A representation theorem for stochastic kernels and its application in comparison of experiments

Abstract

In the present paper we show that every stochastic kernel mapping the measurable space is generated according to a probability measure on the set of all -measurable functions – only provided contains all sets {x}xeX. This theorem is the generalization of the wellknown statement that every stochastic matrix may be represented as a convex linear combination of permutation matrices. The result is applied to comparison relations for statistical experiments.