The Annals of Probability

The Borel–Cantelli Lemmas, Probability Laws and Kolmogorov Complexity

George Davie

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We formulate effective versions of the Borel–Cantelli lemmas using a coefficient from Kolmogorov complexity. We then use these effective versions to lift the effective content of the law of large numbers and the law of the iterated logarithm.

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Ann. Probab., Volume 29, Number 4 (2001), 1426-1434.

First available in Project Euclid: 5 March 2002

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Primary: 68Q30: Algorithmic information theory (Kolmogorov complexity, etc.) [See also 03D32] 60A05: Axioms; other general questions

Effective Borel-Cantelli lemmas Kolmogorov complexity compressibility coefficient probability law


Davie, George. The Borel–Cantelli Lemmas, Probability Laws and Kolmogorov Complexity. Ann. Probab. 29 (2001), no. 4, 1426--1434. doi:10.1214/aop/1015345756.

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