International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 385-392
doi:10.1155/S0161171291000455
Measure characterizations and properties of normal and regular lattices
Department of Mathematics, Hofstra University, Hempstead 11550, New York, USA
Received 15 October 1989
Copyright © 1991 Peter M. Grassi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.