Theorems · Theorem · probability

ProbabilityTheory.IsRatCondKernelCDFAux.iInf_rat_gt_eq

∀ {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),
      ∀ᵐ (t : β) ∂ν a, ∀ (q : ℚ), ⨅ r, f (a, t) ↑r = f (a, t) q

Defined in

Mathlib.Probability.Kernel.Disintegration.CDFToKernel

Cited by

1 results in Mathlib

Foundations

Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

ProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernel