
 
+@[simp]
+theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ :=
+  by
+  refine' eq_top_iff.2 <| le_trans (le_infₛ fun x hx => _) (le_sum_caratheodory _)
+  exact
+    let ⟨y, hy⟩ := hx
+    ((le_of_eq (dirac_caratheodory y).symm).trans (le_smul_caratheodory _ _)).trans (le_of_eq hy)
+#align pmf.to_outer_measure_caratheodory Pmf.toOuterMeasure_caratheodory
+
 @[simp]
 theorem toOuterMeasure_apply_finset (s : Finset α) : p.toOuterMeasure s = ∑ x in s, p x :=
   by
@@ -169,6 +181,18 @@ theorem toOuterMeasure_apply_singleton (a : α) : p.toOuterMeasure {a} = p a :=
   · exact ite_eq_left_iff.2 fun ha' => False.elim <| ha' rfl
 #align pmf.to_outer_measure_apply_singleton Pmf.toOuterMeasure_apply_singleton
 
+theorem toOuterMeasure_injective : (toOuterMeasure : Pmf α → OuterMeasure α).Injective :=
+  fun p q h =>
+  Pmf.ext fun x =>
+    (p.toOuterMeasure_apply_singleton x).symm.trans
+      ((congr_fun (congr_arg _ h) _).trans <| q.toOuterMeasure_apply_singleton x)
+#align pmf.to_outer_measure_injective Pmf.toOuterMeasure_injective
+
+@[simp]
+theorem toOuterMeasure_inj {p q : Pmf α} : p.toOuterMeasure = q.toOuterMeasure ↔ p = q :=
+  toOuterMeasure_injective.eq_iff
+#align pmf.to_outer_measure_inj Pmf.toOuterMeasure_inj
+
 theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p.support s :=
   by
   rw [to_outer_measure_apply, Ennreal.tsum_eq_zero]
@@ -216,15 +240,6 @@ theorem toOuterMeasure_apply_fintype [Fintype α] : p.toOuterMeasure s = ∑ x,
   (p.toOuterMeasure_apply s).trans (tsum_eq_sum fun x h => absurd (Finset.mem_univ x) h)
 #align pmf.to_outer_measure_apply_fintype Pmf.toOuterMeasure_apply_fintype
 
-@[simp]
-theorem toOuterMeasure_caratheodory (p : Pmf α) : (toOuterMeasure p).caratheodory = ⊤ :=
-  by
-  refine' eq_top_iff.2 <| le_trans (le_infₛ fun x hx => _) (le_sum_caratheodory _)
-  obtain ⟨y, hy⟩ := hx
-  exact
-    ((le_of_eq (dirac_caratheodory y).symm).trans (le_smul_caratheodory _ _)).trans (le_of_eq hy)
-#align pmf.to_outer_measure_caratheodory Pmf.toOuterMeasure_caratheodory
-
 end OuterMeasure
 
 section Measure
@@ -254,7 +269,7 @@ theorem toMeasure_apply (hs : MeasurableSet s) : p.toMeasure s = ∑' x, s.indic
 
 theorem toMeasure_apply_singleton (a : α) (h : MeasurableSet ({a} : Set α)) :
     p.toMeasure {a} = p a := by
-  simp [to_measure_apply_eq_to_outer_measure_apply p {a} h, to_outer_measure_apply_singleton]
+  simp [to_measure_apply_eq_to_outer_measure_apply _ _ h, to_outer_measure_apply_singleton]
 #align pmf.to_measure_apply_singleton Pmf.toMeasure_apply_singleton
 
 theorem toMeasure_apply_eq_zero_iff (hs : MeasurableSet s) :
@@ -289,6 +304,18 @@ section MeasurableSingletonClass
 
 variable [MeasurableSingletonClass α]
 
+theorem toMeasure_injective : (toMeasure : Pmf α → Measure α).Injective := fun p q h =>
+  Pmf.ext fun x =>
+    (p.toMeasure_apply_singleton x <| measurableSet_singleton x).symm.trans
+      ((congr_fun (congr_arg _ h) _).trans <|
+        q.toMeasure_apply_singleton x <| measurableSet_singleton x)
+#align pmf.to_measure_injective Pmf.toMeasure_injective
+
+@[simp]
+theorem toMeasure_inj {p q : Pmf α} : p.toMeasure = q.toMeasure ↔ p = q :=
+  toMeasure_injective.eq_iff
+#align pmf.to_measure_inj Pmf.toMeasure_inj
+
 @[simp]
 theorem toMeasure_apply_finset (s : Finset α) : p.toMeasure s = ∑ x in s, p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.MeasurableSet).trans
@@ -307,14 +334,75 @@ theorem toMeasure_apply_fintype [Fintype α] : p.toMeasure s = ∑ x, s.indicato
 
 end MeasurableSingletonClass
 
+end Measure
+
+end Pmf
+
+namespace MeasureTheory
+
+open Pmf
+
+namespace Measure
+
+/-- Given that `α` is a countable, measurable space with all singleton sets measurable,
+we can convert any probability measure into a `pmf`, where the mass of a point
+is the measure of the singleton set under the original measure. -/
+def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
+    [h : IsProbabilityMeasure μ] : Pmf α :=
+  ⟨fun x => μ ({x} : Set α),
+    Ennreal.summable.hasSum_iff.2
+      (trans
+        (symm <|
+          (tsum_indicator_apply_singleton μ Set.univ MeasurableSet.univ).symm.trans
+            (tsum_congr fun x => congr_fun (Set.indicator_univ _) x))
+        h.measure_univ)⟩
+#align measure_theory.measure.to_pmf MeasureTheory.Measure.toPmf
+
+variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
+  [IsProbabilityMeasure μ]
+
+theorem toPmf_apply (x : α) : μ.toPmf x = μ {x} :=
+  rfl
+#align measure_theory.measure.to_pmf_apply MeasureTheory.Measure.toPmf_apply
+
+@[simp]
+theorem toPmf_toMeasure : μ.toPmf.toMeasure = μ :=
+  Measure.ext fun s hs => by
+    simpa only [μ.to_pmf.to_measure_apply s hs, ← μ.tsum_indicator_apply_singleton s hs]
+#align measure_theory.measure.to_pmf_to_measure MeasureTheory.Measure.toPmf_toMeasure
+
+end Measure
+
+end MeasureTheory
+
+namespace Pmf
+
+open MeasureTheory
+
 /-- The measure associated to a `pmf` by `to_measure` is a probability measure -/
-instance toMeasure.isProbabilityMeasure (p : Pmf α) : IsProbabilityMeasure p.toMeasure :=
+instance toMeasure.isProbabilityMeasure [MeasurableSpace α] (p : Pmf α) :
+    IsProbabilityMeasure p.toMeasure :=
   ⟨by
     simpa only [MeasurableSet.univ, to_measure_apply_eq_to_outer_measure_apply, Set.indicator_univ,
       to_outer_measure_apply, Ennreal.coe_eq_one] using tsum_coe p⟩
 #align pmf.to_measure.is_probability_measure Pmf.toMeasure.isProbabilityMeasure
 
