Journal of Mathematical Logic 14 (1):1450004 (2014)

Abstract
We consider effective versions of two classical theorems, the Lebesgue density theorem and the Denjoy–Young–Saks theorem. For the first, we show that a Martin-Löf random real z ∈ [0, 1] is Turing incomplete if and only if every effectively closed class
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DOI 10.1142/s0219061314500044
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References found in this work BETA

Almost Everywhere Domination and Superhighness.Stephen G. Simpson - 2007 - Mathematical Logic Quarterly 53 (4):462-482.
Randomness and Computability: Open Questions.Joseph S. Miller & André Nies - 2006 - Bulletin of Symbolic Logic 12 (3):390-410.
Demuth Randomness and Computational Complexity.Antonín Kučera & André Nies - 2011 - Annals of Pure and Applied Logic 162 (7):504-513.
Almost Everywhere Domination.Natasha L. Dobrinen & Stephen G. Simpson - 2004 - Journal of Symbolic Logic 69 (3):914-922.
Demuth’s Path to Randomness.Antonín Kučera, André Nies & Christopher P. Porter - 2015 - Bulletin of Symbolic Logic 21 (3):270-305.

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Citations of this work BETA

Computing From Projections of Random Points.Noam Greenberg, Joseph S. Miller & André Nies - 2019 - Journal of Mathematical Logic 20 (1):1950014.
Lebesgue Density and Classes.Mushfeq Khan - 2016 - Journal of Symbolic Logic 81 (1):80-95.

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