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

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

2007-09-06

arxiv.org/abs/0709.0907v2

Computer Science

Information Theory

29 pages

Scientific paper

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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