Mathlib Map

Theorems · Theorem · probability

MeasureTheory.pdf_def

∀ {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.pdf X ℙ μ = (MeasureTheory.Measure.map X ℙ).rnDeriv μ
Defined in
Mathlib.Probability.Density
Cited by
6 results in Mathlib
Foundations
Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpace
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.map_eq_withDensity_pdf · cited by 6MeasureTheory.map_eq_with…MeasureTheory.pdf_of_not_aemeasurable · cited by 1MeasureTheory.pdf_of_not_…MeasureTheory.pdf.integral_pdf_smul · cited by 1pdf.integral_pdf_smulMeasureTheory.pdf.congr · cited by 0pdf.congrMeasureTheory.pdf.integrable_pdf_smul_iff · cited by 0pdf.integrable_pdf_smul_i…MeasureTheory.pdf.lintegral_pdf_mul · cited by 0pdf.lintegral_pdf_mulMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealMeasureTheory.Measure.map · cited by 858Measure.mapMeasureTheory.Measure.rnDeriv · cited by 234Measure.rnDerivMeasureTheory.pdf · cited by 32MeasureTheory.pdfMeasureTheory.pdf_defCITED BYCITES

Cites6

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

Cited by6

Results whose statement or proof uses this declaration.