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