Theorems · Theorem · probability
MeasureTheory.map_eq_withDensity_pdf
∀ {Ω : Type u_1} {E : Type u_2} [inst : MeasurableSpace E] {m : MeasurableSpace Ω} (X : Ω → E)
(ℙ : MeasureTheory.Measure Ω) (μ : autoParam (MeasureTheory.Measure E) MeasureTheory.map_eq_withDensity_pdf._auto_1)
[hX : MeasureTheory.HasPDF X ℙ μ], MeasureTheory.Measure.map X ℙ = μ.withDensity (MeasureTheory.pdf X ℙ μ)- Defined in
- Mathlib.Probability.Density
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- ENNRealproof · cited by 9,879
- MeasureTheory.Measure.mapstatement and proof · cited by 858
- MeasureTheory.Measure.withDensitystatement and proof · cited by 265
- MeasureTheory.HasPDFstatement and proof · cited by 37
- MeasureTheory.pdfstatement · cited by 32
- MeasureTheory.Measure.withDensity_rnDeriv_eqproof · cited by 31
- MeasureTheory.HasPDF.absolutelyContinuousproof · cited by 13
- MeasureTheory.pdf_defproof · cited by 6
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.pdf.eq_of_map_eq_withDensityproof · cited by 2
- MeasureTheory.map_eq_setLIntegral_pdfproof · cited by 2
- MeasureTheory.pdf.integral_pdf_smulproof · cited by 1
- ProbabilityTheory.HasPDF.hasLawproof · cited by 0
- MeasureTheory.pdf.eq_of_map_eq_withDensity'proof · cited by 0
- MeasureTheory.pdf.integrable_pdf_smul_iffproof · cited by 0