Theorems · Theorem · probability
PMF.toOuterMeasure_apply
∀ {α : Type u_1} (p : PMF α) (s : Set α), p.toOuterMeasure s = ∑' (x : α), s.indicator (⇑p) x- Cited by
- 16 results in Mathlib
- Foundations
- Depth 143 from the axioms · uses propext, Classical.choice, Quot.sound
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
- ENNRealstatement · cited by 9,879
- SummationFilter.unconditionalstatement · cited by 2,068
- tsumstatement · cited by 1,148
- Set.indicatorstatement · cited by 723
- MeasureTheory.OuterMeasurestatement · cited by 287
- PMFstatement and proof · cited by 127
- tsum_congrproof · cited by 64
- PMF.toOuterMeasurestatement · cited by 26
- MeasureTheory.OuterMeasure.smul_dirac_applyproof · cited by 1
Cited by16
Results whose statement or proof uses this declaration.
- PMF.toOuterMeasure_apply_inter_supportproof · cited by 2
- PMF.toOuterMeasure_apply_singletonproof · cited by 2
- PMF.toOuterMeasure_bind_applyproof · cited by 2
- PMF.toOuterMeasure_pure_applyproof · cited by 2
- PMF.toOuterMeasure_uniformOfFinset_applyproof · cited by 2
- PMF.toMeasure_applyproof · cited by 1
- PMF.toOuterMeasure_apply_eq_one_iffproof · cited by 1
- PMF.toOuterMeasure_apply_eq_zero_iffproof · cited by 1
- PMF.toOuterMeasure_apply_finsetproof · cited by 1
- PMF.toOuterMeasure_apply_fintypeproof · cited by 1
- PMF.toOuterMeasure_bindOnSupport_applyproof · cited by 1
- PMF.toOuterMeasure_map_applyproof · cited by 1