Theorems · Theorem · probability

ProbabilityTheory.IsRatCondKernelCDFAux.setIntegral_iInf_rat_gt

∀ {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},
  ProbabilityTheory.IsRatCondKernelCDFAux f κ ν →
    ∀ [ProbabilityTheory.IsFiniteKernel κ] [ProbabilityTheory.IsFiniteKernel ν] (a : α) (q : ℚ) {A : Set β},
      MeasurableSet A → ∫ (t : β) in A, ⨅ r, f (a, t) ↑r ∂ν a = (κ a).real (A ×ˢ Set.Iic ↑q)

Defined in

Mathlib.Probability.Kernel.Disintegration.CDFToKernel

Cited by

1 results in Mathlib

Foundations

Depth 256 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernel