  This note identifies compact and {\sigma}-compact subsets of probability
measures on a class of metric spaces with respect to the weak convergence
topology. Moreover, it is shown by an example, that the space of probability
measures on a {\sigma}-compact metric spaces not need to be {\sigma}-compact
space, even though the converse statement holds true for metric spaces. The
results are applied to an extended form of the distribution free newsvendor
problem.

Optimization and Control;Probability