Levy's zero-one law in game-theoretic probability

Details Levy's zero-one law in game-theoretic probability Levy's zero-one law in game-theoretic probability

2009-05-03

arxiv.org/abs/0905.0254v3

Mathematics

Probability

26 pages

Scientific paper

We prove a game-theoretic version of Levy's zero-one law, and deduce several corollaries from it, including non-stochastic versions of Kolmogorov's zero-one law, the ergodicity of Bernoulli shifts, and a zero-one law for dependent trials. Our secondary goal is to explore the basic definitions of game-theoretic probability theory, with Levy's zero-one law serving a useful role.

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