Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
426671 | Information and Computation | 2009 | 18 Pages |
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).
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics