Journal of Symbolic Logic 68 (4):1362-1376 (2003)

Abstract
It is shown that the class of Kolmogorov-Loveland stochastic sequences is not closed under selecting subsequences by monotonic computable selection rules. This result gives a strong negative answer to the question whether the Kolmogorov-Loveland stochastic sequences are closed under selecting sequences by Kolmogorov-Loveland selection rules, i.e., by not necessarily monotonic, partial computable selection rules. The following previously known results are obtained as corollaries. The Mises-Wald-Church stochastic sequences are not closed under computable permutations, hence in particular they form a strict superclass of the class of Kolmogorov-Loveland stochastic sequences. The Kolmogorov-Loveland selection rules are not closed under composition
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DOI 10.2178/jsl/1067620192
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References found in this work BETA

A New Interpretation of the von Mises' Concept of Random Sequence.Donald Loveland - 1966 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 12 (1):279-294.

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Uniform Distribution and Algorithmic Randomness.Jeremy Avigad - 2013 - Journal of Symbolic Logic 78 (1):334-344.
Computable Randomness and Betting for Computable Probability Spaces.Jason Rute - 2016 - Mathematical Logic Quarterly 62 (4-5):335-366.

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