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.