measure_theory.decomposition.unsigned_hahn

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

0f1becb7

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

781cb2ee

bump to nightly-2024-03-17-08

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

22f01ce4

Diff

@@ -93,7 +93,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     rcases exists_lt_of_lt_csSup c_nonempty this with ⟨r, ⟨s, hs, rfl⟩, hlt⟩
     exact ⟨s, hs, hlt⟩
   rcases Classical.axiom_of_choice this with ⟨e, he⟩
-  change ℕ → Set α at e 
+  change ℕ → Set α at e
   have he₁ : ∀ n, MeasurableSet (e n) := fun n => (he n).1
   have he₂ : ∀ n, γ - (1 / 2) ^ n < d (e n) := fun n => (he n).2
   let f : ℕ → ℕ → Set α := fun n m => (Finset.Ico n (m + 1)).inf e

781cb2ee

bump to nightly-2024-02-02-06

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

1f9867d7

Diff

@@ -154,7 +154,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
       exact
         tendsto_const_nhds.sub <|
           tendsto_const_nhds.mul <|
-            tendsto_pow_atTop_nhds_0_of_lt_1 (le_of_lt <| half_pos <| zero_lt_one)
+            tendsto_pow_atTop_nhds_zero_of_lt_one (le_of_lt <| half_pos <| zero_lt_one)
               (half_lt_self zero_lt_one)
     have hd : tendsto (fun m => d (⋂ n, f m n)) at_top (𝓝 (d (⋃ m, ⋂ n, f m n))) :=
       by

781cb2ee

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
-import Mathbin.MeasureTheory.Measure.MeasureSpace
+import MeasureTheory.Measure.MeasureSpace
 
 #align_import measure_theory.decomposition.unsigned_hahn from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"

781cb2ee

bump to nightly-2023-08-02-01

mathlib commit https://github.com/leanprover-community/mathlib/commit/63721b2c3eba6c325ecf8ae8cca27155a4f6306f

7aca3f15

Diff

@@ -79,7 +79,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
           (ENNReal.tendsto_toNNReal <| _).comp <| tendsto_measure_Inter hs hm _
     exacts [hμ _, ⟨0, hμ _⟩, hν _, ⟨0, hν _⟩]
   have bdd_c : BddAbove c := by
-    use (μ univ).toNNReal
+    use(μ univ).toNNReal
     rintro r ⟨s, hs, rfl⟩
     refine' le_trans (sub_le_self _ <| NNReal.coe_nonneg _) _
     rw [NNReal.coe_le_coe, ← ENNReal.coe_le_coe, to_nnreal_μ, to_nnreal_μ]

781cb2ee

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module measure_theory.decomposition.unsigned_hahn
-! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Measure.MeasureSpace
 
+#align_import measure_theory.decomposition.unsigned_hahn from "leanprover-community/mathlib"@"781cb2eed038c4caf53bdbd8d20a95e5822d77df"
+
 /-!
 # Unsigned Hahn decomposition theorem

781cb2ee

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -38,6 +38,7 @@ namespace MeasureTheory
 
 variable {α : Type _} [MeasurableSpace α] {μ ν : Measure α}
 
+#print MeasureTheory.hahn_decomposition /-
 /-- **Hahn decomposition theorem** -/
 theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     ∃ s,
@@ -196,6 +197,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     rw [← to_nnreal_μ, ← to_nnreal_ν, ENNReal.coe_le_coe, ← NNReal.coe_le_coe]
     simpa only [d, sub_le_iff_le_add, zero_add] using this
 #align measure_theory.hahn_decomposition MeasureTheory.hahn_decomposition
+-/
 
 end MeasureTheory

781cb2ee

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -145,7 +145,6 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
             exact (he₁ _).union (hf _ _)
             exact he₁ _
           _ ≤ γ + d (f m (n + 1)) := add_le_add_right (d_le_γ _ <| (he₁ _).union (hf _ _)) _
-          
       exact (add_le_add_iff_left γ).1 this
   let s := ⋃ m, ⋂ n, f m n
   have γ_le_d_s : γ ≤ d s :=
@@ -183,7 +182,6 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
           γ + 0 ≤ d s := by rw [add_zero] <;> exact γ_le_d_s
           _ = d (s \ t) + d t := by rw [d_split _ _ hs ht, inter_eq_self_of_subset_right hts]
           _ ≤ γ + d t := add_le_add (d_le_γ _ (hs.diff ht)) le_rfl
-          
     rw [← to_nnreal_μ, ← to_nnreal_ν, ENNReal.coe_le_coe, ← NNReal.coe_le_coe]
     simpa only [d, le_sub_iff_add_le, zero_add] using this
   · intro t ht hts
@@ -195,7 +193,6 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
             rw [d_split _ _ (hs.union ht) ht, union_diff_right, union_inter_cancel_right,
               (subset_compl_iff_disjoint_left.1 hts).sdiff_eq_left]
           _ ≤ γ + 0 := by rw [add_zero] <;> exact d_le_γ _ (hs.union ht)
-          
     rw [← to_nnreal_μ, ← to_nnreal_ν, ENNReal.coe_le_coe, ← NNReal.coe_le_coe]
     simpa only [d, sub_le_iff_le_add, zero_add] using this
 #align measure_theory.hahn_decomposition MeasureTheory.hahn_decomposition

781cb2ee

bump to nightly-2023-06-04-18

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

3fb4268b

Diff

@@ -39,13 +39,13 @@ namespace MeasureTheory
 variable {α : Type _} [MeasurableSpace α] {μ ν : Measure α}
 
 /-- **Hahn decomposition theorem** -/
-theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
+theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     ∃ s,
       MeasurableSet s ∧
         (∀ t, MeasurableSet t → t ⊆ s → ν t ≤ μ t) ∧ ∀ t, MeasurableSet t → t ⊆ sᶜ → μ t ≤ ν t :=
   by
   let d : Set α → ℝ := fun s => ((μ s).toNNReal : ℝ) - (ν s).toNNReal
-  let c : Set ℝ := d '' { s | MeasurableSet s }
+  let c : Set ℝ := d '' {s | MeasurableSet s}
   let γ : ℝ := Sup c
   have hμ : ∀ s, μ s ≠ ∞ := measure_ne_top μ
   have hν : ∀ s, ν s ≠ ∞ := measure_ne_top ν

