Abstract. We consider random fields with iid random variables and prove strong laws for delayed sums, i.e., sums over rectangular blocks of these random variables. We show that strong laws hold iff appropriate moment conditions are satisfied. These moment conditions depend on the size and shape of the blocks on which the delayed sums are based.

AMS Subject Classification (1991): 60F05

Keyword(s): strong laws, random fields, delayed sums, sums over rectangular blocks, moment conditions

Received October 2, 2008, and in final form September 14, 2009. (Registered under 6437/2009.)