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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1998-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S016117129800091X |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |