Capacities and Choquet averages of ultrafilters
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- by Simone Cerreia-Vioglio, Paolo Leonetti, Fabio Maccheroni and Massimo Marinacci
- Proc. Amer. Math. Soc. 152 (2024), 1139-1151
- DOI: https://doi.org/10.1090/proc/16642
- Published electronically: January 5, 2024
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Abstract:
We show that a normalized capacity $\nu : \mathcal {P}(\mathbf {N})\to \mathbf {R}$ is invariant with respect to an ideal $\mathcal {I}$ on $\mathbf {N}$ if and only if it can be represented as a Choquet average of $\{0,1\}$-valued finitely additive probability measures corresponding to the ultrafilters containing the dual filter of $\mathcal {I}$. This is obtained as a consequence of an abstract analogue in the context of Archimedean Riesz spaces.References
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Bibliographic Information
- Simone Cerreia-Vioglio
- Affiliation: Universitá “Luigi Bocconi”, Department of Decision Sciences, Milan, Italy
- MR Author ID: 941013
- Email: simone.cerreia@unibocconi.it
- Paolo Leonetti
- Affiliation: Universitá degli Studi dell’Insubria, Department of Economics, via Monte Generoso 71, 21100 Varese, Italy
- MR Author ID: 1100670
- ORCID: 0000-0001-7819-5301
- Email: leonetti.paolo@gmail.com
- Fabio Maccheroni
- Affiliation: Universitá “Luigi Bocconi”, Department of Decision Sciences, Milan, Italy
- MR Author ID: 651058
- Email: fabio.maccheroni@unibocconi.it
- Massimo Marinacci
- Affiliation: Universitá “Luigi Bocconi”, Department of Decision Sciences, Milan, Italy
- MR Author ID: 613278
- ORCID: 0000-0002-0079-4176
- Email: massimo.marinacci@unibocconi.it
- Received by editor(s): July 15, 2022
- Received by editor(s) in revised form: July 4, 2023
- Published electronically: January 5, 2024
- Additional Notes: The first and fourth authors were financially supported by ERC (grants SDDM-TEA and INDIMACRO, respectively). The second and third authors were financially supported by PRIN (grant 2017CY2NCA)
- Communicated by: Vera Fischer
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 1139-1151
- MSC (2020): Primary 28A12, 40A35, 46A40; Secondary 28A25, 46B45, 54D35
- DOI: https://doi.org/10.1090/proc/16642
- MathSciNet review: 4693672