Borel sets of probability measures

Kenneth Lamar Lange

Vol. 48 (1973), No. 1, 141–161

DOI: 10.2140/pjm.1973.48.141

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.

Mathematical Subject Classification

Primary: 28A32

Milestones

Received: 11 May 1972

Published: 1 September 1973