Sections, Selections and Prohorov's Theorem

TL;DR

This paper generalizes Prohorov's theorem for Radon probability measures using usco mappings, extending its applicability to completely metrizable and sieve-complete spaces through classical selection theorems.

Contribution

It introduces a new generalization of Prohorov's theorem utilizing usco mappings, broadening its scope to more general topological spaces.

Findings

Generalization of Prohorov's theorem for usco mappings

Application of Michael's selection theorem in metrizable spaces

Extension to sieve-complete spaces

Abstract

The famous Prohorov theorem for Radon probability measures is generalized in terms of usco mappings. In the case of completely metrizable spaces this is achieved by applying a classical Michael result on the existence of usco selections for l.s.c. mappings. A similar approach works when sieve-complete spaces are considered.