Monotone set function
= Monotone set function
{title2=$A\subseteq B\Rightarrow f(A)\leq f(B)$}
A real-valued <set function> is monotone, in the nondecreasing convention, when enlarging its input <subset> cannot decrease its value. Equivalently, each <marginal increment> $\Delta_x f(S)$ is nonnegative. This follows by adding elements individually; the converse follows by considering $S\subseteq S\cup\{x\}$. A <normalised set function> with this property is a <nonnegative function>.