Theorems · Theorem · probability

ProbabilityTheory.Kernel.singularPart_eq_zero_iff_measure_eq_zero

∀ {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 = 0 ↔ (κ a) (κ.mutuallySingularSetSlice η a) = 0

Defined in

Mathlib.Probability.Kernel.RadonNikodym

Cited by

0 results in Mathlib

Foundations

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

Assumes

MeasurableSpace.CountableOrCountablyGeneratedProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernel