Let $M = (X, \mathcal{F})$ be a D1108: Measurable space.
An D4361: Unsigned basic function $\mu : \mathcal{F} \to [0, \infty]$ is an unsigned basic measure on $M$ if and only if

(1)	$$\begin{equation} \mu(\emptyset) = 0 \end{equation}$$
(2)	$$\begin{equation} \forall \, E_0, E_1, E_2, \dots \in \mathcal{F} \left( \forall \, n, m \in \mathbb{N} \left( n \neq m \quad \implies \quad E_n \cap E_m = \emptyset \right) \quad \implies \quad \mu \left( \bigcup_{n \in \mathbb{N}} E_n \right) = \sum_{n \in \mathbb{N}} \mu(E_n) \right) \end{equation}$$