Theorems · Theorem · real analysis
BoxIntegral.Box.iUnion_Ioo_of_tendsto
∀ {ι : Type u_1} [Finite ι] {I : BoxIntegral.Box ι} {J : ℕ → BoxIntegral.Box ι},
Monotone J →
Filter.Tendsto (BoxIntegral.Box.lower ∘ J) Filter.atTop (nhds I.lower) →
Filter.Tendsto (BoxIntegral.Box.upper ∘ J) Filter.atTop (nhds I.upper) →
⋃ n, BoxIntegral.Box.Ioo (J n) = BoxIntegral.Box.Ioo I- Defined in
- Mathlib.Analysis.BoxIntegral.Box.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 124 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Finite
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Cites29
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- Filter.Tendstostatement and proof · cited by 3,814
- Finitestatement and proof · cited by 3,029
- Set.iUnionstatement · cited by 2,483
- Filter.atTopstatement and proof · cited by 2,405
- Monotonestatement and proof · cited by 1,397
- OrderHomstatement · cited by 934
- Antitoneproof · cited by 563
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