International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 8, Pages 461-474
On finitely subadditive outer measures and modularity properties
Department of Mathematics and Computer Science, St. John's University, 8000 Utopia Parkway, Jamaica 11439, NY, USA
Received 5 August 2002
Copyright © 2003 Charles Traina. 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 be a finite, finitely subadditive outer measure on
for . The measurable sets
and and the set are investigated in general, and in the
presence of regularity or modularity assumptions on . This is also done for
. General properties of are derived when is
weakly submodular. Applications and numerous examples are given.