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- Title
Algorithmic randomness over general spaces.
- Authors
Miyabe, Kenshi
- Abstract
The study of Martin-Löf randomness on a computable metric space with a computable measure has seen much progress recently. In this paper we study Martin-Löf randomness on a more general space, that is, a computable topological space with a computable measure. On such a space, Martin-Löf randomness may not be a natural notion because there is no universal test, and Martin-Löf randomness and complexity randomness (defined in this paper) do not coincide in general. We show that SCT3 is a sufficient condition for the existence and coincidence, and study how much we can weaken this condition.
- Subjects
SET theory; TOPOLOGICAL spaces; FUNCTION spaces; MATHEMATICAL logic; AGGREGATED data
- Publication
Mathematical Logic Quarterly, 2014, Vol 60, Issue 3, p184
- ISSN
0942-5616
- Publication type
Article
- DOI
10.1002/malq.201200051