Spaces of non-additive measures generated by triangular norms
We consider non-additive measures on the compact Hausdorff spaces, which are generalizations of the idempotent measures and max-min measures. These measures are related to the continuous triangular norms and they are defined as functionals on the spaces of continuous functions from a compact Hausdor...
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| Main Author: | |
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| Format: | Article |
| Language: | German |
| Published: |
Ivan Franko National University of Lviv
2023-06-01
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| Series: | Математичні Студії |
| Subjects: | |
| Online Access: | http://matstud.org.ua/ojs/index.php/matstud/article/view/430 |
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| Summary: | We consider non-additive measures on the compact Hausdorff spaces, which are generalizations of the idempotent measures and max-min measures. These measures are related to the continuous triangular norms and they are defined as functionals on the spaces of continuous functions from a compact Hausdorff space into the unit segment.
The obtained space of measures (called ∗-measures, where ∗ is a triangular norm) are endowed with the weak* topology. This construction determines a functor in the category of compact Hausdorff spaces. It is proved, in particular, that the ∗-measures of finite support are dense in the spaces of ∗-measures. One of the main results of the paper provides an alternative description of ∗-measures on a compact Hausdorff space X, namely as hyperspaces of certain subsets in X × [0, 1]. This is an analog of a theorem for max-min measures proved by Brydun and Zarichnyi. |
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| ISSN: | 1027-4634 2411-0620 |