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International Journal of Mathematics and Mathematical Sciences
Volume 15 (1992), Issue 4, Pages 701-718
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 1 and 2 be lattices of subsets of a nonempty set X. Suppose 2 coallocates 1 and 1 is a subset of 2. We show that any 1-regular finitely additive measure on the algebra generated by 1 can be uniquely extended to an 2-regular measure on the algebra generated by 2. The case when 1 is not necessary contained in 2, as well as the measure enlargement problem are considered. Furthermore, some discussions on normal lattices and separation of lattices are also given.