| 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:
|
http://hdl.handle.net/10338.dmlcz/118801 |
| . |
| 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 |
| . |
