Theorems · Theorem · probability

MeasureTheory.Measure.absolutelyContinuous_compProd_right_iff

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {μ : MeasureTheory.Measure α}
  {κ η : ProbabilityTheory.Kernel α β} [ProbabilityTheory.IsFiniteKernel κ] [ProbabilityTheory.IsFiniteKernel η]
  [MeasurableSpace.CountableOrCountablyGenerated α β] [MeasureTheory.SFinite μ],
  (μ.compProd κ).AbsolutelyContinuous (μ.compProd η) ↔ ∀ᵐ (a : α) ∂μ, (κ a).AbsolutelyContinuous (η a)

Defined in

Mathlib.Probability.Kernel.Composition.AbsolutelyContinuous

Cited by

0 results in Mathlib

Foundations

Depth 336 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernelMeasurableSpace.CountableOrCountablyGeneratedMeasureTheory.SFinite