-end Measure
+variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (p : Pmf α) (μ : Measure α)
+  [IsProbabilityMeasure μ]
+
+@[simp]
+theorem toMeasure_toPmf : p.toMeasure.toPmf = p :=
+  Pmf.ext fun x => by
+    rw [← p.to_measure_apply_singleton x (measurable_set_singleton x), p.to_measure.to_pmf_apply]
+#align pmf.to_measure_to_pmf Pmf.toMeasure_toPmf
+
+theorem toMeasure_eq_iff_eq_toPmf (μ : Measure α) [IsProbabilityMeasure μ] :
+    p.toMeasure = μ ↔ p = μ.toPmf := by rw [← to_measure_inj, measure.to_pmf_to_measure]
+#align pmf.to_measure_eq_iff_eq_to_pmf Pmf.toMeasure_eq_iff_eq_toPmf
+
+theorem toPmf_eq_iff_toMeasure_eq (μ : Measure α) [IsProbabilityMeasure μ] :
+    μ.toPmf = p ↔ μ = p.toMeasure := by rw [← to_measure_inj, measure.to_pmf_to_measure]
+#align pmf.to_pmf_eq_iff_to_measure_eq Pmf.toPmf_eq_iff_toMeasure_eq
 
 end Pmf
 

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

I removed some redundant instance arguments throughout Mathlib. To do this, I used VS Code's regex search. See https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/repeating.20instances.20from.20variable.20command I closed the previous PR for this and reopened it.

@@ -283,7 +283,7 @@ theorem toMeasure_apply_inter_support (hs : MeasurableSet s) (hp : MeasurableSet
 #align pmf.to_measure_apply_inter_support PMF.toMeasure_apply_inter_support
 
 @[simp]
-theorem restrict_toMeasure_support [MeasurableSpace α] [MeasurableSingletonClass α]  (p : PMF α) :
+theorem restrict_toMeasure_support [MeasurableSingletonClass α]  (p : PMF α) :
     Measure.restrict (toMeasure p) (support p) = toMeasure p := by
   ext s hs
   apply (MeasureTheory.Measure.restrict_apply hs).trans

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

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

@@ -36,7 +36,8 @@ noncomputable section
 
 variable {α β γ : Type*}
 
-open Classical BigOperators NNReal ENNReal MeasureTheory
+open scoped Classical
+open BigOperators NNReal ENNReal MeasureTheory
 
 /-- A probability mass function, or discrete probability measures is a function `α → ℝ≥0∞` such
   that the values have (infinite) sum `1`. -/

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>

@@ -116,8 +116,7 @@ theorem apply_eq_one_iff (p : PMF α) (a : α) : p a = 1 ↔ p.support = {a} :=
     fun a' ha' => ha'.symm ▸ (p.mem_support_iff a).2 fun ha => zero_ne_one <| ha.symm.trans h,
     fun h => _root_.trans (symm <| tsum_eq_single a
       fun a' ha' => (p.apply_eq_zero_iff a').2 (h.symm ▸ ha')) p.tsum_coe⟩
-  suffices : 1 < ∑' a, p a
-  exact ne_of_lt this p.tsum_coe.symm
+  suffices 1 < ∑' a, p a from ne_of_lt this p.tsum_coe.symm
   have : 0 < ∑' b, ite (b = a) 0 (p b) := lt_of_le_of_ne' zero_le'
     ((tsum_ne_zero_iff ENNReal.summable).2
       ⟨a', ite_ne_left_iff.2 ⟨ha, Ne.symm <| (p.mem_support_iff a').2 ha'⟩⟩)
@@ -205,9 +204,9 @@ theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support 
     have hsa : s.indicator p a < p a := hs'.symm ▸ (p.apply_pos_iff a).2 hap
     exact ENNReal.tsum_lt_tsum (p.tsum_coe_indicator_ne_top s)
       (fun x => Set.indicator_apply_le fun _ => le_rfl) hsa
-  · suffices : ∀ (x) (_ : x ∉ s), p x = 0
-    exact _root_.trans (tsum_congr
-      fun a => (Set.indicator_apply s p a).trans (ite_eq_left_iff.2 <| symm ∘ this a)) p.tsum_coe
+  · suffices ∀ (x) (_ : x ∉ s), p x = 0 from
+      _root_.trans (tsum_congr
+        fun a => (Set.indicator_apply s p a).trans (ite_eq_left_iff.2 <| symm ∘ this a)) p.tsum_coe
     exact fun a ha => (p.apply_eq_zero_iff a).2 <| Set.not_mem_subset h ha
 #align pmf.to_outer_measure_apply_eq_one_iff PMF.toOuterMeasure_apply_eq_one_iff
 

This follows up from #9785, which renamed FunLike to DFunLike, by introducing a new abbreviation FunLike F α β := DFunLike F α (fun _ => β), to make the non-dependent use of FunLike easier.

I searched for the pattern DFunLike.*fun and DFunLike.*λ in all files to replace expressions of the form DFunLike F α (fun _ => β) with FunLike F α β. I did this everywhere except for extends clauses for two reasons: it would conflict with #8386, and more importantly extends must directly refer to a structure with no unfolding of defs or abbrevs.

@@ -46,10 +46,10 @@ def PMF.{u} (α : Type u) : Type u :=
 
 namespace PMF
 
-instance instDFunLike : DFunLike (PMF α) α fun _ => ℝ≥0∞ where
+instance instFunLike : FunLike (PMF α) α ℝ≥0∞ where
   coe p a := p.1 a
   coe_injective' _ _ h := Subtype.eq h
-#align pmf.fun_like PMF.instDFunLike
+#align pmf.fun_like PMF.instFunLike
 
 @[ext]
 protected theorem ext {p q : PMF α} (h : ∀ x, p x = q x) : p = q :=

This prepares for the introduction of a non-dependent synonym of FunLike, which helps a lot with keeping #8386 readable.

This is entirely search-and-replace in 680197f combined with manual fixes in 4145626, e900597 and b8428f8. The commands that generated this change:

sed -i 's/\bFunLike\b/DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoFunLike\b/toDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/import Mathlib.Data.DFunLike/import Mathlib.Data.FunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bHom_FunLike\b/Hom_DFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean     
sed -i 's/\binstFunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\bfunLike\b/instDFunLike/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean
sed -i 's/\btoo many metavariables to apply `fun_like.has_coe_to_fun`/too many metavariables to apply `DFunLike.hasCoeToFun`/g' {Archive,Counterexamples,Mathlib,test}/**/*.lean

Co-authored-by: Anne Baanen <Vierkantor@users.noreply.github.com>

@@ -46,18 +46,18 @@ def PMF.{u} (α : Type u) : Type u :=
 
 namespace PMF
 
-instance funLike : FunLike (PMF α) α fun _ => ℝ≥0∞ where
+instance instDFunLike : DFunLike (PMF α) α fun _ => ℝ≥0∞ where
   coe p a := p.1 a
   coe_injective' _ _ h := Subtype.eq h
-#align pmf.fun_like PMF.funLike
+#align pmf.fun_like PMF.instDFunLike
 
 @[ext]
 protected theorem ext {p q : PMF α} (h : ∀ x, p x = q x) : p = q :=
-  FunLike.ext p q h
+  DFunLike.ext p q h
 #align pmf.ext PMF.ext
 
 theorem ext_iff {p q : PMF α} : p = q ↔ ∀ x, p x = q x :=
-  FunLike.ext_iff
+  DFunLike.ext_iff
 #align pmf.ext_iff PMF.ext_iff
 
 theorem hasSum_coe_one (p : PMF α) : HasSum p 1 :=

Search and replace Pmf with PMF.

