Theorems · Theorem · probability
ProbabilityTheory.tsum_prob_mem_Ioi_lt_top
∀ {Ω : Type u_1} [inst : MeasureTheory.MeasureSpace Ω] [MeasureTheory.IsProbabilityMeasure MeasureTheory.volume]
{X : Ω → ℝ},
MeasureTheory.Integrable X MeasureTheory.volume → 0 ≤ X → ∑' (j : ℕ), MeasureTheory.volume {ω | X ω ∈ Set.Ioi ↑j} < ⊤- Defined in
- Mathlib.Probability.StrongLaw
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites41
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
- Realstatement and proof · cited by 25,697
- MeasureTheory.Measurestatement · cited by 10,939
- ENNRealstatement · cited by 9,879
- Top.topstatement · cited by 9,680
- Set.ofPredstatement and proof · cited by 6,101
- nhdsproof · cited by 5,554
- Finset.sumproof · cited by 5,195
- Filter.Tendstoproof · cited by 3,814
- LE.le.transproof · cited by 3,151
- Set.iUnionproof · cited by 2,483
Cited by1
Results whose statement or proof uses this declaration.
- ProbabilityTheory.strong_law_aux5proof · cited by 1