  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.
