How to extend Carath\'eodory's theorem to lattice-valued functionals
Substituting in the definition of outer measure the addition with the maximum (or the supremum, or the join) operation we obtain a new set function called retuo measure. It is proved that every retuo measure is an outer measure. We give necessary and sufficient conditions for a set function to be a...
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| Format: | Article |
| Language: | English |
| Published: |
Erdal KARAPINAR
2020-09-01
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| Series: | Results in Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/tr/download/article-file/1187107 |
| Summary: | Substituting in the definition of outer measure the addition with the maximum (or the supremum, or the join) operation we obtain a new set function called retuo measure. It is proved that every retuo measure is an outer measure. We give necessary and sufficient conditions for a set function to be a retuo measure. Similarly as in the case of outer measure, we propose a way to construct retuo measures. We consider some theoretical applications for constructed pairs of outer and retuo measures in the image of the Hausdorff
measure and dimension. |
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| ISSN: | 2636-7556 2636-7556 |