International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 723-728

Weak regularity of probability measures

Dale Siegel

Kingsborough Community College, Mathematics/Computer Science Department, 2001 Oriental Boulevard, Brooklyn 11235, New York, USA

Received 9 September 1996; Revised 7 January 1997

Copyright © 1998 Dale Siegel. 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.


This paper examines smoothness attributes of probability measures on lattices which indicate regularity, and then discusses weaker forms of regularity; specifically, weakly regular and vaguely regular. They are obtained from commonly used outer measures, and we study them mainly for the case of M() or for those components of M() with added smoothness prerequisites. This is a generalization of many concepts presented in my earlier paper (see [1]).