Lévy’s Zero–One Law in Game-Theoretic Probability

Glenn Shafer (), Vladimir Vovk () and Akimichi Takemura ()
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Glenn Shafer: Rutgers Business School—Newark and New Brunswick
Vladimir Vovk: Royal Holloway, University of London
Akimichi Takemura: University of Tokyo

Journal of Theoretical Probability, 2012, vol. 25, issue 1, 1-24

Abstract: Abstract We prove a nonstochastic version of Lévy’s zero–one law and deduce several corollaries from it, including nonstochastic versions of Kolmogorov’s zero–one law and the ergodicity of Bernoulli shifts. Our secondary goal is to explore the basic definitions of game-theoretic probability theory, with Lévy’s zero–one law serving a useful role.

Keywords: Doob’s martingale convergence theorem; Ergodicity of Bernoulli shifts; Kolmogorov’s zero–one law; Lévy’s martingale convergence theorem; 60F20; 60G42; 60A05 (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1007/s10959-011-0390-3

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