International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 4, Pages 785-793

Double sequence core theorems

Richard F. Patterson

Department of Mathematics and Computer Sciences, Duquesne University, 440 College Hall, Pittsburgh 15282, PA, USA

Received 13 April 1998; Revised 1 September 1998

Copyright © 1999 Richard F. Patterson. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.