We prove an analogue of Topsøe's criterion for relative compactness of a family of probability measures which are regular with respect to a family sets. We consider measures whose values are compact convex sets in a locally convex linear topological space.
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In [15] Topsoe characterizes the narrowly compact subsets of measures in general situations. The basie tool used is extension of a content to a measure. In this paper we generalize to tight set-valued map these theorems of extension [15, Theorem l, p. 198; Theorem 2 and 3, p. 201]. In our next papers we shall apply these results to the study of compactness in space of set-valued measures.
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