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Theorems · Theorem · probability

MeasureTheory.HasPDF.quasiMeasurePreserving_of_measurable

∀ {Ω : Type u_1} {E : Type u_2} [inst : MeasurableSpace E] {x : MeasurableSpace Ω} (X : Ω → E)
  (ℙ : MeasureTheory.Measure Ω) (μ : MeasureTheory.Measure E) [MeasureTheory.HasPDF X ℙ μ],
  Measurable X → MeasureTheory.Measure.QuasiMeasurePreserving X ℙ μ

A random variable that HasPDF is quasi-measure-preserving.

Defined in
Mathlib.Probability.Density
Cited by
0 results in Mathlib
Foundations
Depth 198 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpaceMeasureTheory.HasPDF
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MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasurable · cited by 1499MeasurableMeasureTheory.Measure.QuasiMeasurePreserving · cited by 101Measure.QuasiMeasurePrese…MeasureTheory.HasPDF · cited by 37MeasureTheory.HasPDFMeasureTheory.HasPDF.absolutelyContinuous · cited by 13HasPDF.absolutelyContinuo…HasPDF.quasiMeasurePreserving…CITED BYCITES

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