Abstract
This chapter reproduces the English translation by B. Seckler of the paper by Vapnik and Chervonenkis in which they gave proofs for the innovative results they had obtained in a draft form in July 1966 and announced in 1968 in their note in Soviet Mathematics Doklady. The paper was first published in Russian as Вапник В. Н. and Червоненкис А. Я. О равномерноЙ сходимости частот появления событиЙ к их вероятностям. Теория вероятностеЙ и ее применения 16(2), 264–279 (1971).
Theory of Probability and Its Applications, Volume XVI, Number 2, pages 264–280, 1971.
Translated by B. Seckler.
Received by the editors on May 7, 1969.
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Vapnik, V.N., Chervonenkis, A.Ya.: On the uniform convergence of relative frequencies of events to their probabilities. Dokl. Akad. Nauk SSSR 181(4), 781–783 (1968) (In Russian)
Gnedenko, B.V.: Theory of Probability, 4th edn. Chelsea Publishing Co., New York (1968)
Khinchin, A.Ya.: On basic theorems of information theory. Uspekhi Mat. Nauk XI(1), 17–75 (1956) (In Russian)
Feller, W.: Introduction to Probability Theory and Its Applications, vol. 1, 2nd edn. Wiley, New York (1957)
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Vapnik, V.N., Chervonenkis, A.Y. (2015). On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities. In: Vovk, V., Papadopoulos, H., Gammerman, A. (eds) Measures of Complexity. Springer, Cham. https://doi.org/10.1007/978-3-319-21852-6_3
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