Let $M = (X, \mathcal{F})$ be a D1108: Measurable space.
A D85: Unsigned basic measure $\mu : \mathcal{F} \to [0, \infty]$ is a sigma-bounded measure on $M$ if and only if there exists $E_0, E_1, E_2, \dots \in \mathcal{F}$ such that

(1)	$X = \bigcup_{n \in \mathbb{N}} E_n$ (D74: Set cover)
(2)	$\forall \, n \in \mathbb{N} : \mu(E_n) < \infty$