Algorithmic randomness over general spaces

Mathematical Logic Quarterly 60 (3):184-204 (2014)
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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.

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Computable randomness and betting for computable probability spaces.Jason Rute - 2016 - Mathematical Logic Quarterly 62 (4-5):335-366.

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References found in this work

Computability Theory.Barry Cooper - 2010 - Journal of the Indian Council of Philosophical Research 27 (1).
Computable metrization.Tanja Grubba, Matthias Schröder & Klaus Weihrauch - 2007 - Mathematical Logic Quarterly 53 (4‐5):381-395.
Admissible representations for probability measures.Matthias Schröder - 2007 - Mathematical Logic Quarterly 53 (4):431-445.

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