Subtractive set function

Definition

A set function $$f:E\rightarrow[0,\infty]\subset\mathbb{R}\cup\{-\infty,\infty\}$$ is subtractive if whenever $A,B\in E$ we have

$$A\subseteq B\wedge B-A\in E\wedge |f(B)|<\infty\implies f(B-A)=f(B)-f(A)$$

See also

• Monotonic set function