Algorithmic randomness over general spaces |
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Authors: | Kenshi Miyabe |
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Institution: | Research Institute for Mathematical Sciences, Kyoto University, , Kyoto 606‐8502 Japan |
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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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