On the uniform convergence of the frequencies of occurrence of events to their probabilities

Abstract

This chapter is a translation of Vapnik and Chervonenkis’s pathbreaking note В. Н. Вапник, А. Я. Червоненкис, О равномерной сходимости частот появления событий к их вероятностям, Доклады Академии Наук СССР 181(4), 781-783 (1968) essentially following the excellent translation V. N. Vapnik, A. Ya. Červonenkis, Uniform Convergence of Frequencies of Occurrence of Events to Their Probabilities, Soviet Mathematics Doklady 9(4), 915–918 (1968) by Lisa Rosenblatt (the editors only corrected a few minor mistakes and in some places made the translation follow more closely the Russian original). (Presented by Academician V. A. Trapeznikov, 6 October 1967).