Theorems · Theorem · probability

ProbabilityTheory.Kernel.singularPart_eq_singularPart_measure

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

Defined in

Mathlib.Probability.Kernel.RadonNikodym

Cited by

2 results in Mathlib

Foundations

Depth 333 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace.CountableOrCountablyGeneratedProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernel