Existence of Conditional Probabilities.

Abstract

1. Introduction. Let (i2,2l,P) be a probability space, (S, Σ) a measurable space and ρ a measurable map from (12,21) into (8,Σ). Given ρ we then want to construct a regular conditional probability of P, that is, we want to con struct a map, R, from 21 χ S into [0,1] satisfying … (1) R(· ,s) is a probability  …