781cb2ee

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -79,7 +79,7 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
       refine'
         NNReal.tendsto_coe.2 <|
           (ENNReal.tendsto_toNNReal <| _).comp <| tendsto_measure_Inter hs hm _
-    exacts[hμ _, ⟨0, hμ _⟩, hν _, ⟨0, hν _⟩]
+    exacts [hμ _, ⟨0, hμ _⟩, hν _, ⟨0, hν _⟩]
   have bdd_c : BddAbove c := by
     use (μ univ).toNNReal
     rintro r ⟨s, hs, rfl⟩
@@ -95,7 +95,7 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     rcases exists_lt_of_lt_csSup c_nonempty this with ⟨r, ⟨s, hs, rfl⟩, hlt⟩
     exact ⟨s, hs, hlt⟩
   rcases Classical.axiom_of_choice this with ⟨e, he⟩
-  change ℕ → Set α at e
+  change ℕ → Set α at e 
   have he₁ : ∀ n, MeasurableSet (e n) := fun n => (he n).1
   have he₂ : ∀ n, γ - (1 / 2) ^ n < d (e n) := fun n => (he n).2
   let f : ℕ → ℕ → Set α := fun n m => (Finset.Ico n (m + 1)).inf e
@@ -124,7 +124,7 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
       simp only [f]
       rw [Nat.Ico_succ_singleton, Finset.inf_singleton]
       linarith
-    · intro n(hmn : m ≤ n)ih
+    · intro n (hmn : m ≤ n) ih
       have : γ + (γ - 2 * (1 / 2) ^ m + (1 / 2) ^ (n + 1)) ≤ γ + d (f m (n + 1)) := by
         calc
           γ + (γ - 2 * (1 / 2) ^ m + (1 / 2) ^ (n + 1)) ≤

781cb2ee

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -32,7 +32,7 @@ Hahn decomposition
 
 open Set Filter
 
-open Classical Topology ENNReal
+open scoped Classical Topology ENNReal
 
 namespace MeasureTheory

781cb2ee

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -38,12 +38,6 @@ namespace MeasureTheory
 
 variable {α : Type _} [MeasurableSpace α] {μ ν : Measure α}
 
-/- warning: measure_theory.hahn_decomposition -> MeasureTheory.hahn_decomposition is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {ν : MeasureTheory.Measure.{u1} α _inst_1} [_inst_2 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 μ] [_inst_3 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 ν], Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (MeasurableSet.{u1} α _inst_1 s) (And (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (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) ν t) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) μ t))) (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s)) -> (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) μ t) (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) ν t)))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {ν : MeasureTheory.Measure.{u1} α _inst_1} [_inst_2 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 μ] [_inst_3 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 ν], Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (MeasurableSet.{u1} α _inst_1 s) (And (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) -> (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 ν) t) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) t))) (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) s)) -> (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 μ) t) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 ν) t)))))
-Case conversion may be inaccurate. Consider using '#align measure_theory.hahn_decomposition MeasureTheory.hahn_decompositionₓ'. -/
 /-- **Hahn decomposition theorem** -/
 theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     ∃ s,

781cb2ee

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -57,9 +57,7 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
   have hν : ∀ s, ν s ≠ ∞ := measure_ne_top ν
   have to_nnreal_μ : ∀ s, ((μ s).toNNReal : ℝ≥0∞) = μ s := fun s => ENNReal.coe_toNNReal <| hμ _
   have to_nnreal_ν : ∀ s, ((ν s).toNNReal : ℝ≥0∞) = ν s := fun s => ENNReal.coe_toNNReal <| hν _
-  have d_empty : d ∅ = 0 := by
-    change _ - _ = _
-    rw [measure_empty, measure_empty, sub_self]
+  have d_empty : d ∅ = 0 := by change _ - _ = _; rw [measure_empty, measure_empty, sub_self]
   have d_split : ∀ s t, MeasurableSet s → MeasurableSet t → d s = d (s \ t) + d (s ∩ t) :=
     by
     intro s t hs ht
@@ -176,10 +174,8 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     have : tendsto (fun n => d (f m n)) at_top (𝓝 (d (⋂ n, f m n))) :=
       by
       refine' d_Inter _ _ _
-      · intro n
-        exact hf _ _
-      · intro n m hnm
-        exact f_subset_f le_rfl hnm
+      · intro n; exact hf _ _
+      · intro n m hnm; exact f_subset_f le_rfl hnm
     refine' ge_of_tendsto this (eventually_at_top.2 ⟨m, fun n hmn => _⟩)
     change γ - 2 * (1 / 2) ^ m ≤ d (f m n)
     refine' le_trans _ (le_d_f _ _ hmn)

781cb2ee

bump to nightly-2023-05-16-16

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

9cb92e8c

Diff

@@ -40,7 +40,7 @@ variable {α : Type _} [MeasurableSpace α] {μ ν : Measure α}
 
 /- warning: measure_theory.hahn_decomposition -> MeasureTheory.hahn_decomposition is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {ν : MeasureTheory.Measure.{u1} α _inst_1} [_inst_2 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 μ] [_inst_3 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 ν], Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (MeasurableSet.{u1} α _inst_1 s) (And (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (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) ν t) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) μ t))) (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s)) -> (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) μ t) (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) ν t)))))
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {ν : MeasureTheory.Measure.{u1} α _inst_1} [_inst_2 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 μ] [_inst_3 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 ν], Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (MeasurableSet.{u1} α _inst_1 s) (And (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (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) ν t) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) μ t))) (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s)) -> (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) μ t) (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) ν t)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {ν : MeasureTheory.Measure.{u1} α _inst_1} [_inst_2 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 μ] [_inst_3 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 ν], Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (MeasurableSet.{u1} α _inst_1 s) (And (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) -> (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 ν) t) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) t))) (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) s)) -> (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 μ) t) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 ν) t)))))
 Case conversion may be inaccurate. Consider using '#align measure_theory.hahn_decomposition MeasureTheory.hahn_decompositionₓ'. -/

781cb2ee

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -95,12 +95,12 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     rw [NNReal.coe_le_coe, ← ENNReal.coe_le_coe, to_nnreal_μ, to_nnreal_μ]
     exact measure_mono (subset_univ _)
   have c_nonempty : c.nonempty := nonempty.image _ ⟨_, MeasurableSet.empty⟩
-  have d_le_γ : ∀ s, MeasurableSet s → d s ≤ γ := fun s hs => le_csupₛ bdd_c ⟨s, hs, rfl⟩
+  have d_le_γ : ∀ s, MeasurableSet s → d s ≤ γ := fun s hs => le_csSup bdd_c ⟨s, hs, rfl⟩
   have : ∀ n : ℕ, ∃ s : Set α, MeasurableSet s ∧ γ - (1 / 2) ^ n < d s :=
     by
     intro n
     have : γ - (1 / 2) ^ n < γ := sub_lt_self γ (pow_pos (half_pos zero_lt_one) n)
-    rcases exists_lt_of_lt_csupₛ c_nonempty this with ⟨r, ⟨s, hs, rfl⟩, hlt⟩
+    rcases exists_lt_of_lt_csSup c_nonempty this with ⟨r, ⟨s, hs, rfl⟩, hlt⟩
     exact ⟨s, hs, hlt⟩
   rcases Classical.axiom_of_choice this with ⟨e, he⟩
   change ℕ → Set α at e
@@ -109,13 +109,13 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
   let f : ℕ → ℕ → Set α := fun n m => (Finset.Ico n (m + 1)).inf e
   have hf : ∀ n m, MeasurableSet (f n m) := by
     intro n m
-    simp only [f, Finset.inf_eq_infᵢ]
-    exact MeasurableSet.binterᵢ (to_countable _) fun i _ => he₁ _
+    simp only [f, Finset.inf_eq_iInf]
+    exact MeasurableSet.biInter (to_countable _) fun i _ => he₁ _
   have f_subset_f : ∀ {a b c d}, a ≤ b → c ≤ d → f a d ⊆ f b c :=
     by
     intro a b c d hab hcd
     dsimp only [f]
-    rw [Finset.inf_eq_infᵢ, Finset.inf_eq_infᵢ]
+    rw [Finset.inf_eq_iInf, Finset.inf_eq_iInf]
     exact bInter_subset_bInter_left (Finset.Ico_subset_Ico hab <| Nat.succ_le_succ hcd)
   have f_succ : ∀ n m, n ≤ m → f n (m + 1) = f n m ∩ e (m + 1) :=
     by
@@ -184,7 +184,7 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     change γ - 2 * (1 / 2) ^ m ≤ d (f m n)
     refine' le_trans _ (le_d_f _ _ hmn)
     exact le_add_of_le_of_nonneg le_rfl (pow_nonneg (le_of_lt <| half_pos <| zero_lt_one) _)
-  have hs : MeasurableSet s := MeasurableSet.unionᵢ fun n => MeasurableSet.interᵢ fun m => hf _ _
+  have hs : MeasurableSet s := MeasurableSet.iUnion fun n => MeasurableSet.iInter fun m => hf _ _
   refine' ⟨s, hs, _, _⟩
   · intro t ht hts
     have : 0 ≤ d t :=

781cb2ee

bump to nightly-2023-05-12-06

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

c1990cb3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module measure_theory.decomposition.unsigned_hahn
-! leanprover-community/mathlib commit 0f1becb755b3d008b242c622e248a70556ad19e6
+! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.MeasureTheory.Measure.MeasureSpace
 /-!
 # Unsigned Hahn decomposition theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves the unsigned version of the Hahn decomposition theorem.
 
 ## Main statements

0f1becb7

bump to nightly-2023-05-12-04

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

a0458e84

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module measure_theory.decomposition.unsigned_hahn
-! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
+! leanprover-community/mathlib commit 0f1becb755b3d008b242c622e248a70556ad19e6
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,9 +13,6 @@ import Mathbin.MeasureTheory.Measure.MeasureSpace
 /-!
 # Unsigned Hahn decomposition theorem
 
-> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
-> Any changes to this file require a corresponding PR to mathlib4.
-
 This file proves the unsigned version of the Hahn decomposition theorem.
 
 ## Main statements

781cb2ee

bump to nightly-2023-05-12-02

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

de75b5e2

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 
 ! This file was ported from Lean 3 source module measure_theory.decomposition.unsigned_hahn
-! leanprover-community/mathlib commit 0f1becb755b3d008b242c622e248a70556ad19e6
+! leanprover-community/mathlib commit 781cb2eed038c4caf53bdbd8d20a95e5822d77df
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.MeasureTheory.Measure.MeasureSpace
 /-!
 # Unsigned Hahn decomposition theorem
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file proves the unsigned version of the Hahn decomposition theorem.
 
