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