International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 1, Pages 83-88

On outer measures and semi-separation of lattices

Robert W. Schutz

P.O. Box 1149, West Babylon, N.Y. 11704, USA

Received 13 October 1992; Revised 21 September 1993

Copyright © 1995 Robert W. Schutz. 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.


This present paper is concerned with set functions related to {0,1} two valued measures. These set functions are either outer measures or have many of the same characteristics. We investigate their properties and look at relations among them. We note in particular their association with the semi-separation of lattices.

To be more specific, we define three set functions μ, μ, and μ˜ related to μ ϵ I(L) the {0,1} two valued set functions defined on the algebra generated by the lattice of sets L st μ is a finitely additive monotone set function for which μ(ϕ)=0. We note relations among them and properties they possess.ln particular necessary and sufficient conditions are given for the semi-separation of lattices in terms of equality of set functions over a lattice of subsets.

Finally the notion of I-lattice is defined, we look at some properties of these with certain other side conditions assume, and end with an application involving semi-separation and I-lattices.