Let $M = (X, \mathcal{F}, \mu)$ be a D1158: Measure space such that

(i)	$\mathcal{G} \subseteq \mathcal{F}$ is a D470: Subsigma-algebra of $\mathcal{F}$ on $X$

An D4361: Unsigned basic function $\nu : \mathcal{G} \to [0, \infty]$ is a submeasure of $\mu$ on $M$ with respect to $\mathcal{G}$ if and only if $$\begin{equation} \forall \, E \in \mathcal{G} : \nu(E) = \mu(E) \end{equation}$$