Theorems · Theorem · probability

ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {f : α × β → ℚ → ℝ}
  {κ : ProbabilityTheory.Kernel α (β × ℝ)} {ν : ProbabilityTheory.Kernel α β},
  ProbabilityTheory.IsRatCondKernelCDFAux f κ ν →
    ∀ (a : α) {A : Set β}, MeasurableSet A → ∀ (q : ℚ), ∫ (c : β) in A, f (a, c) q ∂ν a = (κ a).real (A ×ˢ Set.Iic ↑q)

Defined in

Mathlib.Probability.Kernel.Disintegration.CDFToKernel

Cited by

3 results in Mathlib

Foundations

Depth 250 from the axioms · uses propext, Classical.choice, Quot.sound