Statistical Science

The Sources of Kolmogorov’s Grundbegriffe

Glenn Shafer and Vladimir Vovk

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Andrei Kolmogorov’s Grundbegriffe der Wahrscheinlichkeits-rechnung put probability’s modern mathematical formalism in place. It also provided a philosophy of probability—an explanation of how the formalism can be connected to the world of experience. In this article, we examine the sources of these two aspects of the Grundbegriffe—the work of the earlier scholars whose ideas Kolmogorov synthesized.

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Statist. Sci., Volume 21, Number 1 (2006), 70-98.

First available in Project Euclid: 6 June 2006

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Axioms for probability Borel classical probability Cournot’s principle frequentism Grundbegriffe der Wahrscheinlichkeits-rechnung history of probability Kolmogorov measure theory


Shafer, Glenn; Vovk, Vladimir. The Sources of Kolmogorov’s Grundbegriffe. Statist. Sci. 21 (2006), no. 1, 70--98. doi:10.1214/088342305000000467.

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