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

Glenn Shafer; Vladimir Vovk; Akimichi Takemura

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arXiv · 0905.0254

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

Glenn Shafer·Vladimir Vovk·Akimichi Takemura

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Abstract

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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Glenn Shafer, Vladimir Vovk, Akimichi Takemura. 2009-05-03. Levy's zero-one law in game-theoretic probability. https://arxiv.org/abs/0905.0254

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