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Oct 31, 2015 at 3:14 comment added Fabio For example the function $f(\lambda)=(1/N)H(\cdot-\lambda)$ ($H$ the Heaviside) will work. This correspond to the cumulative distribution function of the set $S$. As a side comment I found out that the function $(1/N)\sum_{i}^{N}H(x_i-\lambda)$ is a maximal invariant w.r.t. the permutation group (of order $N$) and any bijective function of it is still a maximally invariant.
Oct 30, 2015 at 21:40 history answered Mark Fischler CC BY-SA 3.0