@@ -15,15 +15,15 @@ This file is about probability mass functions or discrete probability measures:
 a function `α → ℝ≥0∞` such that the values have (infinite) sum `1`.
 
 Construction of monadic `pure` and `bind` is found in `ProbabilityMassFunction/Monad.lean`,
-other constructions of `Pmf`s are found in `ProbabilityMassFunction/Constructions.lean`.
+other constructions of `PMF`s are found in `ProbabilityMassFunction/Constructions.lean`.
 
-Given `p : Pmf α`, `Pmf.toOuterMeasure` constructs an `OuterMeasure` on `α`,
+Given `p : PMF α`, `PMF.toOuterMeasure` constructs an `OuterMeasure` on `α`,
 by assigning each set the sum of the probabilities of each of its elements.
 Under this outer measure, every set is Carathéodory-measurable,
-so we can further extend this to a `Measure` on `α`, see `Pmf.toMeasure`.
-`Pmf.toMeasure.isProbabilityMeasure` shows this associated measure is a probability measure.
+so we can further extend this to a `Measure` on `α`, see `PMF.toMeasure`.
+`PMF.toMeasure.isProbabilityMeasure` shows this associated measure is a probability measure.
 Conversely, given a probability measure `μ` on a measurable space `α` with all singleton sets
-measurable, `μ.toPmf` constructs a `Pmf` on `α`, setting the probability mass of a point `x`
+measurable, `μ.toPMF` constructs a `PMF` on `α`, setting the probability mass of a point `x`
 to be the measure of the singleton set `{x}`.
 
 ## Tags
@@ -40,78 +40,78 @@ open Classical BigOperators NNReal ENNReal MeasureTheory
 
 /-- A probability mass function, or discrete probability measures is a function `α → ℝ≥0∞` such
   that the values have (infinite) sum `1`. -/
-def Pmf.{u} (α : Type u) : Type u :=
+def PMF.{u} (α : Type u) : Type u :=
   { f : α → ℝ≥0∞ // HasSum f 1 }
-#align pmf Pmf
+#align pmf PMF
 
-namespace Pmf
+namespace PMF
 
-instance funLike : FunLike (Pmf α) α fun _ => ℝ≥0∞ where
+instance funLike : FunLike (PMF α) α fun _ => ℝ≥0∞ where
   coe p a := p.1 a
   coe_injective' _ _ h := Subtype.eq h
-#align pmf.fun_like Pmf.funLike
+#align pmf.fun_like PMF.funLike
 
 @[ext]
-protected theorem ext {p q : Pmf α} (h : ∀ x, p x = q x) : p = q :=
+protected theorem ext {p q : PMF α} (h : ∀ x, p x = q x) : p = q :=
   FunLike.ext p q h
-#align pmf.ext Pmf.ext
+#align pmf.ext PMF.ext
 
-theorem ext_iff {p q : Pmf α} : p = q ↔ ∀ x, p x = q x :=
+theorem ext_iff {p q : PMF α} : p = q ↔ ∀ x, p x = q x :=
   FunLike.ext_iff
-#align pmf.ext_iff Pmf.ext_iff
+#align pmf.ext_iff PMF.ext_iff
 
-theorem hasSum_coe_one (p : Pmf α) : HasSum p 1 :=
+theorem hasSum_coe_one (p : PMF α) : HasSum p 1 :=
   p.2
-#align pmf.has_sum_coe_one Pmf.hasSum_coe_one
+#align pmf.has_sum_coe_one PMF.hasSum_coe_one
 
 @[simp]
-theorem tsum_coe (p : Pmf α) : ∑' a, p a = 1 :=
+theorem tsum_coe (p : PMF α) : ∑' a, p a = 1 :=
   p.hasSum_coe_one.tsum_eq
-#align pmf.tsum_coe Pmf.tsum_coe
+#align pmf.tsum_coe PMF.tsum_coe
 
-theorem tsum_coe_ne_top (p : Pmf α) : ∑' a, p a ≠ ∞ :=
+theorem tsum_coe_ne_top (p : PMF α) : ∑' a, p a ≠ ∞ :=
   p.tsum_coe.symm ▸ ENNReal.one_ne_top
-#align pmf.tsum_coe_ne_top Pmf.tsum_coe_ne_top
+#align pmf.tsum_coe_ne_top PMF.tsum_coe_ne_top
 
-theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : ∑' a, s.indicator p a ≠ ∞ :=
+theorem tsum_coe_indicator_ne_top (p : PMF α) (s : Set α) : ∑' a, s.indicator p a ≠ ∞ :=
   ne_of_lt (lt_of_le_of_lt
     (tsum_le_tsum (fun _ => Set.indicator_apply_le fun _ => le_rfl) ENNReal.summable
       ENNReal.summable)
     (lt_of_le_of_ne le_top p.tsum_coe_ne_top))
-#align pmf.tsum_coe_indicator_ne_top Pmf.tsum_coe_indicator_ne_top
+#align pmf.tsum_coe_indicator_ne_top PMF.tsum_coe_indicator_ne_top
 
 @[simp]
-theorem coe_ne_zero (p : Pmf α) : ⇑p ≠ 0 := fun hp =>
+theorem coe_ne_zero (p : PMF α) : ⇑p ≠ 0 := fun hp =>
   zero_ne_one ((tsum_zero.symm.trans (tsum_congr fun x => symm (congr_fun hp x))).trans p.tsum_coe)
-#align pmf.coe_ne_zero Pmf.coe_ne_zero
+#align pmf.coe_ne_zero PMF.coe_ne_zero
 
-/-- The support of a `Pmf` is the set where it is nonzero. -/
-def support (p : Pmf α) : Set α :=
+/-- The support of a `PMF` is the set where it is nonzero. -/
+def support (p : PMF α) : Set α :=
   Function.support p
-#align pmf.support Pmf.support
+#align pmf.support PMF.support
 
 @[simp]
-theorem mem_support_iff (p : Pmf α) (a : α) : a ∈ p.support ↔ p a ≠ 0 := Iff.rfl
-#align pmf.mem_support_iff Pmf.mem_support_iff
+theorem mem_support_iff (p : PMF α) (a : α) : a ∈ p.support ↔ p a ≠ 0 := Iff.rfl
+#align pmf.mem_support_iff PMF.mem_support_iff
 
 @[simp]
-theorem support_nonempty (p : Pmf α) : p.support.Nonempty :=
+theorem support_nonempty (p : PMF α) : p.support.Nonempty :=
   Function.support_nonempty_iff.2 p.coe_ne_zero
-#align pmf.support_nonempty Pmf.support_nonempty
+#align pmf.support_nonempty PMF.support_nonempty
 
 @[simp]
-theorem support_countable (p : Pmf α) : p.support.Countable :=
+theorem support_countable (p : PMF α) : p.support.Countable :=
   Summable.countable_support_ennreal (tsum_coe_ne_top p)
 
-theorem apply_eq_zero_iff (p : Pmf α) (a : α) : p a = 0 ↔ a ∉ p.support := by
+theorem apply_eq_zero_iff (p : PMF α) (a : α) : p a = 0 ↔ a ∉ p.support := by
   rw [mem_support_iff, Classical.not_not]
-#align pmf.apply_eq_zero_iff Pmf.apply_eq_zero_iff
+#align pmf.apply_eq_zero_iff PMF.apply_eq_zero_iff
 
-theorem apply_pos_iff (p : Pmf α) (a : α) : 0 < p a ↔ a ∈ p.support :=
+theorem apply_pos_iff (p : PMF α) (a : α) : 0 < p a ↔ a ∈ p.support :=
   pos_iff_ne_zero.trans (p.mem_support_iff a).symm
-#align pmf.apply_pos_iff Pmf.apply_pos_iff
+#align pmf.apply_pos_iff PMF.apply_pos_iff
 
-theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} := by
+theorem apply_eq_one_iff (p : PMF α) (a : α) : p a = 1 ↔ p.support = {a} := by
   refine' ⟨fun h => Set.Subset.antisymm (fun a' ha' => by_contra fun ha => _)
     fun a' ha' => ha'.symm ▸ (p.mem_support_iff a).2 fun ha => zero_ne_one <| ha.symm.trans h,
     fun h => _root_.trans (symm <| tsum_eq_single a
@@ -131,36 +131,36 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
       exact symm (tsum_eq_single a fun b hb => if_neg hb)
     _ = ∑' b, (ite (b = a) (p b) 0 + ite (b = a) 0 (p b)) := ENNReal.tsum_add.symm
     _ = ∑' b, p b := tsum_congr fun b => by split_ifs <;> simp only [zero_add, add_zero, le_rfl]
-#align pmf.apply_eq_one_iff Pmf.apply_eq_one_iff
+#align pmf.apply_eq_one_iff PMF.apply_eq_one_iff
 
-theorem coe_le_one (p : Pmf α) (a : α) : p a ≤ 1 := by
+theorem coe_le_one (p : PMF α) (a : α) : p a ≤ 1 := by
   refine' hasSum_le (fun b => _) (hasSum_ite_eq a (p a)) (hasSum_coe_one p)
   split_ifs with h <;> simp only [h, zero_le', le_rfl]
-#align pmf.coe_le_one Pmf.coe_le_one
+#align pmf.coe_le_one PMF.coe_le_one
 
-theorem apply_ne_top (p : Pmf α) (a : α) : p a ≠ ∞ :=
+theorem apply_ne_top (p : PMF α) (a : α) : p a ≠ ∞ :=
   ne_of_lt (lt_of_le_of_lt (p.coe_le_one a) ENNReal.one_lt_top)
-#align pmf.apply_ne_top Pmf.apply_ne_top
+#align pmf.apply_ne_top PMF.apply_ne_top
 
-theorem apply_lt_top (p : Pmf α) (a : α) : p a < ∞ :=
+theorem apply_lt_top (p : PMF α) (a : α) : p a < ∞ :=
   lt_of_le_of_ne le_top (p.apply_ne_top a)
-#align pmf.apply_lt_top Pmf.apply_lt_top
+#align pmf.apply_lt_top PMF.apply_lt_top
 
 section OuterMeasure
 
 open MeasureTheory MeasureTheory.OuterMeasure
 
-/-- Construct an `OuterMeasure` from a `Pmf`, by assigning measure to each set `s : Set α` equal
+/-- Construct an `OuterMeasure` from a `PMF`, by assigning measure to each set `s : Set α` equal
   to the sum of `p x` for each `x ∈ α`. -/
-def toOuterMeasure (p : Pmf α) : OuterMeasure α :=
+def toOuterMeasure (p : PMF α) : OuterMeasure α :=
   OuterMeasure.sum fun x : α => p x • dirac x
-#align pmf.to_outer_measure Pmf.toOuterMeasure
+#align pmf.to_outer_measure PMF.toOuterMeasure
 
-variable (p : Pmf α) (s t : Set α)
+variable (p : PMF α) (s t : Set α)
 
 theorem toOuterMeasure_apply : p.toOuterMeasure s = ∑' x, s.indicator p x :=
   tsum_congr fun x => smul_dirac_apply (p x) x s
-#align pmf.to_outer_measure_apply Pmf.toOuterMeasure_apply
+#align pmf.to_outer_measure_apply PMF.toOuterMeasure_apply
 
 @[simp]
 theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ := by
@@ -168,35 +168,35 @@ theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ := by
   have ⟨y, hy⟩ := hx
   exact
     ((le_of_eq (dirac_caratheodory y).symm).trans (le_smul_caratheodory _ _)).trans (le_of_eq hy)
-#align pmf.to_outer_measure_caratheodory Pmf.toOuterMeasure_caratheodory
+#align pmf.to_outer_measure_caratheodory PMF.toOuterMeasure_caratheodory
 
 @[simp]
 theorem toOuterMeasure_apply_finset (s : Finset α) : p.toOuterMeasure s = ∑ x in s, p x := by
   refine' (toOuterMeasure_apply p s).trans ((tsum_eq_sum (s := s) _).trans _)
   · exact fun x hx => Set.indicator_of_not_mem (Finset.mem_coe.not.2 hx) _
   · exact Finset.sum_congr rfl fun x hx => Set.indicator_of_mem (Finset.mem_coe.2 hx) _
-#align pmf.to_outer_measure_apply_finset Pmf.toOuterMeasure_apply_finset
+#align pmf.to_outer_measure_apply_finset PMF.toOuterMeasure_apply_finset
 
 theorem toOuterMeasure_apply_singleton (a : α) : p.toOuterMeasure {a} = p a := by
   refine' (p.toOuterMeasure_apply {a}).trans ((tsum_eq_single a fun b hb => _).trans _)
   · exact ite_eq_right_iff.2 fun hb' => False.elim <| hb hb'
   · exact ite_eq_left_iff.2 fun ha' => False.elim <| ha' rfl
-#align pmf.to_outer_measure_apply_singleton Pmf.toOuterMeasure_apply_singleton
+#align pmf.to_outer_measure_apply_singleton PMF.toOuterMeasure_apply_singleton
 
