Borel sets of probability measures

Abstract

Let M(X) be the collection of probability measures on the Borel sets of a Polish space X. The Borel structure of M(X) generated by the weak* topology is investigated. Various collections of probability measures arising in nonparametric statistics are shown to Borel sets of M(X). Attention is particularly focused on collections arising from restrictions on distribution functions, density functions, and supports of the underlying probability measures. © 1973 Pacific Journal of Mathematics All Rights Reserved.