International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 4, Pages 773-779
Lattice separation, coseparation and regular measures
The Rockefeller Group, 1230 Avenue of the Americas, New York 10020-1579, NY, USA
Received 14 November 1994; Revised 10 January 1995
Copyright © 1996 Maurice C. Figueres. 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 non-empty set, and let , ,
be lattices of subsets of
and . designates the algebra generated by and , these finite, non-trivial,
non-negative finitely additive measures on . denotes those elements of which assume
only the values zero and one. In terms of a or , various outer measures are introduced.
Their properties are investigated. The interplay of
measurability, smoothness of , regularity of and
lattice topological properties on these outer measures is also investigated.
Finally, applications of these outer measures to separation type
properties between pairs of
lattices , where are developed. In
terms of measures from , necessary and sufficient
conditions are established for to semi-separate , for to separate , and finally for to coseparate .