On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities

Vapnik, Vladimir N.; Chervonenkis, Alexey Ya.

doi:10.1137/1116025

On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities

Vladimir N. Vapnik, Alexey Ya. Chervonenkis

Notable Works 1971 pp. 264-280

doi:10.1137/1116025 /misc/1971/vapnik1971misc-uniform/

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).

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Text

Vapnik and Chervonenkis. "On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities." Theory of Probability and Its Applications, 1971. doi:10.1137/1116025

Markdown

[Vapnik and Chervonenkis. "On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities." Theory of Probability and Its Applications, 1971.](https://mlanthology.org/misc/1971/vapnik1971misc-uniform/) doi:10.1137/1116025

BibTeX

@misc{vapnik1971misc-uniform,
  title     = {{On the Uniform Convergence of Relative Frequencies of Events to Their Probabilities}},
  author    = {Vapnik, Vladimir N. and Chervonenkis, Alexey Ya.},
  howpublished = {Theory of Probability and Its Applications},
  year      = {1971},
  pages     = {264-280},
  doi       = {10.1137/1116025},
  volume    = {16},
  number    = {2},
  url       = {https://mlanthology.org/misc/1971/vapnik1971misc-uniform/}
}