%0 Journal Article
%T Game-theoretic versions of strong law of large numbers for unbounded variables
%A Masayuki Kumon
%A Akimichi Takemura
%A Kei Takeuchi
%J Mathematics
%D 2006
%I arXiv
%R 10.1080/17442500701323023
%X 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's moves are unbounded. Our game-theoretic versions of SLLN largely correspond to standard measure-theoretic results. However game-theoretic proofs are different from measure-theoretic ones in the explicit consideration of various hedges. In measure-theoretic proofs existence of moments are assumed, whereas in our game-theoretic proofs we assume availability of various hedges to Skeptic for finite prices.
%U http://arxiv.org/abs/math/0603184v1