This research examines probability limits over classes of sets and functions. Empirical measures can be applied to sets or to functions to define empirical processes. Earlier results in empirical process theory established that convergence in distribution to a Gaussian holds uniformly for certain classes of sets and functions. This research seeks to find larger classes of sets for which statistical functionals are differentiable and therefore can be approximated by a process with this convergence property, plus a remainder of lower order.
