Theorems · Theorem · measure theory
MeasureTheory.isProbabilityMeasure_bind
∀ {α : Type u_1} {β : Type u_2} [inst : MeasurableSpace α] [inst_1 : MeasurableSpace β] {m : MeasureTheory.Measure α}
[MeasureTheory.IsProbabilityMeasure m] {f : α → MeasureTheory.Measure β},
AEMeasurable f m →
(∀ᵐ (μ : α) ∂m, MeasureTheory.IsProbabilityMeasure (f μ)) → MeasureTheory.IsProbabilityMeasure (m.bind f)- Cited by
- 0 results in Mathlib
- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Set.univproof · cited by 3,945
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasurableSetproof · cited by 3,075
- MeasureTheory.aestatement and proof · cited by 2,352
- AEMeasurablestatement and proof · cited by 840
- MeasureTheory.IsProbabilityMeasurestatement and proof · cited by 392
- MeasureTheory.Measure.bindstatement · cited by 173
- MeasureTheory.Measure.bind_applyproof · cited by 21
- MeasureTheory.lintegral_eq_constproof · cited by 3
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