Definition:Monotone (Measure Theory)

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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 if and only if:

$\forall A, B \in \SS: A \subseteq B \iff \map f A \le \map f B$