Monotonic set function

Sometimes called Monotone set function.

Definition

A set function $f:E\rightarrow [0,\infty]\subset\mathbb{R}$ is monotonic if for $A,B\in E$ we have $A\subseteq B\implies f(A)\le f(B)$

We do not require a function that maps to $[0,\infty]$ any linearly ordered set will do. It will likely be encountered in this form though.

See also

• Subtractive set function