Theorems · Theorem · probability

MeasureTheory.Measure.MutuallySingular.compProd_of_right

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

Defined in

Mathlib.Probability.Kernel.Composition.AbsolutelyContinuous

Cited by

3 results in Mathlib

Foundations

Depth 334 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernelMeasurableSpace.CountableOrCountablyGenerated