\begin{definition}[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''' {{iff}}:
:$\forall A, B \in \SS: A \subseteq B \iff \map f A \le \map f B$
Category:Definitions/Set Systems
\end{definition}