Abstract
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 language | English |
|---|---|
| Pages (from-to) | 1-24 |
| Number of pages | 24 |
| Journal | Journal of Theoretical Probability |
| Volume | 25 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2012 |
Keywords
- Doob’s martingale convergence theorem
- ergodicity of Bernoulli shifts
- Kolmogorov’s zero-one law
- Levy’s martingale convergence theorem