Theorems · Theorem · probability

ProbabilityTheory.Kernel.apply_eq_measure_condKernel_of_compProd_eq

∀ {α : Type u_1} {β : Type u_2} {Ω : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  [inst : MeasurableSpace Ω] [inst_1 : StandardBorelSpace Ω] [inst_2 : Nonempty Ω]
  {ρ : ProbabilityTheory.Kernel α (β × Ω)} [inst_3 : ProbabilityTheory.IsFiniteKernel ρ]
  {κ : ProbabilityTheory.Kernel (α × β) Ω} [ProbabilityTheory.IsFiniteKernel κ],
  ρ.fst.compProd κ = ρ → ∀ (a : α), (fun b => κ (a, b)) =ᵐ[ρ.fst a] ⇑(ρ a).condKernel

Defined in

Mathlib.Probability.Kernel.Disintegration.Unique

Cited by

2 results in Mathlib

Foundations

Depth 282 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceStandardBorelSpaceNonemptyProbabilityTheory.IsFiniteKernelProbabilityTheory.IsFiniteKernel