-theorem toOuterMeasure_injective : (toOuterMeasure : Pmf α → OuterMeasure α).Injective :=
-  fun p q h => Pmf.ext fun x => (p.toOuterMeasure_apply_singleton x).symm.trans
+theorem toOuterMeasure_injective : (toOuterMeasure : PMF α → OuterMeasure α).Injective :=
+  fun p q h => PMF.ext fun x => (p.toOuterMeasure_apply_singleton x).symm.trans
     ((congr_fun (congr_arg _ h) _).trans <| q.toOuterMeasure_apply_singleton x)
-#align pmf.to_outer_measure_injective Pmf.toOuterMeasure_injective
+#align pmf.to_outer_measure_injective PMF.toOuterMeasure_injective
 
 @[simp]
-theorem toOuterMeasure_inj {p q : Pmf α} : p.toOuterMeasure = q.toOuterMeasure ↔ p = q :=
+theorem toOuterMeasure_inj {p q : PMF α} : p.toOuterMeasure = q.toOuterMeasure ↔ p = q :=
   toOuterMeasure_injective.eq_iff
-#align pmf.to_outer_measure_inj Pmf.toOuterMeasure_inj
+#align pmf.to_outer_measure_inj PMF.toOuterMeasure_inj
 
 theorem toOuterMeasure_apply_eq_zero_iff : p.toOuterMeasure s = 0 ↔ Disjoint p.support s := by
   rw [toOuterMeasure_apply, ENNReal.tsum_eq_zero]
   exact Function.funext_iff.symm.trans Set.indicator_eq_zero'
-#align pmf.to_outer_measure_apply_eq_zero_iff Pmf.toOuterMeasure_apply_eq_zero_iff
+#align pmf.to_outer_measure_apply_eq_zero_iff PMF.toOuterMeasure_apply_eq_zero_iff
 
 theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support ⊆ s := by
   refine' (p.toOuterMeasure_apply s).symm ▸ ⟨fun h a hap => _, fun h => _⟩
@@ -209,30 +209,30 @@ theorem toOuterMeasure_apply_eq_one_iff : p.toOuterMeasure s = 1 ↔ p.support 
     exact _root_.trans (tsum_congr
       fun a => (Set.indicator_apply s p a).trans (ite_eq_left_iff.2 <| symm ∘ this a)) p.tsum_coe
     exact fun a ha => (p.apply_eq_zero_iff a).2 <| Set.not_mem_subset h ha
-#align pmf.to_outer_measure_apply_eq_one_iff Pmf.toOuterMeasure_apply_eq_one_iff
+#align pmf.to_outer_measure_apply_eq_one_iff PMF.toOuterMeasure_apply_eq_one_iff
 
 @[simp]
 theorem toOuterMeasure_apply_inter_support :
     p.toOuterMeasure (s ∩ p.support) = p.toOuterMeasure s := by
-  simp only [toOuterMeasure_apply, Pmf.support, Set.indicator_inter_support]
-#align pmf.to_outer_measure_apply_inter_support Pmf.toOuterMeasure_apply_inter_support
+  simp only [toOuterMeasure_apply, PMF.support, Set.indicator_inter_support]
+#align pmf.to_outer_measure_apply_inter_support PMF.toOuterMeasure_apply_inter_support
 
 /-- Slightly stronger than `OuterMeasure.mono` having an intersection with `p.support`. -/
 theorem toOuterMeasure_mono {s t : Set α} (h : s ∩ p.support ⊆ t) :
     p.toOuterMeasure s ≤ p.toOuterMeasure t :=
   le_trans (le_of_eq (toOuterMeasure_apply_inter_support p s).symm) (p.toOuterMeasure.mono h)
-#align pmf.to_outer_measure_mono Pmf.toOuterMeasure_mono
+#align pmf.to_outer_measure_mono PMF.toOuterMeasure_mono
 
 theorem toOuterMeasure_apply_eq_of_inter_support_eq {s t : Set α}
     (h : s ∩ p.support = t ∩ p.support) : p.toOuterMeasure s = p.toOuterMeasure t :=
   le_antisymm (p.toOuterMeasure_mono (h.symm ▸ Set.inter_subset_left t p.support))
     (p.toOuterMeasure_mono (h ▸ Set.inter_subset_left s p.support))
-#align pmf.to_outer_measure_apply_eq_of_inter_support_eq Pmf.toOuterMeasure_apply_eq_of_inter_support_eq
+#align pmf.to_outer_measure_apply_eq_of_inter_support_eq PMF.toOuterMeasure_apply_eq_of_inter_support_eq
 
 @[simp]
 theorem toOuterMeasure_apply_fintype [Fintype α] : p.toOuterMeasure s = ∑ x, s.indicator p x :=
   (p.toOuterMeasure_apply s).trans (tsum_eq_sum fun x h => absurd (Finset.mem_univ x) h)
-#align pmf.to_outer_measure_apply_fintype Pmf.toOuterMeasure_apply_fintype
+#align pmf.to_outer_measure_apply_fintype PMF.toOuterMeasure_apply_fintype
 
 end OuterMeasure
 
@@ -240,50 +240,50 @@ section Measure
 
 open MeasureTheory
 
-/-- Since every set is Carathéodory-measurable under `Pmf.toOuterMeasure`,
+/-- Since every set is Carathéodory-measurable under `PMF.toOuterMeasure`,
   we can further extend this `OuterMeasure` to a `Measure` on `α`. -/
-def toMeasure [MeasurableSpace α] (p : Pmf α) : Measure α :=
+def toMeasure [MeasurableSpace α] (p : PMF α) : Measure α :=
   p.toOuterMeasure.toMeasure ((toOuterMeasure_caratheodory p).symm ▸ le_top)
-#align pmf.to_measure Pmf.toMeasure
+#align pmf.to_measure PMF.toMeasure
 
-variable [MeasurableSpace α] (p : Pmf α) (s t : Set α)
+variable [MeasurableSpace α] (p : PMF α) (s t : Set α)
 
 theorem toOuterMeasure_apply_le_toMeasure_apply : p.toOuterMeasure s ≤ p.toMeasure s :=
   le_toMeasure_apply p.toOuterMeasure _ s
-#align pmf.to_outer_measure_apply_le_to_measure_apply Pmf.toOuterMeasure_apply_le_toMeasure_apply
+#align pmf.to_outer_measure_apply_le_to_measure_apply PMF.toOuterMeasure_apply_le_toMeasure_apply
 
 theorem toMeasure_apply_eq_toOuterMeasure_apply (hs : MeasurableSet s) :
     p.toMeasure s = p.toOuterMeasure s :=
   toMeasure_apply p.toOuterMeasure _ hs
-#align pmf.to_measure_apply_eq_to_outer_measure_apply Pmf.toMeasure_apply_eq_toOuterMeasure_apply
+#align pmf.to_measure_apply_eq_to_outer_measure_apply PMF.toMeasure_apply_eq_toOuterMeasure_apply
 
 theorem toMeasure_apply (hs : MeasurableSet s) : p.toMeasure s = ∑' x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs).trans (p.toOuterMeasure_apply s)
-#align pmf.to_measure_apply Pmf.toMeasure_apply
+#align pmf.to_measure_apply PMF.toMeasure_apply
 
 theorem toMeasure_apply_singleton (a : α) (h : MeasurableSet ({a} : Set α)) :
     p.toMeasure {a} = p a := by
   simp [toMeasure_apply_eq_toOuterMeasure_apply _ _ h, toOuterMeasure_apply_singleton]
-#align pmf.to_measure_apply_singleton Pmf.toMeasure_apply_singleton
+#align pmf.to_measure_apply_singleton PMF.toMeasure_apply_singleton
 
 theorem toMeasure_apply_eq_zero_iff (hs : MeasurableSet s) :
     p.toMeasure s = 0 ↔ Disjoint p.support s := by
   rw [toMeasure_apply_eq_toOuterMeasure_apply p s hs, toOuterMeasure_apply_eq_zero_iff]
-#align pmf.to_measure_apply_eq_zero_iff Pmf.toMeasure_apply_eq_zero_iff
+#align pmf.to_measure_apply_eq_zero_iff PMF.toMeasure_apply_eq_zero_iff
 
 theorem toMeasure_apply_eq_one_iff (hs : MeasurableSet s) : p.toMeasure s = 1 ↔ p.support ⊆ s :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs).symm ▸ p.toOuterMeasure_apply_eq_one_iff s
-#align pmf.to_measure_apply_eq_one_iff Pmf.toMeasure_apply_eq_one_iff
+#align pmf.to_measure_apply_eq_one_iff PMF.toMeasure_apply_eq_one_iff
 
 @[simp]
 theorem toMeasure_apply_inter_support (hs : MeasurableSet s) (hp : MeasurableSet p.support) :
     p.toMeasure (s ∩ p.support) = p.toMeasure s := by
   simp [p.toMeasure_apply_eq_toOuterMeasure_apply s hs,
     p.toMeasure_apply_eq_toOuterMeasure_apply _ (hs.inter hp)]
-#align pmf.to_measure_apply_inter_support Pmf.toMeasure_apply_inter_support
+#align pmf.to_measure_apply_inter_support PMF.toMeasure_apply_inter_support
 
 @[simp]
-theorem restrict_toMeasure_support [MeasurableSpace α] [MeasurableSingletonClass α]  (p : Pmf α) :
+theorem restrict_toMeasure_support [MeasurableSpace α] [MeasurableSingletonClass α]  (p : PMF α) :
     Measure.restrict (toMeasure p) (support p) = toMeasure p := by
   ext s hs
   apply (MeasureTheory.Measure.restrict_apply hs).trans
@@ -292,63 +292,63 @@ theorem restrict_toMeasure_support [MeasurableSpace α] [MeasurableSingletonClas
 theorem toMeasure_mono {s t : Set α} (hs : MeasurableSet s) (ht : MeasurableSet t)
     (h : s ∩ p.support ⊆ t) : p.toMeasure s ≤ p.toMeasure t := by
   simpa only [p.toMeasure_apply_eq_toOuterMeasure_apply, hs, ht] using toOuterMeasure_mono p h
-#align pmf.to_measure_mono Pmf.toMeasure_mono
+#align pmf.to_measure_mono PMF.toMeasure_mono
 
 theorem toMeasure_apply_eq_of_inter_support_eq {s t : Set α} (hs : MeasurableSet s)
     (ht : MeasurableSet t) (h : s ∩ p.support = t ∩ p.support) : p.toMeasure s = p.toMeasure t := by
   simpa only [p.toMeasure_apply_eq_toOuterMeasure_apply, hs, ht] using
     toOuterMeasure_apply_eq_of_inter_support_eq p h
-#align pmf.to_measure_apply_eq_of_inter_support_eq Pmf.toMeasure_apply_eq_of_inter_support_eq
+#align pmf.to_measure_apply_eq_of_inter_support_eq PMF.toMeasure_apply_eq_of_inter_support_eq
 
 section MeasurableSingletonClass
 
 variable [MeasurableSingletonClass α]
 
-theorem toMeasure_injective : (toMeasure : Pmf α → Measure α).Injective := by
+theorem toMeasure_injective : (toMeasure : PMF α → Measure α).Injective := by
   intro p q h
   ext x
   rw [← p.toMeasure_apply_singleton x <| measurableSet_singleton x,
     ← q.toMeasure_apply_singleton x <| measurableSet_singleton x, h]
-#align pmf.to_measure_injective Pmf.toMeasure_injective
+#align pmf.to_measure_injective PMF.toMeasure_injective
 
 @[simp]
-theorem toMeasure_inj {p q : Pmf α} : p.toMeasure = q.toMeasure ↔ p = q :=
+theorem toMeasure_inj {p q : PMF α} : p.toMeasure = q.toMeasure ↔ p = q :=
   toMeasure_injective.eq_iff
-#align pmf.to_measure_inj Pmf.toMeasure_inj
+#align pmf.to_measure_inj PMF.toMeasure_inj
 
 @[simp]
 theorem toMeasure_apply_finset (s : Finset α) : p.toMeasure s = ∑ x in s, p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.measurableSet).trans
     (p.toOuterMeasure_apply_finset s)
-#align pmf.to_measure_apply_finset Pmf.toMeasure_apply_finset
+#align pmf.to_measure_apply_finset PMF.toMeasure_apply_finset
 
 theorem toMeasure_apply_of_finite (hs : s.Finite) : p.toMeasure s = ∑' x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s hs.measurableSet).trans (p.toOuterMeasure_apply s)
-#align pmf.to_measure_apply_of_finite Pmf.toMeasure_apply_of_finite
+#align pmf.to_measure_apply_of_finite PMF.toMeasure_apply_of_finite
 
 @[simp]
 theorem toMeasure_apply_fintype [Fintype α] : p.toMeasure s = ∑ x, s.indicator p x :=
   (p.toMeasure_apply_eq_toOuterMeasure_apply s s.toFinite.measurableSet).trans
     (p.toOuterMeasure_apply_fintype s)
-#align pmf.to_measure_apply_fintype Pmf.toMeasure_apply_fintype
+#align pmf.to_measure_apply_fintype PMF.toMeasure_apply_fintype
 
 end MeasurableSingletonClass
 
 end Measure
 
-end Pmf
+end PMF
 
 namespace MeasureTheory
 
-open Pmf
+open PMF
 
 namespace Measure
 
 /-- Given that `α` is a countable, measurable space with all singleton sets measurable,
-we can convert any probability measure into a `Pmf`, where the mass of a point
+we can convert any probability measure into a `PMF`, where the mass of a point
 is the measure of the singleton set under the original measure. -/
-def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
-    [h : IsProbabilityMeasure μ] : Pmf α :=
+def toPMF [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
+    [h : IsProbabilityMeasure μ] : PMF α :=
   ⟨fun x => μ ({x} : Set α),
     ENNReal.summable.hasSum_iff.2
       (_root_.trans
@@ -356,52 +356,52 @@ def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ
           (tsum_indicator_apply_singleton μ Set.univ MeasurableSet.univ).symm.trans
             (tsum_congr fun x => congr_fun (Set.indicator_univ _) x))
         h.measure_univ)⟩
-#align measure_theory.measure.to_pmf MeasureTheory.Measure.toPmf
+#align measure_theory.measure.to_pmf MeasureTheory.Measure.toPMF
 
 variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
   [IsProbabilityMeasure μ]
 
