Department of Mathematics, Faculty of Electrical Engineering and Computer Science, Lublin University of Technology, Nadbystrzycka Street 38A, 20-618 Lublin, Poland
Copyright © 2009 Zbigniew A. Lagodowski. 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 extend to random fields case, the results of Woyczynski, who proved
Brunk's type strong law of large numbers (SLLNs) for -valued random vectors under geometric
assumptions. Also, we give probabilistic requirements for above-mentioned
SLLN, related to results obtained by Acosta as well as necessary and sufficient probabilistic
conditions for the geometry of Banach space associated to the strong and
weak law of large numbers for multidimensionally indexed random vectors.