International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 4, Pages 785-793
doi:10.1155/S0161171299227858
Double sequence core theorems
Richard F. Patterson
Department of Mathematics and Computer Sciences, Duquesne University, 440 College Hall, Pittsburgh 15282, PA, USA
Abstract
In 1900, Pringsheim gave a definition of the convergence of double sequences. In this paper, that notion is extended by presenting definitions for the limit inferior and limit superior of double sequences. Also the core of a double sequence is defined. By using these definitions and the notion of regularity for 4-dimensional matrices, extensions, and variations of the Knopp Core theorem are proved.