ABSTRACT
Let (Ω, ℱ, P) be a probability space, and let S and Τ be two random functions with values in the measurable spaces (L, A) and (Μ, Β), respectively. Consider the conditional distribution P(S ∈ A | Τ = t) of S given Τ, that is, t ↷ P(S ∈ A | Τ = t) is the ΡT -a.s. unique measurable function from (M, ℬ) into Ṝ satisfying
