  A Central Limit Theorem is proved for linear random fields when sums are
taken over finite disjoint union of rectangles. The approach does not rely upon
the use of Beveridge Nelson decomposition and the conditions needed are similar
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
Ibragimov result is obtained with a lot of uniformity.
