Definition:Monotone (Measure Theory)

Definition
Let $\mathcal S$ be an algebra of sets.

Let $f: \mathcal S \to \overline {\R}$ be a real-valued function where $\overline {\R}$ denotes the set of extended real numbers.

Then $f$ is defined as monotone or monotonic iff:
 * $\forall A, B \in \mathcal S: A \subseteq B \iff f \left({A}\right) \le f \left({B}\right)$