On convergence for series of random elements
Journal
Nonlinear Analysis, Theory, Methods and Applications
Journal Volume
47
Journal Issue
2
Pages
1297-1308
Date Issued
2001
Author(s)
Hu, T.-C.
Abstract
In this paper, we extend some relevant concepts for Banach space valued random elements and some preliminary results are presented which axe used to obtain our main results. We show that the sufficiency half of Kolmogorov's three series theorem holds for the convergence of series of independent random elements under suitable geometric conditions on the Banach space. However, the necessity part is not true in general as will be shown by a counter-example. From the main result, a strong law of numbers for independent random elements can be obtained. Some equivalent conditions for Banach spaces being of Rademacher-type p are also provided.
Type
journal article