Theorems · Theorem · probability

MeasureTheory.pdf_of_not_haveLebesgueDecomposition

∀ {Ω : Type u_1} {E : Type u_2} [inst : MeasurableSpace E] {x : MeasurableSpace Ω} {ℙ : MeasureTheory.Measure Ω}
  {μ : MeasureTheory.Measure E} {X : Ω → E},
  ¬(MeasureTheory.Measure.map X ℙ).HaveLebesgueDecomposition μ → MeasureTheory.pdf X ℙ μ = 0

Defined in: Mathlib.Probability.Density
Cited by: 1 results in Mathlib
Foundations: Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement · cited by 9,879
MeasureTheory.Measure.mapstatement and proof · cited by 858
MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
MeasureTheory.pdfstatement · cited by 32
MeasureTheory.Measure.rnDeriv_of_not_haveLebesgueDecompositionproof · cited by 3

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.hasPDF_of_pdf_ne_zeroproof · cited by 0