Abstract
We extend to random fields case, the results of Woyczynski, who proved Brunk's type strong law of large numbers (SLLNs) forđč-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.
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