Theorems · Theorem · probability

ProbabilityTheory.IsCondKernelCDF.integrable

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {f : α × β → StieltjesFunction ℝ}
  {κ : ProbabilityTheory.Kernel α (β × ℝ)} {ν : ProbabilityTheory.Kernel α β},
  ProbabilityTheory.IsCondKernelCDF f κ ν → ∀ (a : α) (x : ℝ), MeasureTheory.Integrable (fun b => ↑(f (a, b)) x) (ν a)

Defined in

Mathlib.Probability.Kernel.Disintegration.CDFToKernel

Cited by

2 results in Mathlib

Foundations

Depth 177 from the axioms · uses propext, Classical.choice, Quot.sound