Theorems · Theorem · measure theory
Antitone.measure_iUnion
∀ {α : Type u_1} {ι : Type u_5} {m : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : Preorder ι]
[IsCodirectedOrder ι] [Filter.atBot.IsCountablyGenerated] {s : ι → Set α}, Antitone s → μ (⋃ i, s i) = ⨆ i, μ (s i)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- Preorderstatement and proof · cited by 7,952
- Set.iUnionstatement · cited by 2,483
- iSupstatement · cited by 2,415
- Antitonestatement and proof · cited by 563
- Filter.atBotstatement and proof · cited by 512
- Filter.IsCountablyGeneratedstatement and proof · cited by 220
- IsCodirectedOrderstatement and proof · cited by 95
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.