International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 701-718
doi:10.1155/S0161171292000929
Measures on coallocation and normal lattices
Norden Systems, 75 Maxess Road, Melville, New York 11747, USA
Received 29 January 1991; Revised 15 April 1991
Copyright © 1992 Jack-Kang Chan. 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
Let ℒ1 and ℒ2 be lattices of subsets of a nonempty set X. Suppose ℒ2 coallocates ℒ1 and ℒ1 is a subset of ℒ2. We show that any ℒ1-regular finitely additive measure on the algebra generated by ℒ1 can be uniquely extended to an ℒ2-regular measure on the algebra generated by ℒ2. The case when ℒ1 is not necessary contained in ℒ2, as well as the measure enlargement problem are considered. Furthermore, some discussions on normal lattices and separation of lattices are also given.