Outer measure analysis of topological lattice properties

Abstract

Let X be a set and ℒ a lattice of subsets of X such that ∅, X∈ℒ. A(ℒ) is the algebra generated by ℒ, M(ℒ) the set of nontrivial, finite, normegative, finitely additive measures on A(ℒ) and I(ℒ) those elements of M(ℒ) which just assume the values zero and one. Various subsets of M(ℒ) and I(ℒ) are included which display smoothness and regularity properties.

Keywords

• lattice
• measure
• associated outer measure
• regular outer measure
• weakly regular
• vaguely regular
• almost countably compact
• complement generated
• countably paracompact
• delta
• normal
• semi-separation
• separation
• coseparation.