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A constructive version of Birkhoff's ergodic theorem for Martin-Lof random points
Abstract
Improved version of the CiE'10 paper, with the strong form of Birkhoff's ergodic theorem for random pointsInternational audienceA 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- info:eu-repo/semantics/article
- Journal articles
- Algorithmic randomness
- Birkhoff's ergodic theorem
- Poincaré recurrence theorem
- Martin-Löf randomness
- [INFO.INFO-LO]Computer Science [cs]/Logic in Computer Science [cs.LO]
- [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS]
- [MATH.MATH-PR]Mathematics [math]/Probability [math.PR]