Theorems · Theorem · measure theory
MeasurableSet.biInter
∀ {α : Type u_1} {β : Type u_2} {m : MeasurableSpace α} {f : β → Set α} {s : Set β},
s.Countable → (∀ b ∈ s, MeasurableSet (f b)) → MeasurableSet (⋂ b ∈ s, f b)- Cited by
- 13 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- MeasurableSetstatement and proof · cited by 3,075
- Set.iInterstatement · cited by 1,084
- Set.Countablestatement and proof · cited by 545
- MeasurableSet.complproof · cited by 172
- MeasurableSet.biUnionproof · cited by 25
- MeasurableSet.of_complproof · cited by 11
- Set.compl_iInter₂proof · cited by 5
Cited by13
Results whose statement or proof uses this declaration.
- MeasurableSet.piproof · cited by 14
- MeasureTheory.measurableSet_exists_tendstoproof · cited by 4
- MeasurableSet.sInterproof · cited by 4
- MeasurableSet.measurableAtom_of_countableproof · cited by 3
- measurableSet_tendstoproof · cited by 2
- MeasureTheory.hahn_decompositionproof · cited by 2
- MeasureTheory.NullMeasurableSet.biInterproof · cited by 2
- Set.Finite.measurableSet_biInterproof · cited by 2
- ProbabilityTheory.iCondIndepSets_iffproof · cited by 2
- MeasureTheory.IsStoppingTime.biInfproof · cited by 2
- MeasureTheory.aemeasurable_of_exist_almost_disjoint_supersetsproof · cited by 1
- MeasureTheory.AECover.biInter_Ici_aecoverproof · cited by 1