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) | $\forall \, n \in \mathbb{N} : \mu(E_n) < \infty$ |