On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity

Charles Traina

International Journal of Mathematics and Mathematical Sciences, 2008, vol. 2008, 1-13

Abstract:

Given a nonempty abstract set ð ‘‹ , and a covering class ð ’ž , and a finite, finitely subadditive outer measure 𠜈 , we construct an outer measure 𠜈 and investigate conditions for 𠜈 to be submodular. We then consider several other set functions associated with 𠜈 and obtain conditions for equality of these functions on the lattice generated by ð ’ž . Lastly, we describe a construction of a finite, finitely subadditive outer measure given an arbitrary family of subsets, ℬ , of ð ‘‹ and a nonnegative, finite set function ð œ defined on ℬ .

Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:896480

DOI: 10.1155/2008/896480

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