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The generality of the zero-one laws

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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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Authors and Affiliations

  1. Department of Mathematical Informatics, Graduate School of Information Science and Technology, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan

    Akimichi Takemura

  2. Computer Learning Research Centre, Department of Computer Science, Royal Holloway, University of London, Egham, Surrey, TW20 0EX, UK

    Vladimir Vovk & Glenn Shafer

  3. Department of Accounting and Information Systems, Rutgers Business School-Newark and New Brunswick, 1 Washington Park, Newark, NJ, 07102, USA

    Glenn Shafer

Authors
  1. Akimichi Takemura
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  2. Vladimir Vovk
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  3. Glenn Shafer
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Correspondence to Akimichi Takemura.

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Takemura, A., Vovk, V. & Shafer, G. The generality of the zero-one laws. Ann Inst Stat Math 63, 873–885 (2011). https://doi.org/10.1007/s10463-009-0262-0

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  • DOI: https://doi.org/10.1007/s10463-009-0262-0

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