Vapnik, V. N.; Chervonenkis, A. Ya. On the uniform convergence of relative frequencies of events to their probabilities. (English) Zbl 1337.60009 Vovk, Vladimir (ed.) et al., Measures of complexity. Festschrift for Alexey Chervonenkis. Cham: Springer (ISBN 978-3-319-21851-9/hbk; 978-3-319-21852-6/ebook). 11-30 (2015). Summary: This chapter reproduces the English translation by B.Seckler of the paper [Theory Probab. Appl. 16, 264–280 (1971); translation from Teor. Veroyatn. Primen. 16, 264–279 (1971; Zbl 0247.60005)] in which the authors gave proofs for the innovative results they had obtained in a draft form in July 1966 and announced in 1968 in their note in [Sov. Math., Dokl. 9, 915–918 (1968); translation from Dokl. Akad. Nauk SSSR 181, 781–783 (1968; Zbl 0247.60004)].For the entire collection see [Zbl 1331.68020]. Cited in 1 ReviewCited in 36 Documents MSC: 60A05 Axioms; other general questions in probability 60F15 Strong limit theorems 01A75 Collected or selected works; reprintings or translations of classics Citations:Zbl 0247.60005; Zbl 0247.60004 PDFBibTeX XMLCite \textit{V. N. Vapnik} and \textit{A. Ya. Chervonenkis}, in: Measures of complexity. Festschrift for Alexey Chervonenkis. Cham: Springer. 11--30 (2015; Zbl 1337.60009) Full Text: DOI References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.