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 $A \subseteq B \iff f \left({A}\right) \le f \left({B}\right)$.