Theorems · Theorem · measure theory
MeasurableSet.iInter
∀ {α : Type u_1} {ι : Sort u_6} {m : MeasurableSpace α} [Countable ι] {f : ι → Set α},
(∀ (b : ι), MeasurableSet (f b)) → MeasurableSet (⋂ b, f b)- Cited by
- 31 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Countable
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
- Countablestatement and proof · cited by 633
- MeasurableSet.complproof · cited by 172
- MeasurableSet.iUnionproof · cited by 81
- Set.compl_iInterproof · cited by 31
- MeasurableSet.of_complproof · cited by 11
Cited by31
Results whose statement or proof uses this declaration.
- MeasureTheory.OuterMeasure.exists_measurable_superset_eq_trimproof · cited by 4
- NumberField.mixedEmbedding.measurableSet_plusPartproof · cited by 3
- MeasureTheory.OuterMeasure.exists_measurable_superset_forall_eq_trimproof · cited by 3
- AEMeasurable.sum_measureproof · cited by 3
- MeasurableSet.measurableSet_blimsupproof · cited by 2
- measurableSet_of_differentiableAt_of_isCompleteproof · cited by 2
- measurableSet_of_differentiableAt_of_isComplete_with_paramproof · cited by 2
- Measurable.liminf'proof · cited by 2
- MeasurableSpace.measurableSet_countablyGeneratedAtomproof · cited by 2
- measurableSet_of_differentiableWithinAt_Ici_of_isCompleteproof · cited by 2
- Measurable.forallproof · cited by 2
- measurableSet_tendstoproof · cited by 2