| Title:
|
Strongly mixing sequences of measure preserving transformations (English) |
| Author:
|
Behrends, Ehrhard |
| Author:
|
Schmeling, Jörg |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
377-385 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We call a sequence $(T_n)$ of measure preserving transformations strongly mixing if $P(T_n^{-1}A\cap B)$ tends to $P(A)P(B)$ for arbitrary measurable $A$, $B$. We investigate whether one can pass to a suitable subsequence $(T_{n_k})$ such that $\frac{1}{K} \sum _{k=1}^K f(T_{n_k}) \longrightarrow \int f \mathrm{d}P$ almost surely for all (or “many”) integrable $f$. (English) |
| Keyword:
|
ergodic transformation |
| Keyword:
|
strongly mixing |
| Keyword:
|
Birkhoff ergodic theorem |
| Keyword:
|
Komlós theorem |
| MSC:
|
28D05 |
| MSC:
|
37A05 |
| MSC:
|
37A25 |
| MSC:
|
37A30 |
| idZBL:
|
Zbl 0980.28011 |
| idMR:
|
MR1844317 |
| . |
| Date available:
|
2009-09-24T10:43:19Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127654 |
| . |
| Reference:
|
[1] P. Billingsley: Probability and Measure.John Wiley & Sons, New York, 1995. Zbl 0822.60002, MR 1324786 |
| Reference:
|
[2] J. Bourgain: Almost sure convergence and bounded entropy.Israel J. Math. 63 (1988), 79–97. Zbl 0677.60042, MR 0959049, 10.1007/BF02765022 |
| Reference:
|
[3] J. Komlós: A generalization of a problem of Steinhaus.Acta Math. Acad. Sci. Hungar 18 (1967), 217–229. MR 0210177, 10.1007/BF02020976 |
| Reference:
|
[4] J. M. Rosenblatt and M. Wierdl: Pointwise ergodic theorems via harmonic analysis.Ergodic theory and its connections with harmonic analysis, K. M. Petersen and I. A. Salama (eds.), London Math. Soc. Lecture Note Series 205, Cambridge Univ. Press, 1995. MR 1325697 |
| Reference:
|
[5] F. Schweiger: Ergodic theory of fibred systems and metric number theory.Oxford Science Publications, 1995. Zbl 0819.11027, MR 1419320 |
| Reference:
|
[6] P. Walters: An Introduction to Ergodic Theory.Springer, 1982. Zbl 0475.28009, MR 0648108 |
| . |
