Theorems · Theorem · measure theory
MeasureTheory.exists_measure_pos_of_not_measure_iUnion_null
∀ {α : Type u_1} {ι : Sort u_5} [inst : MeasurableSpace α] {μ : MeasureTheory.Measure α} [Countable ι] {s : ι → Set α},
μ (⋃ n, s n) ≠ 0 → ∃ n, 0 < μ (s n)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpaceCountable
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.
- DFunLike.coestatement and proof · 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
- Set.iUnionstatement and proof · cited by 2,483
- Countablestatement and proof · cited by 633
- nonpos_iff_eq_zeroproof · cited by 100
- MeasureTheory.measure_iUnion_nullproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.exists_positive_of_not_mutuallySingularproof · cited by 1