Definition:Monotone (Measure Theory)

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:
 * $$\forall A, B \in \mathcal S: A \subseteq B \iff f \left({A}\right) \le f \left({B}\right)$$