On normal lattices and separation and semi‐separation of lattices

Abstract

ABSTRACT. This present paper is concerned with two main conditions,that of normality of a lattice, and separation and semi-separation of two lattices,both looked at using measure theoretic techniques.We look at each property using {0,1 two valued measures and associated {0,1 valued set functions.For normal lattices we look at consequences of normality in terms of properties of their measures and closely allied set functions.For separation and semi-separation of two lattices,we investigate the realtionship between regular measures of both lattices, define the notion of weak going up and look at this notion in terms of separation and semi-separation.We then give necessary and sufficent conditions for semi-separation in terms of equality of two set fuctions, derived from regular measures on the smaller lattice on the larger lattice.

Finitely subadditive and countably subadditive outer measures

“…Our notation and terminology is consistent with that of the following papers [2,4,7,8]. We give a brief review ofjust those concepts relevant to this paper in section two for the reader's convenience.…”