Theorems · Theorem · probability

ProbabilityTheory.lintegral_toKernel_mem

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {κ : ProbabilityTheory.Kernel α (β × ℝ)} {ν : ProbabilityTheory.Kernel α β} {f : α × β → StieltjesFunction ℝ}
  [ProbabilityTheory.IsFiniteKernel κ] (hf : ProbabilityTheory.IsCondKernelCDF f κ ν) (a : α) {s : Set (β × ℝ)},
  MeasurableSet s →
    ∫⁻ (b : β), ((ProbabilityTheory.IsCondKernelCDF.toKernel f hf) (a, b)) (Prod.mk b ⁻¹' s) ∂ν a = (κ a) s

Defined in

Mathlib.Probability.Kernel.Disintegration.CDFToKernel

Cited by

1 results in Mathlib

Foundations

Depth 261 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsFiniteKernel