Theorems · Theorem · probability

MeasureTheory.Measure.AbsolutelyContinuous.mutuallySingular_compProd_iff

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ ν : MeasureTheory.Measure α}
  {κ η : ProbabilityTheory.Kernel α β} [MeasureTheory.SigmaFinite μ] [MeasureTheory.SigmaFinite ν],
  μ.AbsolutelyContinuous ν →
    ((μ.compProd κ).MutuallySingular (ν.compProd η) ↔ (μ.compProd κ).MutuallySingular (μ.compProd η))

Defined in

Mathlib.Probability.Kernel.Composition.MeasureCompProd

Cited by

1 results in Mathlib

Foundations

Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasureTheory.SigmaFiniteMeasureTheory.SigmaFinite