Computability of probability measures and Martin-Löf randomness over metric spaces
by
Cristóbal Rojas
| Venue: | Information and Computation |
| Citations: | 11 - 6 self |
BibTeX
@ARTICLE{Rojas_computabilityof,
author = {Cristóbal Rojas},
title = {Computability of probability measures and Martin-Löf randomness over metric spaces},
journal = {Information and Computation},
year = {}
}
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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). 1
