International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 2, Pages 391-400
Remarks on -measurbale sets: regularity, -smootheness, and measurability
Pace University, Pace Plaza, New York 10038, NY, USA
Received 10 September 1996; Revised 3 March 1998
Copyright © 1999 Carman Vlad. 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 be an arbitrary nonempty set and a lattice of subsets of such that . is the algebra generated by and denotes those nonnegative, finite, finitely additive measures on . denotes the subset of of nontrivial zero-one valued measures. Associated with (or ) are the outer measures and considered in detail. In addition, measurability conditions and regularity conditions are investigated and specific characteristics are given for , the set of -measurable sets. Notions of strongly -smooth and vaguely regular measures are also discussed. Relationships between regularity, -smoothness and measurability are investigated for zero-one valued measures and certain results are extended to the case of a pair of lattices where .