Weak Compactness Problem for Sets of Bounded Radon Measures on Various Topological Spaces
DOI:
https://doi.org/10.5890/DNC.2020.12.012Abstract
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.References
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