# Definition:Monotone (Measure Theory)

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 if and only if:
$\forall A, B \in \SS: A \subseteq B \iff \map f A \le \map f B$