On ws-convergence of product measures

Abstract

A canonical redecomposition makes it possible to study the wstopology for measures on a product space by means of recent techniques developed for the narrow topology for transition probabilities Thus a central result is obtained that generalizes both Prohorovs theorem and Komlos theorem it is in terms of pointwise wconvergence of averages of transition measures Komlosconvergence New results for sequential wsconvergence follow these include two versions of Prohorovs theorem for relative sequential ws compactness and a complete characterization of sequential wsconvergence in terms of Komlosconvergence Specializations yield the criterion for relative wscompactness of Schal

the rened characterizations of wsconvergence of Galdeano and Truert

and a new version of Fatous lemma in several dimensions Separately a nonsequential extension of Prohorovs theorem for relative wscompactness is presented as well it generalizes the corresponding relative wscompactness criterion of Jacod and Memin