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Kolmogorov's Contributions to the Foundations of Probability

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Abstract

Andrei Nikolaevich Kolmogorov was the foremost contributor to the mathematical and philosophical foundations of probability in the twentieth century, and his thinking on the topic is still potent today. In this article we first review the three stages of Kolmogorov's work on the foundations of probability: (1) his formulation of measure-theoretic probability, 1933; (2) his frequentist theory of probability, 1963; and (3) his algorithmic theory of randomness, 1965–1987. We also discuss another approach to the foundations of probability, based on martingales, which Kolmogorov did not consider.

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Authors and Affiliations

  1. Department of Computer Science, Royal Holloway, University of London, UK

    V. G. Vovk

  2. Rutgers School of Business – Newark and New Brunswick, UK

    G. R. Shafer

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  1. V. G. Vovk
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Vovk, V.G., Shafer, G.R. Kolmogorov's Contributions to the Foundations of Probability. Problems of Information Transmission 39, 21–31 (2003). https://doi.org/10.1023/A:1023674330295

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