Theorems · Theorem · probability

ProbabilityTheory.Kernel.IsCondKernel.isProbabilityMeasure_ae

∀ {α : Type u_1} {β : Type u_2} {Ω : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mΩ : MeasurableSpace Ω} (κ : ProbabilityTheory.Kernel α (β × Ω)) (κCond : ProbabilityTheory.Kernel (α × β) Ω)
  [ProbabilityTheory.IsFiniteKernel κ.fst] [κ.IsCondKernel κCond] (a : α),
  ∀ᵐ (b : β) ∂κ.fst a, MeasureTheory.IsProbabilityMeasure (κCond (a, b))

A conditional kernel is almost everywhere a probability measure.

Defined in

Mathlib.Probability.Kernel.Disintegration.Basic

Cited by

0 results in Mathlib

Foundations

Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsFiniteKernelProbabilityTheory.Kernel.IsCondKernel