On the functor of comonotonically maxitive functionals
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913798893338624 |
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| author | Radul, Taras |
| author_facet | Radul, Taras |
| contents | We introduce a functor of functionals which preserve maximum of comonotone functions and addition of constants. This functor is a subfunctor of the functor of order-preserving functionals and contains the idempotent measure functor as subfunctor. The main aim of this paper is to show that this functor is isomorphic to the capacity functor. We establish such isomorphism using the fuzzy max-plus integral. In fact, we can consider this result as an idempotent analogue of Riesz Theorem about a correspondence between the set of $σ$-additive regular Borel measures and the set of linear positively defined functionals. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_18345 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the functor of comonotonically maxitive functionals Radul, Taras General Topology 28E10 We introduce a functor of functionals which preserve maximum of comonotone functions and addition of constants. This functor is a subfunctor of the functor of order-preserving functionals and contains the idempotent measure functor as subfunctor. The main aim of this paper is to show that this functor is isomorphic to the capacity functor. We establish such isomorphism using the fuzzy max-plus integral. In fact, we can consider this result as an idempotent analogue of Riesz Theorem about a correspondence between the set of $σ$-additive regular Borel measures and the set of linear positively defined functionals. |
| title | On the functor of comonotonically maxitive functionals |
| topic | General Topology 28E10 |
| url | https://arxiv.org/abs/2407.18345 |