Set function

In mathematics, especially measure theory, a set function is a function whose domain is a family of subsets of some given set and that (usually) takes its values in the extended real number line ${\displaystyle \mathbb {R} \cup \{\pm \infty \},}$ which consists of the real numbers ${\displaystyle \mathbb {R} }$ and ${\displaystyle \pm \infty .}$

A set function generally aims to measure subsets in some way. Measures are typical examples of "measuring" set functions. Therefore, the term "set function" is often used for avoiding confusion between the mathematical meaning of "measure" and its common language meaning.