 ## Main statements

0f1becb7

bump to nightly-2023-05-10-16

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

7e7f42b6

Diff

@@ -35,6 +35,12 @@ namespace MeasureTheory
 
 variable {α : Type _} [MeasurableSpace α] {μ ν : Measure α}
 
+/- warning: measure_theory.hahn_decomposition -> MeasureTheory.hahn_decomposition is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {ν : MeasureTheory.Measure.{u1} α _inst_1} [_inst_2 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 μ] [_inst_3 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 ν], Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (MeasurableSet.{u1} α _inst_1 s) (And (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) -> (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) ν t) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_1) (fun (_x : MeasureTheory.Measure.{u1} α _inst_1) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_1) μ t))) (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s)) -> (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) μ t) (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) ν t)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MeasurableSpace.{u1} α] {μ : MeasureTheory.Measure.{u1} α _inst_1} {ν : MeasureTheory.Measure.{u1} α _inst_1} [_inst_2 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 μ] [_inst_3 : MeasureTheory.FiniteMeasure.{u1} α _inst_1 ν], Exists.{succ u1} (Set.{u1} α) (fun (s : Set.{u1} α) => And (MeasurableSet.{u1} α _inst_1 s) (And (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) -> (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 ν) t) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 μ) t))) (forall (t : Set.{u1} α), (MeasurableSet.{u1} α _inst_1 t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t (HasCompl.compl.{u1} (Set.{u1} α) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} α) (Set.instBooleanAlgebraSet.{u1} α)) s)) -> (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 μ) t) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_1 ν) t)))))
+Case conversion may be inaccurate. Consider using '#align measure_theory.hahn_decomposition MeasureTheory.hahn_decompositionₓ'. -/
 /-- **Hahn decomposition theorem** -/
 theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     ∃ s,

0f1becb7

bump to nightly-2023-05-09-08

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

244524af

Diff

@@ -36,7 +36,7 @@ namespace MeasureTheory
 variable {α : Type _} [MeasurableSpace α] {μ ν : Measure α}
 
 /-- **Hahn decomposition theorem** -/
-theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
+theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     ∃ s,
       MeasurableSet s ∧
         (∀ t, MeasurableSet t → t ⊆ s → ν t ≤ μ t) ∧ ∀ t, MeasurableSet t → t ⊆ sᶜ → μ t ≤ ν t :=

0f1becb7

bump to nightly-2023-03-11-16

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

cd44fb92

Diff

@@ -152,7 +152,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     have hγ : tendsto (fun m : ℕ => γ - 2 * (1 / 2) ^ m) at_top (𝓝 γ) :=
       by
       suffices tendsto (fun m : ℕ => γ - 2 * (1 / 2) ^ m) at_top (𝓝 (γ - 2 * 0)) by
-        simpa only [mul_zero, tsub_zero]
+        simpa only [MulZeroClass.mul_zero, tsub_zero]
       exact
         tendsto_const_nhds.sub <|
           tendsto_const_nhds.mul <|

0f1becb7

bump to nightly-2023-03-01-20

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

20cadee0

Diff

@@ -134,7 +134,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
             linarith
           _ = γ - (1 / 2) ^ (n + 1) + (γ - 2 * (1 / 2) ^ m + (1 / 2) ^ n) := by
             simp only [sub_eq_add_neg] <;> abel
-          _ ≤ d (e (n + 1)) + d (f m n) := add_le_add (le_of_lt <| he₂ _) ih
+          _ ≤ d (e (n + 1)) + d (f m n) := (add_le_add (le_of_lt <| he₂ _) ih)
           _ ≤ d (e (n + 1)) + d (f m n \ e (n + 1)) + d (f m (n + 1)) := by
             rw [f_succ _ _ hmn, d_split (f m n) (e (n + 1)) (hf _ _) (he₁ _), add_assoc]
           _ = d (e (n + 1) ∪ f m n) + d (f m (n + 1)) :=

0f1becb7

bump to nightly-2023-02-27-10

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

49ff026a

Diff

@@ -29,7 +29,7 @@ Hahn decomposition
 
 open Set Filter
 
-open Classical Topology Ennreal
+open Classical Topology ENNReal
 
 namespace MeasureTheory
 
@@ -46,8 +46,8 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
   let γ : ℝ := Sup c
   have hμ : ∀ s, μ s ≠ ∞ := measure_ne_top μ
   have hν : ∀ s, ν s ≠ ∞ := measure_ne_top ν
-  have to_nnreal_μ : ∀ s, ((μ s).toNNReal : ℝ≥0∞) = μ s := fun s => Ennreal.coe_toNnreal <| hμ _
-  have to_nnreal_ν : ∀ s, ((ν s).toNNReal : ℝ≥0∞) = ν s := fun s => Ennreal.coe_toNnreal <| hν _
+  have to_nnreal_μ : ∀ s, ((μ s).toNNReal : ℝ≥0∞) = μ s := fun s => ENNReal.coe_toNNReal <| hμ _
+  have to_nnreal_ν : ∀ s, ((ν s).toNNReal : ℝ≥0∞) = ν s := fun s => ENNReal.coe_toNNReal <| hν _
   have d_empty : d ∅ = 0 := by
     change _ - _ = _
     rw [measure_empty, measure_empty, sub_self]
@@ -56,7 +56,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     intro s t hs ht
     simp only [d]
     rw [← measure_inter_add_diff s ht, ← measure_inter_add_diff s ht,
-      Ennreal.toNnreal_add (hμ _) (hμ _), Ennreal.toNnreal_add (hν _) (hν _), NNReal.coe_add,
+      ENNReal.toNNReal_add (hμ _) (hμ _), ENNReal.toNNReal_add (hν _) (hν _), NNReal.coe_add,
       NNReal.coe_add]
     simp only [sub_eq_add_neg, neg_add]
     abel
@@ -65,7 +65,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     by
     intro s hm
     refine' tendsto.sub _ _ <;>
-      refine' NNReal.tendsto_coe.2 <| (Ennreal.tendsto_toNnreal _).comp <| tendsto_measure_Union hm
+      refine' NNReal.tendsto_coe.2 <| (ENNReal.tendsto_toNNReal _).comp <| tendsto_measure_Union hm
     exact hμ _
     exact hν _
   have d_Inter :
@@ -77,13 +77,13 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     refine' tendsto.sub _ _ <;>
       refine'
         NNReal.tendsto_coe.2 <|
-          (Ennreal.tendsto_toNnreal <| _).comp <| tendsto_measure_Inter hs hm _
+          (ENNReal.tendsto_toNNReal <| _).comp <| tendsto_measure_Inter hs hm _
     exacts[hμ _, ⟨0, hμ _⟩, hν _, ⟨0, hν _⟩]
   have bdd_c : BddAbove c := by
     use (μ univ).toNNReal
     rintro r ⟨s, hs, rfl⟩
     refine' le_trans (sub_le_self _ <| NNReal.coe_nonneg _) _
-    rw [NNReal.coe_le_coe, ← Ennreal.coe_le_coe, to_nnreal_μ, to_nnreal_μ]
+    rw [NNReal.coe_le_coe, ← ENNReal.coe_le_coe, to_nnreal_μ, to_nnreal_μ]
     exact measure_mono (subset_univ _)
   have c_nonempty : c.nonempty := nonempty.image _ ⟨_, MeasurableSet.empty⟩
   have d_le_γ : ∀ s, MeasurableSet s → d s ≤ γ := fun s hs => le_csupₛ bdd_c ⟨s, hs, rfl⟩
@@ -185,7 +185,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
           _ = d (s \ t) + d t := by rw [d_split _ _ hs ht, inter_eq_self_of_subset_right hts]
           _ ≤ γ + d t := add_le_add (d_le_γ _ (hs.diff ht)) le_rfl
           
-    rw [← to_nnreal_μ, ← to_nnreal_ν, Ennreal.coe_le_coe, ← NNReal.coe_le_coe]
+    rw [← to_nnreal_μ, ← to_nnreal_ν, ENNReal.coe_le_coe, ← NNReal.coe_le_coe]
     simpa only [d, le_sub_iff_add_le, zero_add] using this
   · intro t ht hts
     have : d t ≤ 0 :=
@@ -197,7 +197,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
               (subset_compl_iff_disjoint_left.1 hts).sdiff_eq_left]
           _ ≤ γ + 0 := by rw [add_zero] <;> exact d_le_γ _ (hs.union ht)
           
-    rw [← to_nnreal_μ, ← to_nnreal_ν, Ennreal.coe_le_coe, ← NNReal.coe_le_coe]
+    rw [← to_nnreal_μ, ← to_nnreal_ν, ENNReal.coe_le_coe, ← NNReal.coe_le_coe]
     simpa only [d, sub_le_iff_le_add, zero_add] using this
 #align measure_theory.hahn_decomposition MeasureTheory.hahn_decomposition

0f1becb7

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

0f1becb7

chore: adapt to multiple goal linter 1 (#12338)

A PR accompanying #12339.

Zulip discussion

45f93f3f

Diff

@@ -58,8 +58,8 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     intro s hm
     refine' Tendsto.sub _ _ <;>
       refine' NNReal.tendsto_coe.2 <| (ENNReal.tendsto_toNNReal _).comp <| tendsto_measure_iUnion hm
-    exact hμ _
-    exact hν _
+    · exact hμ _
+    · exact hν _
   have d_Inter :
     ∀ s : ℕ → Set α,
       (∀ n, MeasurableSet (s n)) →
@@ -122,9 +122,9 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
             rw [f_succ _ _ hmn, d_split (f m n) (e (n + 1)) (hf _ _) (he₁ _), add_assoc]
           _ = d (e (n + 1) ∪ f m n) + d (f m (n + 1)) := by
             rw [d_split (e (n + 1) ∪ f m n) (e (n + 1)), union_diff_left, union_inter_cancel_left]
-            abel
-            exact (he₁ _).union (hf _ _)
-            exact he₁ _
+            · abel
+            · exact (he₁ _).union (hf _ _)
+            · exact he₁ _
           _ ≤ γ + d (f m (n + 1)) := add_le_add_right (d_le_γ _ <| (he₁ _).union (hf _ _)) _
 
       exact (add_le_add_iff_left γ).1 this

0f1becb7

chore: superfluous parentheses part 2 (#12131)

Co-authored-by: Moritz Firsching <firsching@google.com>

d48d30ac

Diff

@@ -117,7 +117,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
             linarith
           _ = γ - (1 / 2) ^ (n + 1) + (γ - 2 * (1 / 2) ^ m + (1 / 2) ^ n) := by
             simp only [sub_eq_add_neg]; abel
-          _ ≤ d (e (n + 1)) + d (f m n) := (add_le_add (le_of_lt <| he₂ _) ih)
+          _ ≤ d (e (n + 1)) + d (f m n) := add_le_add (le_of_lt <| he₂ _) ih
           _ ≤ d (e (n + 1)) + d (f m n \ e (n + 1)) + d (f m (n + 1)) := by
             rw [f_succ _ _ hmn, d_split (f m n) (e (n + 1)) (hf _ _) (he₁ _), add_assoc]
           _ = d (e (n + 1) ∪ f m n) + d (f m (n + 1)) := by

0f1becb7

chore: scope open Classical (#11199)

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.

c747be0a

Diff

@@ -26,7 +26,8 @@ Hahn decomposition
 
 open Set Filter
 
-open Classical Topology ENNReal
+open scoped Classical
+open Topology ENNReal
 
 namespace MeasureTheory

0f1becb7

chore: move Mathlib to v4.7.0-rc1 (#11162)

