International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 3, Pages 417-436

Norms for copulas

William F. Darsow and Elwood T. Olsen

Department of Mathematics, Illinois Institute of Technology, Chicago 60616, Illinois, USA

Received 19 October 1993; Revised 20 July 1994

Copyright © 1995 William F. Darsow and Elwood T. Olsen. 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.


We consider several norms on the span of the set C of all copulas. Dominance and equivalence relationships among the norms are discussed, and completeness issues are addressed. The motivation for the study is discussed. Applications to the study of one parameter semigroups of copulas are also addressed.