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arXiv · 2307.16823

Capacities and Choquet Averages of Ultrafilters

Simone Cerreia-Vioglio·Paolo Leonetti·Fabio Maccheroni·Massimo Marinacci
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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.

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Simone Cerreia-Vioglio, Paolo Leonetti, Fabio Maccheroni, Massimo Marinacci. 2023-07-31. Capacities and Choquet Averages of Ultrafilters. https://arxiv.org/abs/2307.16823

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