Outer measures and weak regularity of measures

Abstract

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(ℒ) or for those elements of I(ℒ) with added smoothness conditions.

Keywords

• lattice regular
• σ-smooth
• and outer measures. weakly
• vaguely
• and slightly regular measures. normal and complement generated lattices.