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 $\Gamma_\nu$ ( if $\nu$ 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.
Keywords:boolean algebra, topological abelian group, strongly continuous measure, exhaustive measure, uniform exhaustibility of the family of measures, uniform boundedness of the family of measures, poor convergence of measures.
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