| Title:
|
On the convergence of certain sums of independent random elements (English) |
| Author:
|
Ferrando, J. C. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
77-81 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this note we investigate the relationship between the convergence of the sequence $\{S_{n}\}$ of sums of independent random elements of the form $S_{n}=\sum_{i=1}^{n}\varepsilon_{i}x_{i}$ (where $\varepsilon_{i}$ takes the values $\pm\,1$ with the same probability and $x_{i}$ belongs to a real Banach space $X$ for each $i\in \Bbb N$) and the existence of certain weakly unconditionally Cauchy subseries of $\sum_{n=1}^{\infty}x_{n}$. (English) |
| Keyword:
|
independent random elements |
| Keyword:
|
copy of $c_{0}$ |
| Keyword:
|
Pettis integrable function |
| Keyword:
|
perfect measure space |
| MSC:
|
46B09 |
| MSC:
|
46B15 |
| MSC:
|
60B12 |
| idZBL:
|
Zbl 1090.46009 |
| idMR:
|
MR1903308 |
| . |
| Date available:
|
2009-01-08T19:19:38Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119301 |
| . |
| Reference:
|
[1] Cembranos P., Mendoza J.: Banach Spaces of Vector-Valued Functions.LNM 1676, Springer, 1997. Zbl 0902.46017, MR 1489231 |
| Reference:
|
[2] Díaz S., Fernández A., Florencio M., Paúl P.J.: Complemented copies of $c_{0}$ in the space of Pettis integrable functions.Quaestiones Math. 16 (1993), 61-66. MR 1217475 |
| Reference:
|
[3] Diestel J.: Sequences and series in Banach spaces.GTM 92, Springer-Verlag, New York-Berlin-Heidelberg-Tokyo, 1984. MR 0737004 |
| Reference:
|
[4] Diestel J., Uhl J.: Vector measures.Math Surveys 15, Amer. Math. Soc., Providence, 1977. Zbl 0521.46035, MR 0453964 |
| Reference:
|
[5] Ferrando J.C.: On a theorem of Kwapień.Quaestiones Math. 24 (2001), 51-54. Zbl 1019.46010, MR 1824912 |
| Reference:
|
[6] Freniche F.J.: Embedding $c_{0}$ in the space of Pettis integrable functions.Quaestiones Math. 21 (1998), 261-267. Zbl 0963.46025, MR 1701785 |
| Reference:
|
[7] Halmos P.R.: Measure Theory.GTM 18, Springer, New York-Berlin-Heidelberg-Barcelona, 1950. Zbl 0283.28001, MR 0033869 |
| Reference:
|
[8] Kwapień S.: On Banach spaces containing $c_{0}$.Studia Math. 52 (1974), 187-188. MR 0356156 |
| Reference:
|
[9] Vakhania N.N., Tarieladze V.I., Chobanian S.A.: Probability Distributions on Banach Spaces.D. Reidel Publishing Company, Dordrecht, 1987. MR 1435288 |
| . |
