On the sequence of integer parts of a good sequence for the ergodic theorem

Emmanuel Lesigne

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 4, page 737-743
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Lesigne, Emmanuel. "On the sequence of integer parts of a good sequence for the ergodic theorem." Commentationes Mathematicae Universitatis Carolinae 36.4 (1995): 737-743. <http://eudml.org/doc/247730>.

@article{Lesigne1995,
abstract = {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.},
author = {Lesigne, Emmanuel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {ergodic theorem along subsequences; Banach principle; good averaging sequences; measure preserving flow; ergodic theorem along subsequences; Banach principle; mean ergodic theorem; pointwise ergodic theorem},
language = {eng},
number = {4},
pages = {737-743},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the sequence of integer parts of a good sequence for the ergodic theorem},
url = {http://eudml.org/doc/247730},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Lesigne, Emmanuel
TI - On the sequence of integer parts of a good sequence for the ergodic theorem
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 4
SP - 737
EP - 743
AB - 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.
LA - eng
KW - ergodic theorem along subsequences; Banach principle; good averaging sequences; measure preserving flow; ergodic theorem along subsequences; Banach principle; mean ergodic theorem; pointwise ergodic theorem
UR - http://eudml.org/doc/247730
ER -

References

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  1. Bergelson V., Boshernitzan M., Bourgain J., Some results on non-linear recurrence, J. d'Analyse Math. 62 (1994), 29-46. (1994) MR1269198
  2. Boshernitzan M., Jones R., Wierdl M., Integer and fractional parts of good averaging sequences in ergodic theory, preprint, 1994. Zbl0865.28011MR1412600
  3. Bourgain J., Almost sure convergence and bounded entropy, Israel J. Math. 63 (1988), 79-97. (1988) Zbl0677.60042MR0959049
  4. Garsia A., Topics in Almost Everywhere Convergence, Lectures in Advanced Mathematics 4, 1970. Zbl0198.38401MR0261253

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