Uniform and universal Glivenko-Cantelli classes

Assouad, P., and Dudley, R. M. (1989). Minimax nonparametric estimation over classes of sets. Preprint.

Araujo, A., and Gin�, E. (1978). On tails and domains of attraction of stable measures in Banach spaces.Trans. Amer. Math. Soc. 248, 105?119.

Beck, A. (1962). A convexity condition in Banach spaces and the strong law of large numbers.Proc. Amer. Math. Soc. 13, 329?334.

Dobri?, V. (1987). The law of large numbers, examples and counterexamples.Math. Scand. 60, 273?291.

Dudley, R. M. (1984).A Course on Empirical Processes. Ecole d'�t� de probabilit�s de St.-Flour, 1982. Lecture Notes in Mathematics, Vol. 1097, pp. 1?142, Springer, Berlin.

Dudley, R. M. (1987). Universal Donsker classes and metric entropy.Ann. Prob. 15, 1306?1326.

Dudley, R. M. (1989).Real Analysis and Probability. Wadsworth & Brooks/Cole, Pacific Grove, CA.

Fernique, X. (1974).R�gularit� des Trajectoires des Fonctions Al�atoires Gaussiennes. Lecture Notes in Mathematics, Vol. 480, pp. 1?96, Springer, Berlin.

Giesy, D. P., and James, R. C. (1973). Uniformly non-l 1 andB-convex Banach spaces.Studia Math. 48, 61?69.

Gin�, E., and Zinn, J. (1984). Some limit theorems for empirical processes.Ann. Prob. 12, 929?989.

Gin�, E., and Zinn, J. (1989). Gaussian characterization of uniform Donsker classes of functions.Ann. Prob. 19 (to appear).

Gin�, E., and Zinn, J. (1990). Bootstrapping general empirical measures.Ann. Prob. 18, 851?869.

Hausdorff, F. (1936). Summen von ?1 Mengen.Fund. Math. 26, 241?255.

Kol?inskii, V. I. (1981). On the central limit theorem for empirical measures.Theor. Prob. Math. Statist. 24, 71?82.

Kolmogorov, A. N. (1929). Bemerkungen zu meiner Arbeit ?�ber die Summen zuf�lliger Gr�ssen?.Math. Ann. 102, 484?488.

Lusin, N. (1914). Sur un probl�me de M. Baire.Comptes Rendus Acad. Sci. Paris 158, 1258?1261.

Mandrekar, V., and Zinn, J. (1980). Central limit problem for symmetric case: convergence to non-Gaussian laws.Studia Math. 67, 279?296.

Marcus, M. B., and Woyczynski, W. A. (1979). Stable measures and central limit theorems in spaces of stable type.Trans. Amer. Math. Soc. 251, 71?102.

Mourier, E. (1953). El�ments al�atoires dans un espace de Banach.Ann. Inst. H. Poincar� 13, 161?244.

Pisier, G. (1973). Sur les espaces de Banach qui ne contiennent pas uniform�ment del n 1 .Comptes Rendus Acad. Sci. Paris S�r. A 277, 991?994.

Pisier, G. (1975). Le th�or�me limite central et la loi du logarithme it�r� dans les espaces de Banach.Seminaire Maurey-Schwartz 1973?1974, Expos�s III et IV. Ecole Polytechnique, Paris.

Pisier, G. (1984). Remarques sur les classes de Vapnik-?ervonenkis.Ann. Inst. H. Poincar� Prob. Statist. 20, 287?298.

Pollard, D. (1982). A central limit theorem for empirical processes.J. Austral. Math. Soc. Sec. A 33, 235?248.

Shortt, Rae M. (1984). Universally measurable spaces: An invariance theorem and diverse characterizations.Fund. Math. 121, 169?176.

Sierpi?ski, W., and Szpilrajn-Marczewski, E. (1936). Remarque sur le probl�me de la mesure.Fund. Math. 26, 256?261.

Steele, J. Michael (1978). Empirical discrepancies and subadditive processes.Ann. Prob. 6, 118?127.

Sudakov, V. N. (1971). Gaussian random processes and measures of solid angles in Hilbert space.Dokl. Akad. Nauk SSSR 197, 43?45 (Soviet Math. Dokl. 12, 412?415).

Talagrand, M. (1987). The Glivenko-Cantelli problem.Ann. Prob. 15, 837?870.

Vapnik, V. N., and A. Ya. ?ervonenkis (1971). On the uniform convergence of relative frequencies of events to their probabilities.Theor. Prob. Appl. 16, 264?280.

Vapnik, V. N., and A. Ya. ?ervonenkis (1981). Necessary and sufficient conditions for the uniform convergence of means to their expectations.Theor. Prob. Appl. 26, 532?553.

Varadarajan, V. S. (1958). On the convergence of sample probability distributions.Sankhy? 19, 23?26.

Woyczy?ski, W. (1978). Geometry and martingales in Banach spaces?Part II: Independent increments. In J. Kuelbs (Ed.),Probability on Banach Spaces, pp. 267?521, Marcel Dekker, New York.