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The Heroic Age of Probability: Kolmogorov, Doob, Lévy, Khinchin and Feller

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  • Andrew J. Heunis

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada
    Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, ON N2L 3G1, Canada
    Professor Emeritus.)

Abstract

We survey some of the main developments in probability theory during the so-called “heroic age”; that is, the period from the nineteen twenties to the early nineteen fifties. It was during the heroic age that probability finally attained the status of a mathematical discipline in the full sense of the term, with a complete axiomatic basis and incontestable standards of intellectual rigor to complement and support the extraordinarily rich intuitive content that has always been part of probability theory from its very inception. The axiomatic basis and mathematical rigor are themselves rooted in the abstract theory of measure and integration, which now comprises the very bedrock of modern probability, and among the central characters in the measure-theoretic “re-invention” of probability during the heroic age one finds, in particular, Kolmogorov, Doob, Lévy, Khinchin and Feller, each of whom fundamentally shaped the structure of modern probability. In this survey, we attempt a brief sketch of some of the main contributions of each of these pioneers.

Suggested Citation

  • Andrew J. Heunis, 2025. "The Heroic Age of Probability: Kolmogorov, Doob, Lévy, Khinchin and Feller," Mathematics, MDPI, vol. 13(5), pages 1-24, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:867-:d:1606036
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    References listed on IDEAS

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    1. Bolthausen, Erwin & Wüthrich, Mario V., 2013. "Bernoulli's Law of Large Numbers," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 43(02), pages 73-79, May.
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