International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 2, Pages 385-392

Measure characterizations and properties of normal and regular lattices

Peter M. Grassi

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.


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, 01 measures are noted which imply, or are equivalent to, the space being Hausdorff, regular, or prime complete.