Let $M = (X, \mathcal{F})$ be a D1108: Measurable space.
A D85: Unsigned basic measure $\mu : \mathcal{F} \to [0, \infty]$ is a zero measure on $M$ if and only if $$\begin{equation} \forall \, E \in \mathcal{F} : \mu(E) = 0 \end{equation}$$