Abstract
Let $\mathscr{F}$ be a class of square integrable functions. We give necessary and sufficient random geometric conditions for the empirical process indexed by $\mathscr{F}$ to satisfy the CLT. These conditions roughly mean that the trace of $\mathscr{F}$ on a random sample is a small (for the $l^1$ norm) perturbation of a set which is nice for the $l^2$ norm.
Citation
Michel Talagrand. "Donsker Classes and Random Geometry." Ann. Probab. 15 (4) 1327 - 1338, October, 1987. https://doi.org/10.1214/aop/1176991979
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