International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 4, Pages 687-694

Outer measures and associated lattice properties

Peter M. Grassi

Department of Mathematics, Hofstra University, Hempstead 11550, NY, USA

Received 30 January 1992; Revised 18 May 1992

Copyright © 1993 Peter M. Grassi. 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.


Zero-one measure characterizations of lattice properties such as normality are extended to more general measures. For a given measure, we consider two associated “outer” measures and attempt to obtain the “outer”-measurable sets. We also seek necessary and sufficient conditions for the measure and outer measures to be equal on the lattice or its complement.