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