Some notes on the coincidence of the Choquet integral and the pan-integral

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F25%3A00600441" target="_blank" >RIV/67985556:_____/25:00600441 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0165011424003245?via%3Dihub" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0165011424003245?via%3Dihub</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.fss.2024.109178" target="_blank" >10.1016/j.fss.2024.109178</a>

Result language
angličtina
Original language name
Some notes on the coincidence of the Choquet integral and the pan-integral
Original language description
In this note, we provide an example to show the weak (M)-property is really weaker than the (M)-property for some finite monotone measure defined on infinite space, and hence answer an open problem which was proposed in the paper (Li et al. (2023) [9]). We prove that if a monotone measure μ is autocontinuous, then the weak (M)-property and the (M)-property of μ are equivalent. We propose the concept of (C-P)-property of monotone measures and show a set of sufficient and necessary conditions that the Choquet integral coincides with the pan-integral. We further study the relationships between the Choquet integral and the pan-integral in the setting of the ordered pairs of monotone measures, and obtain some interesting properties.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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