PROPERTIES OF MEASURES ON ”STABLE” BOOLEAN ALGEBRAS

Abstract

We study the properties of finitely additive measures with values in a topological abelian group and defined on a wide class of Boolean algebras, which covers algebras with SIP and algebras ???? ( if satisfies some conditions). We establish sufficient conditions for the sequences of such measures to be uniformly strongly continuous. Novelty in this theme is that we do not require uniform exhaustivity and, in some theorems, even exhaustivity for measures. Applications to weak convergence of measures are presented.