Theorems · Theorem · probability

ProbabilityTheory.setIntegral_stieltjesOfMeasurableRat_rat

∀ {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 → ℚ → ℝ}
  (hf : ProbabilityTheory.IsRatCondKernelCDF f κ ν) (a : α) (q : ℚ) {s : Set β},
  MeasurableSet s →
    ∫ (b : β) in s, ↑(ProbabilityTheory.stieltjesOfMeasurableRat f ⋯ (a, b)) ↑q ∂ν a = (κ a).real (s ×ˢ Set.Iic ↑q)

Defined in

Mathlib.Probability.Kernel.Disintegration.CDFToKernel

Cited by

1 results in Mathlib

Foundations

Depth 254 from the axioms · uses propext, Classical.choice, Quot.sound