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 RM_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, we consider instead of C_b(T,G)-weak compactness S(T,G)-weak compactness with respect to the new uniformly closed linear space S(T,G) of all (symmetrizable) metasemicontinuous functions.