The non-mathematical section of Kolmogorov's Grundbegriffe

Vladimir Vovk

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arXiv · 2608.17793

The non-mathematical section of Kolmogorov's Grundbegriffe

Vladimir Vovk

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Abstract

Kolmogorov's "Grundbegriffe der Wahrscheinlichkeitsrechnung" introduced the standard measure-theoretic formalization of probability but included only a two-page section about the relation of the mathematical theory of probability to the world of experience. This note discusses this brief non-mathematical section concentrating on what I regard as its two most controversial features: having two bridges between the mathematical theory and the world of experience instead of the standard one, and the possibility of observing a prespecified event of probability zero in a sequence of trials.

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Vladimir Vovk. 2026-08-18. The non-mathematical section of Kolmogorov's Grundbegriffe. https://arxiv.org/abs/2608.17793

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