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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 $\{0,1\}$-valuedfinitely additive probability measures corresponding to the ultrafilterscontaining the dual filter of $\mathcal{I}$. This is obtained as a consequenceof an abstract analogue in the context of Archimedean Riesz spaces.

Capacities and Choquet Averages of Ultrafilters