Theorems · Theorem · measure theory
MeasurableSet.iInter_of_antitone
∀ {α : Type u_1} [inst : MeasurableSpace α] {ι : Type u_5} [inst_1 : Preorder ι] [IsDirectedOrder ι]
[Filter.atTop.IsCountablyGenerated] {s : ι → Set α},
Antitone s → (∀ (i : ι), MeasurableSet (s i)) → MeasurableSet (⋂ i, s i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- Preorderstatement and proof · cited by 7,952
- MeasurableSetstatement and proof · cited by 3,075
- Filter.atTopstatement and proof · cited by 2,405
- Set.iInterstatement · cited by 1,084
- Antitonestatement and proof · cited by 563
- IsDirectedOrderstatement and proof · cited by 316
- Filter.IsCountablyGeneratedstatement and proof · cited by 220
- MeasurableSet.complproof · cited by 172
- Set.compl_iInterproof · cited by 31
- Antitone.compproof · cited by 10
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.tendsto_setIntegral_of_antitoneproof · cited by 1