English

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

Probability 2011-06-07 v3

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.

Cite

@article{arxiv.0905.0254,
  title  = {Levy's zero-one law in game-theoretic probability},
  author = {Glenn Shafer and Vladimir Vovk and Akimichi Takemura},
  journal= {arXiv preprint arXiv:0905.0254},
  year   = {2011}
}

Comments

26 pages

R2 v1 2026-06-21T12:57:40.147Z