Theorems · Theorem · measure theory
MeasureTheory.exists_pos_measure_of_cover
∀ {α : Type u_1} {ι : Type u_4} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} [Countable ι] {U : ι → Set α},
⋃ i, U i = Set.univ → μ ≠ 0 → ∃ i, 0 < μ (U i)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 198 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.
Cites11
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.univstatement and proof · cited by 3,945
- Set.iUnionstatement and proof · cited by 2,483
- Countablestatement and proof · cited by 633
- nonpos_iff_eq_zeroproof · cited by 100
- MeasureTheory.Measure.measure_univ_eq_zeroproof · cited by 26
- MeasureTheory.measure_iUnion_nullproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.exists_pos_preimage_ballproof · cited by 1