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Discontinuity, Nonlinearity, and Complexity 9(4) (2020) 591--605 | DOI:10.5890/DNC.2020.12.012

Valeriy K. Zakharov, Timofey V. Rodionov

Faculty of Mathematics and Mechanics, Lomonosov Moscow State University, Leninskie Gory, 1, Moscow, GSP-1, 119991, Russia

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Abstract

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

Acknowledgments

This research was partially supported by Russian Foundation for Basic Research (20-01-00584).

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