A category theorem for double sequences

The goal of this paper is to present the following multidimensional category theorem for double sequences via four-dimensional matrix transformations. The set of second category double subsequences of the double sequence (S(k,l)) is summable by a four-dimensional RH-regular matrix A = (a(m,n,k,l)) if and only if (S(k,l)) is P-convergent. This theorem is established using multidimensional sliding hump constructions for bounded and unbounded doubles sequences. (C) 2011 Elsevier Ltd. All rights reserved.