This is a very large PR, but it has been reviewed piecemeal already in PRs to the bump/v4.7.0 branch as we update to intermediate nightlies.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: damiano <adomani@gmail.com>

fa48894a

Diff

@@ -46,7 +46,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
   have to_nnreal_ν : ∀ s, ((ν s).toNNReal : ℝ≥0∞) = ν s := fun s => ENNReal.coe_toNNReal <| hν _
   have d_split : ∀ s t, MeasurableSet s → MeasurableSet t → d s = d (s \ t) + d (s ∩ t) := by
     intro s t _hs ht
-    dsimp only
+    dsimp only [d]
     rw [← measure_inter_add_diff s ht, ← measure_inter_add_diff s ht,
       ENNReal.toNNReal_add (hμ _) (hμ _), ENNReal.toNNReal_add (hν _) (hν _), NNReal.coe_add,
       NNReal.coe_add]
@@ -89,22 +89,22 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
   let f : ℕ → ℕ → Set α := fun n m => (Finset.Ico n (m + 1)).inf e
   have hf : ∀ n m, MeasurableSet (f n m) := by
     intro n m
-    simp only [Finset.inf_eq_iInf]
+    simp only [f, Finset.inf_eq_iInf]
     exact MeasurableSet.biInter (to_countable _) fun i _ => he₁ _
   have f_subset_f : ∀ {a b c d}, a ≤ b → c ≤ d → f a d ⊆ f b c := by
     intro a b c d hab hcd
-    simp_rw [Finset.inf_eq_iInf]
+    simp_rw [f, Finset.inf_eq_iInf]
     exact biInter_subset_biInter_left (Finset.Ico_subset_Ico hab <| Nat.succ_le_succ hcd)
   have f_succ : ∀ n m, n ≤ m → f n (m + 1) = f n m ∩ e (m + 1) := by
     intro n m hnm
     have : n ≤ m + 1 := le_of_lt (Nat.succ_le_succ hnm)
-    simp_rw [Nat.Ico_succ_right_eq_insert_Ico this, Finset.inf_insert, Set.inter_comm]
+    simp_rw [f, Nat.Ico_succ_right_eq_insert_Ico this, Finset.inf_insert, Set.inter_comm]
     rfl
   have le_d_f : ∀ n m, m ≤ n → γ - 2 * (1 / 2) ^ m + (1 / 2) ^ n ≤ d (f m n) := by
     intro n m h
     refine' Nat.le_induction _ _ n h
     · have := he₂ m
-      simp_rw [Nat.Ico_succ_singleton, Finset.inf_singleton]
+      simp_rw [f, Nat.Ico_succ_singleton, Finset.inf_singleton]
       linarith
     · intro n (hmn : m ≤ n) ih
       have : γ + (γ - 2 * (1 / 2) ^ m + (1 / 2) ^ (n + 1)) ≤ γ + d (f m (n + 1)) := by
@@ -163,7 +163,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
           _ ≤ γ + d t := add_le_add (d_le_γ _ (hs.diff ht)) le_rfl
 
     rw [← to_nnreal_μ, ← to_nnreal_ν, ENNReal.coe_le_coe, ← NNReal.coe_le_coe]
-    simpa only [le_sub_iff_add_le, zero_add] using this
+    simpa only [d, le_sub_iff_add_le, zero_add] using this
   · intro t ht hts
     have : d t ≤ 0 :=
       (add_le_add_iff_left γ).1 <|
@@ -175,7 +175,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
           _ ≤ γ + 0 := by rw [add_zero]; exact d_le_γ _ (hs.union ht)
 
     rw [← to_nnreal_μ, ← to_nnreal_ν, ENNReal.coe_le_coe, ← NNReal.coe_le_coe]
-    simpa only [sub_le_iff_le_add, zero_add] using this
+    simpa only [d, sub_le_iff_le_add, zero_add] using this
 #align measure_theory.hahn_decomposition MeasureTheory.hahn_decomposition
 
 end MeasureTheory

0f1becb7

chore(Analysis/SpecificLimits/* and others): rename _0 -> _zero, _1 -> _one (#10077)

See here on Zulip.

This PR changes a bunch of names containing nhds_0 or/and lt_1 to nhds_zero or/and lt_one.

4e65ea9e

Diff

@@ -135,7 +135,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
       exact
         tendsto_const_nhds.sub <|
           tendsto_const_nhds.mul <|
-            tendsto_pow_atTop_nhds_0_of_lt_1 (le_of_lt <| half_pos <| zero_lt_one)
+            tendsto_pow_atTop_nhds_zero_of_lt_one (le_of_lt <| half_pos <| zero_lt_one)
               (half_lt_self zero_lt_one)
     have hd : Tendsto (fun m => d (⋂ n, f m n)) atTop (𝓝 (d (⋃ m, ⋂ n, f m n))) := by
       refine' d_Union _ _

0f1becb7

chore: split MeasureSpace.lean into 3 files (#8389)

The original file MeasureSpace.lean is a mess of 4580 lines, with a lot of changes of namespaces, active variables, and so on. We split it into three files:

MeasureSpace, with 2095 lines left (some stuff could still be moved to other files, but it already makes much more sense)
Restrict, with everything on restriction of measures (1100 lines)
Typeclasses, defining finite measures, sigma-finite measures, and so on (1443 lines)

The new files are still large, but less so. This is 99% moving around and ensuring that variables and namespaces remain the same (#align statements have been very useful for this), and 1% adding classical in proofs and [Decidable ...] assumptions in statements, as I haven't opened Classical in the new files.

5c9c13df

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
 -/
-import Mathlib.MeasureTheory.Measure.MeasureSpace
+import Mathlib.MeasureTheory.Measure.Typeclasses
 
 #align_import measure_theory.decomposition.unsigned_hahn from "leanprover-community/mathlib"@"0f1becb755b3d008b242c622e248a70556ad19e6"

0f1becb7

chore: cleanup some spaces (#7490)

Purely cosmetic PR

39a866a8

Diff

@@ -106,7 +106,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     · have := he₂ m
       simp_rw [Nat.Ico_succ_singleton, Finset.inf_singleton]
       linarith
-    · intro n(hmn : m ≤ n)ih
+    · intro n (hmn : m ≤ n) ih
       have : γ + (γ - 2 * (1 / 2) ^ m + (1 / 2) ^ (n + 1)) ≤ γ + d (f m (n + 1)) := by
         calc
           γ + (γ - 2 * (1 / 2) ^ m + (1 / 2) ^ (n + 1)) ≤

0f1becb7

chore: drop MulZeroClass. in mul_zero/zero_mul (#6682)

