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arXiv · 0709.0907

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

Mathieu Hoyrup·Cristobal Rojas
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Abstract

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).

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Mathieu Hoyrup, Cristobal Rojas. 2008-07-23. Computability of probability measures and Martin-Lof randomness over metric spaces. https://arxiv.org/abs/0709.0907

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