Gaussian characterization of uniform Donsker classes of functions (Q810991)

The main result of the paper is Theorem. Let \({\mathcal F}\) be a measurable class of functions. Then \({\mathcal F}\) is finitely uniformly pre-Gaussian iff \({\mathcal F}\) is a uniform Donsker class. The authors also obtain an improvement of a theorem of Shehy and Wellner on uniformity of the CLT over subsets of probability measures and prove uniform exponential bounds for empirical processes indexed by universal bounded Donsker and uniform Donsker classes of functions.