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

Anna Kuczmaszewska

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 o(1) requirements on specific weighted row-wise sums. Moreover, there are not any conditions assumed on the geometry of the underlying Banach space.