Definition:Monotone (Measure Theory)

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Definition

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

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


Then $f$ is defined as monotone or monotonic iff:

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