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International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 253-262
http://dx.doi.org/10.1155/S016117129600035X

Applications of outer measures to separation properties of lattices and regular or σ-smooth measures

University of Maine, Orono 04669-5752, Maine, USA

Received 1 March 1994; Revised 18 June 1994

Copyright © 1996 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

Associated with a 01 measure μI() where is a lattice of subsets of X are outer measures μ and μ˜; associated with a σ-smooth 01 measure μIσ() is an outer measure μ or with μIσ(), being the complementary lattice, another outer measure μ˜˜. These outer measures and their associated measurable sets are used to establish separation properties on and regularity and σ-smoothness of μ. Separation properties between two lattices 1 and 2, 12, are similarly investigated. Notions of strongly σ-smooth and slightly regular measures are also used.