Maximum of element weights
= Maximum of element weights
{title2=$f(S)=\max_{v\in S}w(v)$}
On nonempty <subsets> of a nonempty <finite set> $V$, take the <maximum> of the contained element weights. Setting $f(\varnothing)=\min_{v\in V}w(v)$ extends this to a <monotone set function> and a <submodular set function>. More generally any value at the <empty set> at most every element weight works, because $\Delta_x f(S)=\max\{0,w(x)-f(S)\}$ satisfies <diminishing returns>.