In this paper Applying the minimax criterion in stochastic recourse programs, it says that if $\mathscr{A}$ is the class of all probability measures with support in some compact set $\Xi$, satisfying a number of generalized moment conditions, $\int\Xi g_i(\xi)\mu(d\xi)\leq \alpha_i,i=1,\cdots,L$, where $g_i(),i=1,\cdots,L$ are bounded continuous function on $\Xi$, then $\mathscr{A}$ is a compact, convex set.
Convexity on $\mathscr{A}$ is easy to check. However, I am not quite understand why $\mathscr{A}$ is compact.
Thank you very much!