Some remarks concerning finitely Subadditive outer measures with applications
The present paper is intended as a first step toward the establishment of a general theory of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive outer measure and an associated finitely additive measure on any space is presented. This is followed by...
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| Format: | Article |
| Language: | English |
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Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117129800091X |
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| _version_ | 1832561702722338816 |
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| author | John E. Knight |
| author_facet | John E. Knight |
| author_sort | John E. Knight |
| collection | DOAJ |
| description | The present paper is intended as a first step toward the establishment of a general theory
of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive
outer measure and an associated finitely additive measure on any space is presented. This is followed by
a discussion of the theory of inner measures, their construction, and the relationship of their properties to
those of an associated finitely subadditive outer measure. In particular, the interconnections between the
measurable sets determined by both the outer measure and its associated inner measure are examined.
Finally, several applications of the general theory are given, with special attention being paid to various
lattice related set functions. |
| format | Article |
| id | doaj-art-50a0becb84a84c6aaa205a816102ed8e |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1998-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-50a0becb84a84c6aaa205a816102ed8e2025-02-03T01:24:28ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251998-01-0121465366910.1155/S016117129800091XSome remarks concerning finitely Subadditive outer measures with applicationsJohn E. Knight0Department of Mathematics, Long Island University, Brooklyn Campus, University Plaza, Brooklyn, New York 11201, USAThe present paper is intended as a first step toward the establishment of a general theory of finitely subadditive outer measures. First, a general method for constructing a finitely subadditive outer measure and an associated finitely additive measure on any space is presented. This is followed by a discussion of the theory of inner measures, their construction, and the relationship of their properties to those of an associated finitely subadditive outer measure. In particular, the interconnections between the measurable sets determined by both the outer measure and its associated inner measure are examined. Finally, several applications of the general theory are given, with special attention being paid to various lattice related set functions.http://dx.doi.org/10.1155/S016117129800091XOuter measureinner measuremeasurable setfinitely subadditive superadditivecountably superadditivesubmodularsupermodularregularapproximately regular condition (M). |
| spellingShingle | John E. Knight Some remarks concerning finitely Subadditive outer measures with applications International Journal of Mathematics and Mathematical Sciences Outer measure inner measure measurable set finitely subadditive superadditive countably superadditive submodular supermodular regular approximately regular condition (M). |
| title | Some remarks concerning finitely Subadditive outer measures with applications |
| title_full | Some remarks concerning finitely Subadditive outer measures with applications |
| title_fullStr | Some remarks concerning finitely Subadditive outer measures with applications |
| title_full_unstemmed | Some remarks concerning finitely Subadditive outer measures with applications |
| title_short | Some remarks concerning finitely Subadditive outer measures with applications |
| title_sort | some remarks concerning finitely subadditive outer measures with applications |
| topic | Outer measure inner measure measurable set finitely subadditive superadditive countably superadditive submodular supermodular regular approximately regular condition (M). |
| url | http://dx.doi.org/10.1155/S016117129800091X |
| work_keys_str_mv | AT johneknight someremarksconcerningfinitelysubadditiveoutermeasureswithapplications |