| Title:
|
Another proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios (English) |
| Author:
|
Sato, Ryotaro |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
47 |
| Issue:
|
1 |
| Year:
|
2006 |
| Pages:
|
155-158 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Using the ratio ergodic theorem for a measure preserving transformation in a $\sigma $-finite measure space we give a straightforward proof of Derriennic's reverse maximal inequality for the supremum of ergodic ratios. (English) |
| Keyword:
|
$\sigma $-finite measure space |
| Keyword:
|
measure preserving transformation |
| Keyword:
|
conservative |
| Keyword:
|
ergodic |
| Keyword:
|
supremum of ergodic ratios |
| Keyword:
|
maximal and reverse maximal inequalities |
| MSC:
|
28D05 |
| MSC:
|
47A35 |
| idZBL:
|
Zbl 1150.28013 |
| idMR:
|
MR2223975 |
| . |
| Date available:
|
2009-05-05T16:56:23Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119582 |
| . |
| Reference:
|
[1] Derriennic Y.: On the integrability of the supremum of ergodic ratios.Ann. Probability 1 (1973), 338-340. Zbl 0263.28015, MR 0352404 |
| Reference:
|
[2] Ephremidze L.: On the distribution function of the majorant of ergodic means.Studia Math. 103 (1992), 1-15. MR 1184098 |
| Reference:
|
[3] Ephremidze L.: A new proof of the ergodic maximal equality.Real Anal. Exchange 29 (2003/04), 409-411. MR 2063082 |
| Reference:
|
[4] Krengel U.: Ergodic Theorems.Walter de Gruyter, Berlin, 1985. Zbl 0649.47042, MR 0797411 |
| Reference:
|
[5] Ornstein D.: A remark on the Birkhoff ergodic theorem.Illinois J. Math. 15 (1971), 77-79. Zbl 0212.40102, MR 0274719 |
| Reference:
|
[6] Sato R.: Maximal functions for a semiflow in an infinite measure space.Pacific J. Math. 100 (1982), 437-443. Zbl 0519.28010, MR 0669336 |
| . |
