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Theorems · Theorem · probability

MeasureTheory.withDensity_pdf_le_map

∀ {Ω : Type u_1} {E : Type u_2} [inst : MeasurableSpace E] {x : MeasurableSpace Ω} (X : Ω → E)
  (ℙ : MeasureTheory.Measure Ω) (μ : autoParam (MeasureTheory.Measure E) MeasureTheory.withDensity_pdf_le_map._auto_1),
  μ.withDensity (MeasureTheory.pdf X ℙ μ) ≤ MeasureTheory.Measure.map X ℙ
Defined in
Mathlib.Probability.Density
Cited by
1 results in Mathlib
Foundations
Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace
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MeasureTheory.setLIntegral_pdf_le_map · cited by 0MeasureTheory.setLIntegra…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.Measure.map · cited by 858Measure.mapMeasureTheory.Measure.withDensity · cited by 265Measure.withDensityMeasureTheory.pdf · cited by 32MeasureTheory.pdfMeasureTheory.Measure.withDensity_rnDeriv_le · cited by 9Measure.withDensity_rnDer…MeasureTheory.withDensity_pdf…CITED BYCITES

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