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]).