Theorems · Theorem · probability
MeasureTheory.aemeasurable_of_pdf_ne_zero
∀ {Ω : Type u_1} {E : Type u_2} [inst : MeasurableSpace E] {m : MeasurableSpace Ω} {ℙ : MeasureTheory.Measure Ω}
{μ : MeasureTheory.Measure E} (X : Ω → E), ¬MeasureTheory.pdf X ℙ μ =ᵐ[μ] 0 → AEMeasurable X ℙ- Defined in
- Mathlib.Probability.Density
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasurableSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- AEMeasurablestatement and proof · cited by 840
- MeasureTheory.pdfstatement and proof · cited by 32
- MeasureTheory.pdf_of_not_aemeasurableproof · cited by 1
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.hasPDF_of_pdf_ne_zeroproof · cited by 0