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
Cerreia-Vioglio, Simone;Leonetti, Paolo;Maccheroni, Fabio;Marinacci, Massimo
2024
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.
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