AN L-p 'COUSIN OF COBOUNDARY' THEOREM FOR RANDOM FIELDS

摘要

It is known that for a given p is an element of [1, infinity) and a given strictly stationary sequence of random variables, the p-norms of the partial sums are bounded if and only if the sequence consists of successive differences from another strictly stationary sequence with finite p-norm. Here this is generalized to random fields, and the assumption of stationarity is relaxed. The index p = infinity is included.