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math.PR2009★ 1 cited
Levy's zero-one law in game-theoretic probability
Glenn Shafer, Vladimir Vovk, Akimichi Takemura
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…
math.PR2006★ 23 cited
Game-theoretic versions of strong law of large numbers for unbounded variables
Masayuki Kumon, Akimichi Takemura, Kei Takeuchi
We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality…