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fix(OuterMeasure): drop an unused DecidablePred assumption (#9496)
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Also add 2 `@[gcongr]` attributes
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urkud committed Jan 8, 2024
1 parent 4fc93c2 commit 2357687
Showing 1 changed file with 4 additions and 3 deletions.
7 changes: 4 additions & 3 deletions Mathlib/MeasureTheory/Measure/OuterMeasure.lean
Expand Up @@ -91,6 +91,7 @@ theorem empty' (m : OuterMeasure α) : m ∅ = 0 :=
m.empty
#align measure_theory.outer_measure.empty' MeasureTheory.OuterMeasure.empty'

@[gcongr]
theorem mono' (m : OuterMeasure α) {s₁ s₂} (h : s₁ ⊆ s₂) : m s₁ ≤ m s₂ :=
m.mono h
#align measure_theory.outer_measure.mono' MeasureTheory.OuterMeasure.mono'
Expand Down Expand Up @@ -188,8 +189,8 @@ theorem iUnion_of_tendsto_zero {ι} (m : OuterMeasure α) {s : ι → Set α} (l
/-- If `s : ℕ → Set α` is a monotone sequence of sets such that `∑' k, m (s (k + 1) \ s k) ≠ ∞`,
then `m (⋃ n, s n) = ⨆ n, m (s n)`. -/
theorem iUnion_nat_of_monotone_of_tsum_ne_top (m : OuterMeasure α) {s : ℕ → Set α}
(h_mono : ∀ n, s n ⊆ s (n + 1)) (h0 : (∑' k, m (s (k + 1) \ s k)) ≠ ∞)
[∀ i:ℕ, DecidablePred (· ∈ s i)] : m (⋃ n, s n) = ⨆ n, m (s n) := by
(h_mono : ∀ n, s n ⊆ s (n + 1)) (h0 : (∑' k, m (s (k + 1) \ s k)) ≠ ∞) :
m (⋃ n, s n) = ⨆ n, m (s n) := by
refine' m.iUnion_of_tendsto_zero atTop _
refine' tendsto_nhds_bot_mono' (ENNReal.tendsto_sum_nat_add _ h0) fun n => _
refine' (m.mono _).trans (m.iUnion _)
Expand Down Expand Up @@ -427,7 +428,7 @@ theorem smul_iSup [SMul R ℝ≥0∞] [IsScalarTower R ℝ≥0∞ ℝ≥0∞] {

end Supremum

@[mono]
@[mono, gcongr]
theorem mono'' {m₁ m₂ : OuterMeasure α} {s₁ s₂ : Set α} (hm : m₁ ≤ m₂) (hs : s₁ ⊆ s₂) :
m₁ s₁ ≤ m₂ s₂ :=
(hm s₁).trans (m₂.mono hs)
Expand Down

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