What non-additive integral for ensemble spaces?
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908804617076736 |
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| author | Carcassi, Gabriele Aidala, Christine A. Thrien, Tobias |
| author_facet | Carcassi, Gabriele Aidala, Christine A. Thrien, Tobias |
| contents | In a previous work we were able to define a non-additive measure that can be used to represent both classical and quantum states in physics. We further extended this idea to work on a generic space of statistical ensembles (i.e. an ensemble space) in a way that connects to Choquet theory. The question of which non-additive integral is suitable to generalize the notion of expectation value remains open. In this paper we show that the Sugeno and Choquet integrals are not suitable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_01470 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | What non-additive integral for ensemble spaces? Carcassi, Gabriele Aidala, Christine A. Thrien, Tobias Quantum Physics Mathematical Physics In a previous work we were able to define a non-additive measure that can be used to represent both classical and quantum states in physics. We further extended this idea to work on a generic space of statistical ensembles (i.e. an ensemble space) in a way that connects to Choquet theory. The question of which non-additive integral is suitable to generalize the notion of expectation value remains open. In this paper we show that the Sugeno and Choquet integrals are not suitable. |
| title | What non-additive integral for ensemble spaces? |
| topic | Quantum Physics Mathematical Physics |
| url | https://arxiv.org/abs/2602.01470 |