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.

Keywords

• lattice space
• lattice normality
• lattice regularity and σ-smoothness of a measure
• weak lattice regularity of a measure
• finitely subadditive outer measure; countably subadditive outer measure.