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International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 2, Pages 279-291

Outer measure analysis of topological lattice properties

Polytechnic University, Brooklyn 11201, New York, USA

Received 21 October 1994; Revised 8 September 1995

Copyright © 1997 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.


Let X be a set and a lattice of subsets of X such that , X. A() is the algebra generated by , M() the set of nontrivial, finite, normegative, finitely additive measures on A() and I() those elements of M() which just assume the values zero and one. Various subsets of M() and I() are included which display smoothness and regularity properties.

We consider several outer measures associated with dements of M() and relate their behavior to smoothness and regularity conditions as well as to various lattice topological properties. In addition, their measurable sets are fully investigated. In the case of two lattices 1, 2, with 12, we present consequences of separation properties between the pair of lattices in terms of these outer measures, and further demonstrate the extension of smoothness conditions on 1 to 2.