-theorem toPmf_apply (x : α) : μ.toPmf x = μ {x} := rfl
-#align measure_theory.measure.to_pmf_apply MeasureTheory.Measure.toPmf_apply
+theorem toPMF_apply (x : α) : μ.toPMF x = μ {x} := rfl
+#align measure_theory.measure.to_pmf_apply MeasureTheory.Measure.toPMF_apply
 
 @[simp]
-theorem toPmf_toMeasure : μ.toPmf.toMeasure = μ :=
+theorem toPMF_toMeasure : μ.toPMF.toMeasure = μ :=
   Measure.ext fun s hs => by
-    rw [μ.toPmf.toMeasure_apply s hs, ← μ.tsum_indicator_apply_singleton s hs]
+    rw [μ.toPMF.toMeasure_apply s hs, ← μ.tsum_indicator_apply_singleton s hs]
     rfl
-#align measure_theory.measure.to_pmf_to_measure MeasureTheory.Measure.toPmf_toMeasure
+#align measure_theory.measure.to_pmf_to_measure MeasureTheory.Measure.toPMF_toMeasure
 
 end Measure
 
 end MeasureTheory
 
-namespace Pmf
+namespace PMF
 
 open MeasureTheory
 
-/-- The measure associated to a `Pmf` by `toMeasure` is a probability measure. -/
-instance toMeasure.isProbabilityMeasure [MeasurableSpace α] (p : Pmf α) :
+/-- The measure associated to a `PMF` by `toMeasure` is a probability measure. -/
+instance toMeasure.isProbabilityMeasure [MeasurableSpace α] (p : PMF α) :
     IsProbabilityMeasure p.toMeasure :=
   ⟨by
     simpa only [MeasurableSet.univ, toMeasure_apply_eq_toOuterMeasure_apply, Set.indicator_univ,
       toOuterMeasure_apply, ENNReal.coe_eq_one] using tsum_coe p⟩
-#align pmf.to_measure.is_probability_measure Pmf.toMeasure.isProbabilityMeasure
+#align pmf.to_measure.is_probability_measure PMF.toMeasure.isProbabilityMeasure
 
-variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (p : Pmf α) (μ : Measure α)
+variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (p : PMF α) (μ : Measure α)
   [IsProbabilityMeasure μ]
 
 @[simp]
-theorem toMeasure_toPmf : p.toMeasure.toPmf = p :=
-  Pmf.ext fun x => by
-    rw [← p.toMeasure_apply_singleton x (measurableSet_singleton x), p.toMeasure.toPmf_apply]
-#align pmf.to_measure_to_pmf Pmf.toMeasure_toPmf
+theorem toMeasure_toPMF : p.toMeasure.toPMF = p :=
+  PMF.ext fun x => by
+    rw [← p.toMeasure_apply_singleton x (measurableSet_singleton x), p.toMeasure.toPMF_apply]
+#align pmf.to_measure_to_pmf PMF.toMeasure_toPMF
 
-theorem toMeasure_eq_iff_eq_toPmf (μ : Measure α) [IsProbabilityMeasure μ] :
-    p.toMeasure = μ ↔ p = μ.toPmf := by rw [← toMeasure_inj, Measure.toPmf_toMeasure]
-#align pmf.to_measure_eq_iff_eq_to_pmf Pmf.toMeasure_eq_iff_eq_toPmf
+theorem toMeasure_eq_iff_eq_toPMF (μ : Measure α) [IsProbabilityMeasure μ] :
+    p.toMeasure = μ ↔ p = μ.toPMF := by rw [← toMeasure_inj, Measure.toPMF_toMeasure]
+#align pmf.to_measure_eq_iff_eq_to_pmf PMF.toMeasure_eq_iff_eq_toPMF
 
-theorem toPmf_eq_iff_toMeasure_eq (μ : Measure α) [IsProbabilityMeasure μ] :
-    μ.toPmf = p ↔ μ = p.toMeasure := by rw [← toMeasure_inj, Measure.toPmf_toMeasure]
-#align pmf.to_pmf_eq_iff_to_measure_eq Pmf.toPmf_eq_iff_toMeasure_eq
+theorem toPMF_eq_iff_toMeasure_eq (μ : Measure α) [IsProbabilityMeasure μ] :
+    μ.toPMF = p ↔ μ = p.toMeasure := by rw [← toMeasure_inj, Measure.toPMF_toMeasure]
+#align pmf.to_pmf_eq_iff_to_measure_eq PMF.toPMF_eq_iff_toMeasure_eq
 
-end Pmf
+end PMF

The main result is that the integral (i.e. the expected value) with regard to a measure derived from a Pmf is a sum weighted by the Pmf.

It also provides the expected value for specific probability mass functions (bernoulli so far).

@@ -99,6 +99,10 @@ theorem support_nonempty (p : Pmf α) : p.support.Nonempty :=
   Function.support_nonempty_iff.2 p.coe_ne_zero
 #align pmf.support_nonempty Pmf.support_nonempty
 
+@[simp]
+theorem support_countable (p : Pmf α) : p.support.Countable :=
+  Summable.countable_support_ennreal (tsum_coe_ne_top p)
+
 theorem apply_eq_zero_iff (p : Pmf α) (a : α) : p a = 0 ↔ a ∉ p.support := by
   rw [mem_support_iff, Classical.not_not]
 #align pmf.apply_eq_zero_iff Pmf.apply_eq_zero_iff
@@ -278,6 +282,13 @@ theorem toMeasure_apply_inter_support (hs : MeasurableSet s) (hp : MeasurableSet
     p.toMeasure_apply_eq_toOuterMeasure_apply _ (hs.inter hp)]
 #align pmf.to_measure_apply_inter_support Pmf.toMeasure_apply_inter_support
 
+@[simp]
+theorem restrict_toMeasure_support [MeasurableSpace α] [MeasurableSingletonClass α]  (p : Pmf α) :
+    Measure.restrict (toMeasure p) (support p) = toMeasure p := by
+  ext s hs
+  apply (MeasureTheory.Measure.restrict_apply hs).trans
+  apply toMeasure_apply_inter_support p s hs p.support_countable.measurableSet
+
 theorem toMeasure_mono {s t : Set α} (hs : MeasurableSet s) (ht : MeasurableSet t)
     (h : s ∩ p.support ⊆ t) : p.toMeasure s ≤ p.toMeasure t := by
   simpa only [p.toMeasure_apply_eq_toOuterMeasure_apply, hs, ht] using toOuterMeasure_mono p h

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

This has nice performance benefits.

