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

2009/05/03 by Glenn Shafer, Vladimir Vovk, Shafer, Glenn +3
Mathematics · #60F20 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:60F20

paper · pdf · doi:10.48550/arxiv.0905.0254

26 pages

arxiv created 2011/06/05 · arxiv updated 2011/06/07

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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