Definition:Monotone (Measure Theory)

Definition
Let $\SS$ be an algebra of sets.

Let $f: \SS \to \overline \R$ be an extended real-valued function, where $\overline \R$ denotes the set of extended real numbers.

Then $f$ is defined as monotone or monotonic :
 * $\forall A, B \in \SS: A \subseteq B \iff \map f A \le \map f B$