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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 16, Pages 2565-2573
http://dx.doi.org/10.1155/IJMMS.2005.2565

On compactness of lattices

Department of Mathematics, Pace University, Pleasantville 10570, NY, USA

Received 13 July 2004; Revised 27 June 2005

Copyright © 2005 Hindawi Publishing Corporation. 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

Let X be an arbitrary set and L a lattice of subsets of X. We denote by I(L) the set of those zero-one-valued nontrivial, finitely additive measures on A(L), the algebra generated by L, and we introduce other subsets of I(L). We study compactness/normality properties either relating to a single lattice L or relating to a pair of lattices L1L2 of subsets of X.