Glivenko-Cantelli type theorems: An application of the convergence theory of stochastic suprema

The uniform convergence of empirical processes on certain classes of sets follows from the convergence theory for random lower semicontinuous functions studies in the context of stochastic optimization. In the process, a richer class of sets for which one can prove this type of result is exhibited.Research supported in part by grants from Ministero Publica Istruzione and the National Science Foundation.