A constructive version of Birkhoff's ergodic theorem for Martin-Löf random points
type: Item
instance of: scholarly article
title: A constructive version of Birkhoff's ergodic theorem for Martin-Löf random points
zbMATH Open document ID: 1257.03067
author: Laurent Bienvenu
author: Adam R. Day
author: Mathieu Hoyrup
author: Ilya Mezhirov
author: A. Shen
published in: Information and Computation
publication date: 2012-05-24T00:00:00Z
full work available at URL: https://arxiv.org/abs/1007.5249
full work available at URL: ergodic-edited.pdf
review text: The authors prove a constructive version of Birkhoff's ergodic theorem for Martin-Löf random reals and effectively open sets. From the proof one can extract a new simple proof of the effective ergodic theorem. The main result was independently obtained by \textit{J. N. Y Franklin}, \textit{N. Greenberg}, \textit{J. S. Miller} and \textit{K. M. Ng} in [``Martin-Löf random points satisfy Birkhoff's ergodic theorem for effectively closed sets'', Proc. Am. Math. Soc. 140, No. 10, 3623--3628 (2012; \url{doi:10.1090/S0002-9939-2012-11179-7})].
reviewed by: Cristian S. Calude
Mathematics Subject Classification ID: 03D32
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 37A30
Mathematics Subject Classification ID: 68Q30
zbMATH DE Number: 6038284
zbMATH Keywords: Martin-Löf random real
zbMATH Keywords: Birkhoff's ergodic theorem
zbMATH Keywords: Poincaré recurrence
MaRDI profile type: Publication
OpenAlex ID: W1593512589
arXiv ID: 1007.5249
Wikidata QID: Q57349503
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DOI: 10.1016/J.IC.2011.10.006
description: scientific article; zbMATH DE number 6038284