Theorems · Definition · probability
PMF.toOuterMeasure
{α : Type u_1} → PMF α → MeasureTheory.OuterMeasure αConstruct an OuterMeasure from a PMF, by assigning measure to each set s : Set α equal
to the sum of p x for each x ∈ α.
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- MeasureTheory.OuterMeasurestatement · cited by 287
- PMFstatement and proof · cited by 127
- MeasureTheory.OuterMeasure.diracproof · cited by 7
- MeasureTheory.OuterMeasure.sumproof · cited by 5
Cited by27
Results whose statement or proof uses this declaration.
- PMF.toMeasureproof · cited by 34
- PMF.toOuterMeasure_applystatement · cited by 16
- PMF.toMeasure_apply_eq_toOuterMeasure_applystatement and proof · cited by 15
- PMF.toMeasure_apply_eq_toOuterMeasurestatement and proof · cited by 3
- PMF.toOuterMeasure_apply_inter_supportstatement · cited by 2
- PMF.toOuterMeasure_apply_singletonstatement · cited by 2
- PMF.toOuterMeasure_bind_applystatement · cited by 2
- PMF.toOuterMeasure_monostatement and proof · cited by 2
- PMF.toOuterMeasure_pure_applystatement · cited by 2
- PMF.toOuterMeasure_uniformOfFinset_applystatement · cited by 2
- PMF.toMeasure_map_applyproof · cited by 1
- PMF.toOuterMeasure_apply_eq_of_inter_support_eqstatement · cited by 1