International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 701-718
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.
Let and be lattices of subsets of a nonempty set . Suppose coallocates and is a subset of . We show that any -regular finitely additive measure on the algebra generated by can be uniquely extended to an -regular measure on the algebra generated by . The case when is not necessary contained in , as well as the measure enlargement problem are considered. Furthermore, some discussions on normal lattices and separation of lattices are also given.