Levy's zero-one law in game-theoretic probability. / Shafer, Glenn; Vovk, Vladimir; Takemura, Akimichi.

In: Journal of Theoretical Probability, Vol. 25, No. 1, 2012, p. 1-24.

Research output: Contribution to journalArticle



We prove a non-stochastic 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.
Original languageEnglish
Pages (from-to)1-24
Number of pages24
JournalJournal of Theoretical Probability
Issue number1
Publication statusPublished - 2012
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ID: 4100034