Abstract
Two problems will be considered. In Part I we consider a class of subsets
of a topological space X and a Radon measure on X; if it is known that, for sufficiently many\(T \subseteqq X\), the restrictions of the sets in
constitutes a uniformity class in T w.r.t. the restriction of the given measure, then we ask if it follows that
is a uniformity class in X.
Part II, which can be read independently of Part I, is concerned with the question whether, to a given convergent sequence of Radon measures, say μn→μ, there always exist “sufficiently many” compact sets K such that μn(K)→μ(K).
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Topsøe, F. Some special results on convergent sequences of radon measures. Manuscripta Math 19, 1–14 (1976). https://doi.org/10.1007/BF01172334
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DOI: https://doi.org/10.1007/BF01172334