International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 23-32
doi:10.1155/S016117129300002X

Lattice normality and outer measures

Abstract

A lattice space is defined to be an ordered pair whose first component is an arbitrary set X and whose second component is an arbitrary lattice L of subsets of X. A lattice space is a generalization of a topological space. The concept of lattice normality plays an important role in the study of lattice spaces.The present work establishes various relationships between normality of lattices of subsets of X and certain “outer measures“ induced by measures associated with the algebras of subsets of X generated by these lattices.