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Title: On the sequence of integer parts of a good sequence for the ergodic theorem (English)
Author: Lesigne, Emmanuel
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 36
Issue: 4
Year: 1995
Pages: 737-743
Category: math
Summary: If $(u_n)$ is a sequence of real numbers which is good for the ergodic theorem, is the sequence of the integer parts $([u_n])$ good for the ergodic theorem\,? The answer is negative for the mean ergodic theorem and affirmative for the pointwise ergodic theorem. (English)
Keyword: ergodic theorem along subsequences
Keyword: Banach principle
MSC: 28D10
MSC: 40A30
MSC: 60F25
idZBL: Zbl 0868.28010
idMR: MR1378695
Date available: 2009-01-08T18:21:24Z
Last updated: 2012-04-30
Stable URL:
Reference: [1] Bergelson V., Boshernitzan M., Bourgain J.: Some results on non-linear recurrence.J. d'Analyse Math. 62 (1994), 29-46. MR 1269198
Reference: [2] Boshernitzan M., Jones R., Wierdl M.: Integer and fractional parts of good averaging sequences in ergodic theory.preprint, 1994. Zbl 0865.28011, MR 1412600
Reference: [3] Bourgain J.: Almost sure convergence and bounded entropy.Israel J. Math. 63 (1988), 79-97. Zbl 0677.60042, MR 0959049
Reference: [4] Garsia A.: Topics in Almost Everywhere Convergence.Lectures in Advanced Mathematics 4, 1970. Zbl 0198.38401, MR 0261253


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