Theorems · Theorem · probability
PMF.toMeasure_map_apply
∀ {α : Type u_1} {β : Type u_2} (f : α → β) (p : PMF α) (s : Set β) {mα : MeasurableSpace α} {mβ : MeasurableSpace β},
Measurable f → MeasurableSet s → (PMF.map f p).toMeasure s = p.toMeasure (f ⁻¹' s)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 172 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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 · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.preimagestatement and proof · cited by 4,946
- MeasurableSetstatement and proof · cited by 3,075
- Measurablestatement and proof · cited by 1,499
- PMFstatement and proof · cited by 127
- PMF.toMeasurestatement and proof · cited by 34
- PMF.toOuterMeasureproof · cited by 26
- PMF.mapstatement and proof · cited by 16
Cited by1
Results whose statement or proof uses this declaration.
- PMF.toMeasure_mapproof · cited by 0