Journal of Probability and Statistics
Volume 2011 (2011), Article ID 701952, 16 pages
http://dx.doi.org/10.1155/2011/701952
Research Article

Weighted Strong Law of Large Numbers for Random Variables Indexed by a Sector

Przemysław Matuła1 and Michał Seweryn2

1Institute of Mathematics, Marie Curie-Skłodowska University, Plac Marii Curie-Skłodowskiej 1, 20-031 Lublin, Poland
2Faculty of Mathematics and Computer Science, University of Łódź, Ulica Banacha 22, 90-238 Łódź, Poland

Received 13 May 2011; Revised 30 September 2011; Accepted 22 October 2011

Academic Editor: Nikolaos E. Limnios

Copyright © 2011 Przemysław Matuła and Michał Seweryn. 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.

Abstract

We find necessary and sufficient conditions for the weighted strong law of large numbers for independent random variables with multidimensional indices belonging to some sector.