A constructive version of Birkhoff's ergodic theorem for Martin-Lof random points - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
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.
Fichier principal
Vignette du fichier
ergodic-edited.pdf (165.25 Ko) Télécharger le fichier
Origin Files produced by the author(s)
Loading...

Dates and versions

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

Identifiers

Cite

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⟩
491 View
259 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More