International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 49-58

Outer measures and weak regularity of measures

Dale Siegel

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

Received 29 January 1992; Revised 7 July 1994

Copyright © 1995 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 investigates smoothness properties of probability measures on lattices which imply regularity, and then considers weaker versions of regularity; in particular, weakly regular, vaguely regular, and slightly regular. They are derived from commonly used outer measures, and we analyze them mainly for the case of I() or for those elements of I() with added smoothness conditions.