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

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

277dea95

Diff

@@ -131,7 +131,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
   have γ_le_d_s : γ ≤ d s := by
     have hγ : Tendsto (fun m : ℕ => γ - 2 * (1 / 2) ^ m) atTop (𝓝 γ) := by
       suffices Tendsto (fun m : ℕ => γ - 2 * (1 / 2) ^ m) atTop (𝓝 (γ - 2 * 0)) by
-        simpa only [MulZeroClass.mul_zero, tsub_zero]
+        simpa only [mul_zero, tsub_zero]
       exact
         tendsto_const_nhds.sub <|
           tendsto_const_nhds.mul <|

0f1becb7

chore: remove unused simps (#6632)

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

916c75c1

Diff

@@ -93,7 +93,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     exact MeasurableSet.biInter (to_countable _) fun i _ => he₁ _
   have f_subset_f : ∀ {a b c d}, a ≤ b → c ≤ d → f a d ⊆ f b c := by
     intro a b c d hab hcd
-    simp_rw [Finset.inf_eq_iInf, Finset.inf_eq_iInf]
+    simp_rw [Finset.inf_eq_iInf]
     exact biInter_subset_biInter_left (Finset.Ico_subset_Ico hab <| Nat.succ_le_succ hcd)
   have f_succ : ∀ n m, n ≤ m → f n (m + 1) = f n m ∩ e (m + 1) := by
     intro n m hnm

0f1becb7

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -30,7 +30,7 @@ open Classical Topology ENNReal
 
 namespace MeasureTheory
 
-variable {α : Type _} [MeasurableSpace α] {μ ν : Measure α}
+variable {α : Type*} [MeasurableSpace α] {μ ν : Measure α}
 
 /-- **Hahn decomposition theorem** -/
 theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :

0f1becb7

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2019 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl
-
-! This file was ported from Lean 3 source module measure_theory.decomposition.unsigned_hahn
-! leanprover-community/mathlib commit 0f1becb755b3d008b242c622e248a70556ad19e6
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Measure.MeasureSpace
 
+#align_import measure_theory.decomposition.unsigned_hahn from "leanprover-community/mathlib"@"0f1becb755b3d008b242c622e248a70556ad19e6"
+
 /-!
 # Unsigned Hahn decomposition theorem

0f1becb7

chore: remove occurrences of semicolon after space (#5713)

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

c795bd35

Diff

@@ -118,7 +118,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
             simp only [pow_add, pow_one, le_sub_iff_add_le]
             linarith
           _ = γ - (1 / 2) ^ (n + 1) + (γ - 2 * (1 / 2) ^ m + (1 / 2) ^ n) := by
-            simp only [sub_eq_add_neg] ; abel
+            simp only [sub_eq_add_neg]; abel
           _ ≤ d (e (n + 1)) + d (f m n) := (add_le_add (le_of_lt <| he₂ _) ih)
           _ ≤ d (e (n + 1)) + d (f m n \ e (n + 1)) + d (f m (n + 1)) := by
             rw [f_succ _ _ hmn, d_split (f m n) (e (n + 1)) (hf _ _) (he₁ _), add_assoc]
@@ -161,7 +161,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     have : 0 ≤ d t :=
       (add_le_add_iff_left γ).1 <|
         calc
-          γ + 0 ≤ d s := by rw [add_zero] ; exact γ_le_d_s
+          γ + 0 ≤ d s := by rw [add_zero]; exact γ_le_d_s
           _ = d (s \ t) + d t := by rw [d_split _ _ hs ht, inter_eq_self_of_subset_right hts]
           _ ≤ γ + d t := add_le_add (d_le_γ _ (hs.diff ht)) le_rfl
 
@@ -175,7 +175,7 @@ theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
           _ = d (s ∪ t) := by
             rw [d_split _ _ (hs.union ht) ht, union_diff_right, union_inter_cancel_right,
               (subset_compl_iff_disjoint_left.1 hts).sdiff_eq_left]
-          _ ≤ γ + 0 := by rw [add_zero] ; exact d_le_γ _ (hs.union ht)
+          _ ≤ γ + 0 := by rw [add_zero]; exact d_le_γ _ (hs.union ht)
 
     rw [← to_nnreal_μ, ← to_nnreal_ν, ENNReal.coe_le_coe, ← NNReal.coe_le_coe]
     simpa only [sub_le_iff_le_add, zero_add] using this

0f1becb7

style: recover Is of Foo which is ported from is_foo (#4639)

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.

0b92c7b7

Diff

@@ -36,7 +36,7 @@ namespace MeasureTheory
 variable {α : Type _} [MeasurableSpace α] {μ ν : Measure α}
 
 /-- **Hahn decomposition theorem** -/
-theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
+theorem hahn_decomposition [IsFiniteMeasure μ] [IsFiniteMeasure ν] :
     ∃ s,
       MeasurableSet s ∧
         (∀ t, MeasurableSet t → t ⊆ s → ν t ≤ μ t) ∧ ∀ t, MeasurableSet t → t ⊆ sᶜ → μ t ≤ ν t := by

0f1becb7

chore: Rename to sSup/iSup (#3938)

