We show that a normalized capacity ν : P(N) → R is invariant with respect to an ideal I on 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 I. This is obtained as a consequence of an abstract analogue in the context of Archimedean Riesz spaces.

Capacities and Choquet averages of ultrafilters

Paolo Leonetti
;
2024-01-01

Abstract

We show that a normalized capacity ν : P(N) → R is invariant with respect to an ideal I on 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 I. This is obtained as a consequence of an abstract analogue in the context of Archimedean Riesz spaces.
2024
2024
https://doi.org/10.1090/proc/16642
Archimedean Riesz space; Stone–˘Cech compactification; Choquet averages; normalized capacities; submeasures; ideal convergence
Leonetti, Paolo; Cerreia-Vioglio, Simone; Maccheroni, Fabio; Marinacci, Massimo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11383/2163276
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