Uniform CLT for empirical process

Empirical processes indexed by classes of functions based on dependent observations are considered. Sufficient conditions in order to satisfy stochastic equicontinuity are given. The derived conditions are in terms of bracketing numbers with respect to a norm arising from a Rosenthal type moment inequality satisfied by the process. The application involves mixing sequences and improves on the result of Andrews and Pollard (Int. Statist. Rev. 62 (1) (1994) 119) for strong mixing, Shao and Yu (Ann. Probab. 24 (4) (1996) 2098) for ρ-mixing sequences, and Csörgő and Mielniczuk (Probab. Theory Relat. Fields 104 (1) (1996) 15) for functions of Gaussian sequences.