A Central Limit Theorem for linear random fields

A Central Limit Theorem is proved for linear random fields when sums are taken over union of finitely many disjoint rectangles. The approach does not rely upon the use of Beveridge–Nelson decomposition and the conditions needed are similar in nature to those given by Ibragimov for linear processes. When specializing this result to the case when sums are being taken over rectangles, a complete analogue of the Ibragimov result is obtained for random fields with a lot of uniformity.