Measure characterizations and properties of normal and regular lattices

Abstract

Various equivalent characterizations of normality are considered and a measure theoretic definition is given for strongly normal lattices. Measure conditions related to the apace of σ-smooth, lattice-regular, 0−1 measures are noted which imply, or are equivalent to, the space being Hausdorff, regular, or prime complete.

Keywords

• lattice
• zero-one measures
• sigma-smooth
• normal
• regular
• Hausdorff
• prime complete
• strongly normal
• filter
• disjunctive.