International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 9, Pages 443-458
On Chung-Teicher type strong law for arrays of vector-valued random variables
Department of Applied Mathematics, Lublin University of Technology, Nadbystrzycka 38D, Lublin 20-618, Poland
Received 2 January 2003
Copyright © 2004 Anna Kuczmaszewska. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We study the equivalence between the weak and strong laws of
large numbers for arrays of row-wise independent random elements
with values in a Banach space . The conditions
under which this equivalence holds are of the Chung or
Chung-Teicher types. These conditions are expressed in terms of
convergence of specific series and requirements on
specific weighted row-wise sums. Moreover, there are not any
conditions assumed on the geometry of the underlying Banach space.