Prokhorov-like conditions for weak compactness of sets of bounded Radon measures on different topological spaces

2019/06/09 by Zakharov, Valeriy K., Rodionov, Timofey V.
#28C05 #28C15 (primary) 28A25 #54D30 #60B05 #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · doi:10.48550/arxiv.1906.03658

Abstract

The paper presents some weak compactness criterion for a subset M of the set \mathfrakRM_b(T,G) of all positive bounded Radon measures on a Hausdorff topological space (T,G) similar to the Prokhorov criterion for a complete separable metric space. Since for a general topological space the classical space C_b(T,G) of all bounded continuous functions on T can be trivial and so does not separate points and closed sets, instead of C_b(T,G)-weak compactness we consider S(T,G)-weak compactness with respect to the new uniformly closed linear space S(T,G) of all (symmetrizable) metasemicontinuous functions.

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