Computability of probability measures and Martin-Lof randomness over metric spaces

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In this paper we investigate algorithmic randomness on more general spaces than the Cantor space, namely computable metric spaces. To do this, we first develop a unified framework allowing computations with probability measures. We show that any computable metric space with a computable probability measure is isomorphic to the Cantor space in a computable and measure-theoretic sense. We show that any computable metric space admits a universal uniform randomness test (without further assumption).
29 pages

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Information Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/165418

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0709.0907
 http://arxiv.org/abs/0709.0907

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arXiv