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

Commentationes Mathematicae Universitatis Carolinae (1995)

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

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topLesigne, 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

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

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