A general measure decomposition theorem by means of the generalized wallman remainder

Abstract

Let £ be a lattice of subsets of a set X. Let MR(t) denote the set of all £-regular (finitely additive) measures on the algebra generated by £. Under the assumption that £ is disjunctive, in the first part of the paper, criteria are obtained for the a-smoothness, r-smoothness, and tightness of elements of MR(t) in terms of the general Wallman remainder. In the second part of the paper, various applications are given, and, in particular, extensions and refinements of the Yosida-Hewitt Decomposition Theorem are obtained.