On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity
Given a nonempty abstract set 𝑋, and a covering class 𝒞, and a finite, finitely subadditive outer measure 𝜈, we construct an outer measure 𝜈 and investigate conditions for 𝜈 to be submodular. We then consider several other set functions associated with 𝜈 and obtain conditions for equality of these f...
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| Format: | Article |
| Language: | English |
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Wiley
2008-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2008/896480 |
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| _version_ | 1849306441089810432 |
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| author | Charles Traina |
| author_facet | Charles Traina |
| author_sort | Charles Traina |
| collection | DOAJ |
| description | Given a nonempty abstract set 𝑋, and a covering class 𝒞, and a finite, finitely subadditive outer measure 𝜈, we construct an outer measure 𝜈 and investigate conditions for 𝜈 to be submodular. We then consider several
other set functions associated with 𝜈 and obtain conditions for equality of these
functions on the lattice generated by 𝒞. Lastly, we describe a construction of a finite, finitely subadditive outer measure given an arbitrary family of subsets, ℬ, of 𝑋 and a nonnegative, finite set function 𝜏 defined on ℬ. |
| format | Article |
| id | doaj-art-3518ae0621044fb7a9eb243797d637a5 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2008-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3518ae0621044fb7a9eb243797d637a52025-08-20T03:55:06ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252008-01-01200810.1155/2008/896480896480On Constructing Finite, Finitely Subadditive Outer Measures, and SubmodularityCharles Traina0Department of Mathematics & Computer Science, St. John's University, 8000 Utopia Parkway Queens, New York, NY 11439, USAGiven a nonempty abstract set 𝑋, and a covering class 𝒞, and a finite, finitely subadditive outer measure 𝜈, we construct an outer measure 𝜈 and investigate conditions for 𝜈 to be submodular. We then consider several other set functions associated with 𝜈 and obtain conditions for equality of these functions on the lattice generated by 𝒞. Lastly, we describe a construction of a finite, finitely subadditive outer measure given an arbitrary family of subsets, ℬ, of 𝑋 and a nonnegative, finite set function 𝜏 defined on ℬ.http://dx.doi.org/10.1155/2008/896480 |
| spellingShingle | Charles Traina On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity International Journal of Mathematics and Mathematical Sciences |
| title | On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity |
| title_full | On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity |
| title_fullStr | On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity |
| title_full_unstemmed | On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity |
| title_short | On Constructing Finite, Finitely Subadditive Outer Measures, and Submodularity |
| title_sort | on constructing finite finitely subadditive outer measures and submodularity |
| url | http://dx.doi.org/10.1155/2008/896480 |
| work_keys_str_mv | AT charlestraina onconstructingfinitefinitelysubadditiveoutermeasuresandsubmodularity |