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

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

2010-07-29

arxiv.org/abs/1007.5249v2

Mathematics

Dynamical Systems

Improved version of the CiE'10 paper, with the strong form of Birkhoff's ergodic theorem for random points

Scientific paper

A theorem of Ku\v{c}era states that given a Martin-L\"of 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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