The generality of the zero-one laws
Akimichi Takemura, Vladimir Vovk, and Glenn Shafer
TL;DR
This paper extends zero-one laws using game-theoretic approaches, explicitly revealing the martingales involved and demonstrating their broader implications beyond traditional measure-theoretic probability.
Contribution
It introduces game-theoretic generalizations of zero-one laws and makes the martingales behind these laws explicit, showing their wider significance.
Findings
Martingale arguments can be applied beyond measure-theoretic probability.
Game-theoretic zero-one laws are established.
Explicit martingale constructions are provided.
Abstract
We prove game-theoretic generalizations of some well known zero-one laws. Our proofs make the martingales behind the laws explicit, and our results illustrate how martingale arguments can have implications going beyond measure-theoretic probability.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Game Theory and Applications · Theoretical and Computational Physics