International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 723-728
doi:10.1155/S0161171298001008
Weak regularity of probability measures
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.
Abstract
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(ℒ) or for those components of M(ℒ) with added smoothness prerequisites. This is a
generalization of many concepts presented in my earlier paper (see [1]).