2023/07/31 by Cerreia-Vioglio, Simone, Leonetti, Paolo, Maccheroni, Fabio +1 · 1 citation
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #General Topology (math.GN)
paper · doi:10.48550/arxiv.2307.16823
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.