Sufficient conditions, which under weak additional assumptions are also necessary, are found for the central limit theorem for empirical processes indexed by classes of functions which have the Vapnik-Cervonenkis property. This improves an earlier theorem of Pollard (1982a), and leads to necessary and sufficient conditions for the CLT for weighted empirical processes indexed by Vapnik-Cervonenkis classes of sets.
"The Central Limit Theorem for Empirical Processes on Vapnik-Cervonenkis Classes." Ann. Probab. 15 (1) 178 - 203, January, 1987. https://doi.org/10.1214/aop/1176992263