Dudley, R. M. A course on empirical processes. (English) Zbl 0554.60029 Ecole d’été de probabilités de Saint-Flour XII - 1982, Lect. Notes Math. 1097, 1-142 (1984). [For the entire collection see Zbl 0541.00006.] This booklet deals with large sample theory of empirical processes indexed by quite arbitrary parameter sets. Special emphasis is given to almost sure uniform convergence (with rates) and functional central limit theorems. This is done within the framework of the so-called Vapnik- Cervonenkis setup. The author also exploits the measure theoretic aspects arising in the absence of separability. Some of the work is strongly related to the recent books by P. Gaenssler, Empirical Processes, IMS Lect. Notes Ser. and D. Pollard, Convergence of stochastic processes, Springer (1984). Reviewer: W.Stute Cited in 7 ReviewsCited in 100 Documents MSC: 60Fxx Limit theorems in probability theory 60G15 Gaussian processes 60E15 Inequalities; stochastic orderings Keywords:Glivenko-Cantelli convergence; Donsker classes; uniform convergence; functional central limit theorems; Vapnik-Cervonenkis setup PDF BibTeX XML