International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 1, Pages 23-32
doi:10.1155/S016117129300002X
Lattice normality and outer measures
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.
Abstract
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.