@@ -34,7 +34,7 @@ probability mass function, discrete probability measure
 
 noncomputable section
 
-variable {α β γ : Type _}
+variable {α β γ : Type*}
 
 open Classical BigOperators NNReal ENNReal MeasureTheory
 

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
 -/
 import Mathlib.Topology.Instances.ENNReal
-import Mathlib.MeasureTheory.Measure.MeasureSpace
+import Mathlib.MeasureTheory.Measure.Dirac
 
 #align_import probability.probability_mass_function.basic from "leanprover-community/mathlib"@"4ac69b290818724c159de091daa3acd31da0ee6d"
 

• 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) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Devon Tuma
-
-! This file was ported from Lean 3 source module probability.probability_mass_function.basic
-! leanprover-community/mathlib commit 4ac69b290818724c159de091daa3acd31da0ee6d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Instances.ENNReal
 import Mathlib.MeasureTheory.Measure.MeasureSpace
 
+#align_import probability.probability_mass_function.basic from "leanprover-community/mathlib"@"4ac69b290818724c159de091daa3acd31da0ee6d"
+
 /-!
 # Probability mass functions
 

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -68,15 +68,15 @@ theorem hasSum_coe_one (p : Pmf α) : HasSum p 1 :=
 #align pmf.has_sum_coe_one Pmf.hasSum_coe_one
 
 @[simp]
-theorem tsum_coe (p : Pmf α) : (∑' a, p a) = 1 :=
+theorem tsum_coe (p : Pmf α) : ∑' a, p a = 1 :=
   p.hasSum_coe_one.tsum_eq
 #align pmf.tsum_coe Pmf.tsum_coe
 
-theorem tsum_coe_ne_top (p : Pmf α) : (∑' a, p a) ≠ ∞ :=
+theorem tsum_coe_ne_top (p : Pmf α) : ∑' a, p a ≠ ∞ :=
   p.tsum_coe.symm ▸ ENNReal.one_ne_top
 #align pmf.tsum_coe_ne_top Pmf.tsum_coe_ne_top
 
-theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : (∑' a, s.indicator p a) ≠ ∞ :=
+theorem tsum_coe_indicator_ne_top (p : Pmf α) (s : Set α) : ∑' a, s.indicator p a ≠ ∞ :=
   ne_of_lt (lt_of_le_of_lt
     (tsum_le_tsum (fun _ => Set.indicator_apply_le fun _ => le_rfl) ENNReal.summable
       ENNReal.summable)
@@ -128,7 +128,7 @@ theorem apply_eq_one_iff (p : Pmf α) (a : α) : p a = 1 ↔ p.support = {a} :=
     _ = (∑' b, ite (b = a) (p b) 0) + ∑' b, ite (b = a) 0 (p b) := by
       congr
       exact symm (tsum_eq_single a fun b hb => if_neg hb)
-    _ = ∑' b, ite (b = a) (p b) 0 + ite (b = a) 0 (p b) := ENNReal.tsum_add.symm
+    _ = ∑' b, (ite (b = a) (p b) 0 + ite (b = a) 0 (p b)) := ENNReal.tsum_add.symm
     _ = ∑' b, p b := tsum_congr fun b => by split_ifs <;> simp only [zero_add, add_zero, le_rfl]
 #align pmf.apply_eq_one_iff Pmf.apply_eq_one_iff
 

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

@@ -340,7 +340,7 @@ namespace Measure
 we can convert any probability measure into a `Pmf`, where the mass of a point
 is the measure of the singleton set under the original measure. -/
 def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
-    [h : ProbabilityMeasure μ] : Pmf α :=
+    [h : IsProbabilityMeasure μ] : Pmf α :=
   ⟨fun x => μ ({x} : Set α),
     ENNReal.summable.hasSum_iff.2
       (_root_.trans
@@ -351,7 +351,7 @@ def toPmf [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ
 #align measure_theory.measure.to_pmf MeasureTheory.Measure.toPmf
 
 variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (μ : Measure α)
-  [ProbabilityMeasure μ]
+  [IsProbabilityMeasure μ]
 
 theorem toPmf_apply (x : α) : μ.toPmf x = μ {x} := rfl
 #align measure_theory.measure.to_pmf_apply MeasureTheory.Measure.toPmf_apply
@@ -372,15 +372,15 @@ namespace Pmf
 open MeasureTheory
 
 /-- The measure associated to a `Pmf` by `toMeasure` is a probability measure. -/
-instance toMeasure.probabilityMeasure [MeasurableSpace α] (p : Pmf α) :
-    ProbabilityMeasure p.toMeasure :=
+instance toMeasure.isProbabilityMeasure [MeasurableSpace α] (p : Pmf α) :
+    IsProbabilityMeasure p.toMeasure :=
   ⟨by
     simpa only [MeasurableSet.univ, toMeasure_apply_eq_toOuterMeasure_apply, Set.indicator_univ,
       toOuterMeasure_apply, ENNReal.coe_eq_one] using tsum_coe p⟩
-#align pmf.to_measure.is_probability_measure Pmf.toMeasure.probabilityMeasure
+#align pmf.to_measure.is_probability_measure Pmf.toMeasure.isProbabilityMeasure
 
 variable [Countable α] [MeasurableSpace α] [MeasurableSingletonClass α] (p : Pmf α) (μ : Measure α)
-  [ProbabilityMeasure μ]
+  [IsProbabilityMeasure μ]
 
 @[simp]
 theorem toMeasure_toPmf : p.toMeasure.toPmf = p :=
@@ -388,11 +388,11 @@ theorem toMeasure_toPmf : p.toMeasure.toPmf = p :=
     rw [← p.toMeasure_apply_singleton x (measurableSet_singleton x), p.toMeasure.toPmf_apply]
 #align pmf.to_measure_to_pmf Pmf.toMeasure_toPmf
 
-theorem toMeasure_eq_iff_eq_toPmf (μ : Measure α) [ProbabilityMeasure μ] :
+theorem toMeasure_eq_iff_eq_toPmf (μ : Measure α) [IsProbabilityMeasure μ] :
     p.toMeasure = μ ↔ p = μ.toPmf := by rw [← toMeasure_inj, Measure.toPmf_toMeasure]
 #align pmf.to_measure_eq_iff_eq_to_pmf Pmf.toMeasure_eq_iff_eq_toPmf
 
-theorem toPmf_eq_iff_toMeasure_eq (μ : Measure α) [ProbabilityMeasure μ] :
+theorem toPmf_eq_iff_toMeasure_eq (μ : Measure α) [IsProbabilityMeasure μ] :
     μ.toPmf = p ↔ μ = p.toMeasure := by rw [← toMeasure_inj, Measure.toPmf_toMeasure]
 #align pmf.to_pmf_eq_iff_to_measure_eq Pmf.toPmf_eq_iff_toMeasure_eq
 

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -163,7 +163,7 @@ theorem toOuterMeasure_apply : p.toOuterMeasure s = ∑' x, s.indicator p x :=
 
 @[simp]
 theorem toOuterMeasure_caratheodory : p.toOuterMeasure.caratheodory = ⊤ := by
-  refine' eq_top_iff.2 <| le_trans (le_infₛ fun x hx => _) (le_sum_caratheodory _)
+  refine' eq_top_iff.2 <| le_trans (le_sInf fun x hx => _) (le_sum_caratheodory _)
   have ⟨y, hy⟩ := hx
   exact
     ((le_of_eq (dirac_caratheodory y).symm).trans (le_smul_caratheodory _ _)).trans (le_of_eq hy)