Definition:Monotone


 * Monotone (Mapping Theory): A mapping from one ordered set to another is monotone iff it is either increasing or decreasing.
 * Monotone (Measure Theory): A mapping $$f: \mathcal S \to \R$$ on an algebra of sets $$\mathcal S$$ is monotone iff $$A \subseteq B \iff f \left({A}\right) \le f \left({B}\right)$$.