A Loeb-measure approach to theorems by Prohorov, Sazonov and Gross

Abstract

Abstract. We use the Loeb-measure of nonstandard analysis to prove three classical results on limit measures: Let {n¡)¡ei be a projective system of Radon measures, we use the Loeb-measure L(jiE) for an infinite E £ */ and a standard part map to construct a Radon limit measure on the projective limit (Prohorov's Theorem). Using the Loeb-measures on hyperfinite dimensional linear spaces, we characterize the Fourier-transforms of measures on Hubert spaces (Sazonov*s Theorem), and extend cylindrical measures on Hubert spaces to o-additive measures on Banach spaces (Gross' Theorem).