International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 23-32

Lattice normality and outer measures

Panagiotis D. Stratigos

Department of Mathematics, Long Island University, Brooklyn 11201, NY, USA

Received 20 August 1991; Revised 26 March 1992

Copyright © 1993 Panagiotis D. Stratigos. 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.


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.

The present work establishes various relationships between normality of lattices of subsets of X and certain “outer measures“ induced by measures associated with the algebras of subsets of X generated by these lattices.