Strong Laws for Blockwise ?-Dependent Random Fields

We consider random fields and introduce a concept of ℳ-dependence for random fields. Using a lemma from summability theory we prove strong laws of large numbers for blockwise ℳ-dependent random fields under various moment conditions, thereby generalizing some results in the literature from independent random fields. This research was started while the first author visited the University of Ulm, Institute of Number Theory & Probability Theory in October 2006; and it was also supported by the Hungarian National Foundation for Scientific Research under Grant T 046192.