Theorems · Theorem · probability

ProbabilityTheory.Kernel.mutuallySingular_singularPart

∀ {α : Type u_1} {γ : Type u_2} {mα : MeasurableSpace α} {mγ : MeasurableSpace γ}
  [hαγ : MeasurableSpace.CountableOrCountablyGenerated α γ] (κ η : ProbabilityTheory.Kernel α γ)
  [inst : ProbabilityTheory.IsFiniteKernel κ] [inst_1 : ProbabilityTheory.IsFiniteKernel η] (a : α),
  ((κ.singularPart η) a).MutuallySingular (η a)

The singular part of κ with respect to η is mutually singular with η.

Defined in

Mathlib.Probability.Kernel.RadonNikodym

Cited by

6 results in Mathlib

Foundations

Depth 330 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountableOrCountablyGeneratedProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernel