Theorems · Theorem · measure theory
MeasurableSet.biUnion
∀ {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
- 25 results in Mathlib
- Foundations
- Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Set.Elemproof · cited by 7,166
- MeasurableSetstatement and proof · cited by 3,075
- Set.iUnionstatement · cited by 2,483
- Countableproof · cited by 633
- Set.Countablestatement and proof · cited by 545
- MeasurableSet.iUnionproof · cited by 81
- Set.biUnion_eq_iUnionproof · cited by 41
- Set.Countable.to_subtypeproof · cited by 33
Cited by25
Results whose statement or proof uses this declaration.
- Set.Countable.measurableSetproof · cited by 14
- MeasurableSet.biInterproof · cited by 13
- borel_eq_generateFrom_Iioproof · cited by 6
- MeasurableSet.sUnionproof · cited by 5
- MeasureTheory.IsStoppingTime.measurableSet_eq_of_countable_rangeproof · cited by 4
- Dense.borel_eq_generateFrom_Ico_mem_auxproof · cited by 3
- Set.Finite.measurableSet_biUnionproof · cited by 3
- MeasureTheory.exists_decomposition_of_monotoneOn_hasDerivWithinAtproof · cited by 3
- Dense.borel_eq_generateFrom_Icc_mem_auxproof · cited by 2
- MeasureTheory.SimpleFunc.measurableSet_cutproof · cited by 2
- MeasureTheory.NullMeasurableSet.biUnionproof · cited by 1
- MeasureTheory.Measure.MeasureDense.of_generateFrom_isSetAlgebra_finiteproof · cited by 1