International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 385-392
doi:10.1155/S0161171291000455

Measure characterization 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.