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 (sk,l)(sk,l) is summable by a four-dimensional RH-regular matrix A=(am,n,k,l)A=(am,n,k,l) if and only if (sk,l)(sk,l) is PP-convergent. This theorem is established using multidimensional sliding hump constructions for bounded and unbounded doubles sequences.