International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 2, Pages 253-262
Applications of outer measures to separation properties of lattices and regular or -smooth measures
University of Maine, Orono 04669-5752, Maine, USA
Received 1 March 1994; Revised 18 June 1994
Copyright © 1996 Pao-Sheng Hsu. 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.
Associated with a measure where is a lattice of subsets of are outer measures and ; associated with a -smooth measure is an outer measure or with , being the complementary lattice, another outer measure . These outer measures and their associated measurable sets are used to establish separation properties on and regularity and -smoothness of . Separation properties between two lattices and , , are similarly investigated. Notions of strongly -smooth and slightly regular measures are also used.