Theorems · Theorem · probability

ProbabilityTheory.HasPDF.hasLaw

∀ {Ω : Type u_1} {𝓧 : Type u_2} {mΩ : MeasurableSpace Ω} {m𝓧 : MeasurableSpace 𝓧} {X : Ω → 𝓧}
  {μ : MeasureTheory.Measure 𝓧} {P : MeasureTheory.Measure Ω} [h : MeasureTheory.HasPDF X P μ],
  ProbabilityTheory.HasLaw X (μ.withDensity (MeasureTheory.pdf X P μ)) P

Defined in: Mathlib.Probability.HasLaw
Cited by: 0 results in Mathlib
Foundations: Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.HasPDF

Mathlib docs Source Loogle LeanSearch

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
MeasureTheory.Measure.withDensitystatement · cited by 265
ProbabilityTheory.HasLawstatement · cited by 69
MeasureTheory.HasPDFstatement and proof · cited by 37
MeasureTheory.pdfstatement · cited by 32
MeasureTheory.HasPDF.aemeasurableproof · cited by 8
MeasureTheory.map_eq_withDensity_pdfproof · cited by 6

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.