International Journal of Mathematics and Mathematical Sciences
Volume 21 (1998), Issue 4, Pages 723-728
doi:10.1155/S0161171298001008

Weak regularity of probability measures

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]).