Monotonic set function

Sometimes called Monotone set function.

Definition

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

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

See also

• Subtractive set function