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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 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.


Let ν be a finite, finitely subadditive outer measure on P(X). Define ρ(E)=ν(X)ν(E) for EX. The measurable sets Sν and Sρ and the set S={EX/ν(E)=ρ(E)} are investigated in general, and in the presence of regularity or modularity assumptions on ν. This is also done for ν0(E)=inf{ν(M)/EMSν}. General properties of ν are derived when ν is weakly submodular. Applications and numerous examples are given.