Smoothness conditions on measures using Wallman spaces - Charles Traina (International Journal of Mathematics and Mathematical Sciences)
In this paper, X denotes an arbitrary nonempty set, ℒ a lattice of subsets of X with ∅,X∈ℒ,A(ℒ) is the algebra generated by ℒ and M(ℒ) is the set of nontrivial, finite, and finitely additive measures on A(ℒ), and MR(ℒ) is the set of elements of M(ℒ) which are ℒ-regular. It is well known that any μ∈M(ℒ) induces a finitely additive measure μ¯ on an associated Wallman space. Whenever μ∈MR(ℒ),μ¯ is countably additive.