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Journal Articles Information and Computation Year : 2012

A constructive version of Birkhoff's ergodic theorem for Martin-Lof random points

Abstract

A theorem of Kucera states that given a Martin-Löf random infinite binary sequence {\omega} and an effectively open set A of measure less than 1, some tail of {\omega} is not in A. We first prove several results in the same spirit and generalize them via an effective version of a weak form of Birkhoff's ergodic theorem. We then use this result to get a stronger form of it, namely a very general effective version of Birkhoff's ergodic theorem, which improves all the results previously obtained in this direction, in particular those of V'Yugin, Nandakumar and Hoyrup, Rojas.
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Dates and versions

hal-00643629 , version 1 (22-11-2011)

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Laurent Bienvenu, Adam Day, Mathieu Hoyrup, Ilya Mezhirov, Alexander Shen. A constructive version of Birkhoff's ergodic theorem for Martin-Lof random points. Information and Computation, 2012, 210, pp.021-030. ⟨10.1016/j.ic.2011.10.006⟩. ⟨hal-00643629⟩
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