Weak Compactness Problem for Sets of Bounded Radon Measures on Various Topological Spaces - Zakharov, Valeriy K.; Rodionov, Timofey V. (Discontinuity, Nonlinearity, and Complexity, 2026)
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.