On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity | Zendy

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On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity

Author(s) -

Charles Traina

Publication year - 2008

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2008/896480

Subject(s) - subadditivity , submodular set function , mathematics , set function , measure (data warehouse) , finite set , combinatorics , class (philosophy) , set (abstract data type) , discrete mathematics , function (biology) , lattice (music) , mathematical analysis , computer science , physics , database , artificial intelligence , evolutionary biology , acoustics , biology , programming language

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

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