Theorems · Theorem · measure theory
MeasureTheory.ProbabilityMeasure.apply_iUnion_le
∀ {Ω : Type u_1} [inst : MeasurableSpace Ω] {μ : MeasureTheory.ProbabilityMeasure Ω} {f : ℕ → Set Ω},
(Summable fun n => μ (f n)) → μ (⋃ n, f n) ≤ ∑' (n : ℕ), μ (f n)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 179 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
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Cites12
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
- NNRealstatement · cited by 4,310
- Set.iUnionstatement and proof · cited by 2,483
- SummationFilter.unconditionalstatement and proof · cited by 2,068
- tsumstatement and proof · cited by 1,148
- Summablestatement and proof · cited by 778
- MeasureTheory.ProbabilityMeasurestatement and proof · cited by 127
- MeasureTheory.measure_iUnion_leproof · cited by 39
- MeasureTheory.ProbabilityMeasure.ennreal_coeFn_eq_coeFn_toMeasureproof · cited by 8
- ENNReal.coe_tsumproof · cited by 7
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