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>

d1eb6264

Diff

@@ -42,7 +42,7 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
         (∀ t, MeasurableSet t → t ⊆ s → ν t ≤ μ t) ∧ ∀ t, MeasurableSet t → t ⊆ sᶜ → μ t ≤ ν t := by
   let d : Set α → ℝ := fun s => ((μ s).toNNReal : ℝ) - (ν s).toNNReal
   let c : Set ℝ := d '' { s | MeasurableSet s }
-  let γ : ℝ := supₛ c
+  let γ : ℝ := sSup c
   have hμ : ∀ s, μ s ≠ ∞ := measure_ne_top μ
   have hν : ∀ s, ν s ≠ ∞ := measure_ne_top ν
   have to_nnreal_μ : ∀ s, ((μ s).toNNReal : ℝ≥0∞) = μ s := fun s => ENNReal.coe_toNNReal <| hμ _
@@ -59,7 +59,7 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     ∀ s : ℕ → Set α, Monotone s → Tendsto (fun n => d (s n)) atTop (𝓝 (d (⋃ n, s n))) := by
     intro s hm
     refine' Tendsto.sub _ _ <;>
-      refine' NNReal.tendsto_coe.2 <| (ENNReal.tendsto_toNNReal _).comp <| tendsto_measure_unionᵢ hm
+      refine' NNReal.tendsto_coe.2 <| (ENNReal.tendsto_toNNReal _).comp <| tendsto_measure_iUnion hm
     exact hμ _
     exact hν _
   have d_Inter :
@@ -70,7 +70,7 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     refine' Tendsto.sub _ _ <;>
       refine'
         NNReal.tendsto_coe.2 <|
-          (ENNReal.tendsto_toNNReal <| _).comp <| tendsto_measure_interᵢ hs hm _
+          (ENNReal.tendsto_toNNReal <| _).comp <| tendsto_measure_iInter hs hm _
     exacts [hμ _, ⟨0, hμ _⟩, hν _, ⟨0, hν _⟩]
   have bdd_c : BddAbove c := by
     use (μ univ).toNNReal
@@ -79,11 +79,11 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     rw [NNReal.coe_le_coe, ← ENNReal.coe_le_coe, to_nnreal_μ, to_nnreal_μ]
     exact measure_mono (subset_univ _)
   have c_nonempty : c.Nonempty := Nonempty.image _ ⟨_, MeasurableSet.empty⟩
-  have d_le_γ : ∀ s, MeasurableSet s → d s ≤ γ := fun s hs => le_csupₛ bdd_c ⟨s, hs, rfl⟩
+  have d_le_γ : ∀ s, MeasurableSet s → d s ≤ γ := fun s hs => le_csSup bdd_c ⟨s, hs, rfl⟩
   have : ∀ n : ℕ, ∃ s : Set α, MeasurableSet s ∧ γ - (1 / 2) ^ n < d s := by
     intro n
     have : γ - (1 / 2) ^ n < γ := sub_lt_self γ (pow_pos (half_pos zero_lt_one) n)
-    rcases exists_lt_of_lt_csupₛ c_nonempty this with ⟨r, ⟨s, hs, rfl⟩, hlt⟩
+    rcases exists_lt_of_lt_csSup c_nonempty this with ⟨r, ⟨s, hs, rfl⟩, hlt⟩
     exact ⟨s, hs, hlt⟩
   rcases Classical.axiom_of_choice this with ⟨e, he⟩
   change ℕ → Set α at e
@@ -92,12 +92,12 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
   let f : ℕ → ℕ → Set α := fun n m => (Finset.Ico n (m + 1)).inf e
   have hf : ∀ n m, MeasurableSet (f n m) := by
     intro n m
-    simp only [Finset.inf_eq_infᵢ]
-    exact MeasurableSet.binterᵢ (to_countable _) fun i _ => he₁ _
+    simp only [Finset.inf_eq_iInf]
+    exact MeasurableSet.biInter (to_countable _) fun i _ => he₁ _
   have f_subset_f : ∀ {a b c d}, a ≤ b → c ≤ d → f a d ⊆ f b c := by
     intro a b c d hab hcd
-    simp_rw [Finset.inf_eq_infᵢ, Finset.inf_eq_infᵢ]
-    exact binterᵢ_subset_binterᵢ_left (Finset.Ico_subset_Ico hab <| Nat.succ_le_succ hcd)
+    simp_rw [Finset.inf_eq_iInf, Finset.inf_eq_iInf]
+    exact biInter_subset_biInter_left (Finset.Ico_subset_Ico hab <| Nat.succ_le_succ hcd)
   have f_succ : ∀ n m, n ≤ m → f n (m + 1) = f n m ∩ e (m + 1) := by
     intro n m hnm
     have : n ≤ m + 1 := le_of_lt (Nat.succ_le_succ hnm)
@@ -143,7 +143,7 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     have hd : Tendsto (fun m => d (⋂ n, f m n)) atTop (𝓝 (d (⋃ m, ⋂ n, f m n))) := by
       refine' d_Union _ _
       exact fun n m hnm =>
-        subset_interᵢ fun i => Subset.trans (interᵢ_subset (f n) i) <| f_subset_f hnm <| le_rfl
+        subset_iInter fun i => Subset.trans (iInter_subset (f n) i) <| f_subset_f hnm <| le_rfl
     refine' le_of_tendsto_of_tendsto' hγ hd fun m => _
     have : Tendsto (fun n => d (f m n)) atTop (𝓝 (d (⋂ n, f m n))) := by
       refine' d_Inter _ _ _
@@ -155,7 +155,7 @@ theorem hahn_decomposition [FiniteMeasure μ] [FiniteMeasure ν] :
     change γ - 2 * (1 / 2) ^ m ≤ d (f m n)
     refine' le_trans _ (le_d_f _ _ hmn)
     exact le_add_of_le_of_nonneg le_rfl (pow_nonneg (le_of_lt <| half_pos <| zero_lt_one) _)
-  have hs : MeasurableSet s := MeasurableSet.unionᵢ fun n => MeasurableSet.interᵢ fun m => hf _ _
+  have hs : MeasurableSet s := MeasurableSet.iUnion fun n => MeasurableSet.iInter fun m => hf _ _
   refine' ⟨s, hs, _, _⟩
   · intro t ht hts
     have : 0 ≤ d t :=

0f1becb7

feat port: MeasureTheory.Decomposition.UnsignedHahn (#3870)

Co-authored-by: Moritz Firsching <firsching@google.com>

48c42c3d

`measure_theory.decomposition.unsigned_hahn` ⟷ `Mathlib.MeasureTheory.Decomposition.UnsignedHahn`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 10 + 609

measure_theory.decomposition.unsigned_hahn ⟷ Mathlib.MeasureTheory.Decomposition.UnsignedHahn

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 10 + 609

`measure_theory.decomposition.unsigned_hahn` ⟷ `Mathlib.MeasureTheory.Decomposition.UnsignedHahn`