Let $M = (X, \mathcal{F})$ be a D1108: Measurable space such that

(i)	$\mu, \nu : \mathcal{F} \to [0, \infty]$ are each an D85: Unsigned basic measure on $M$
(ii)	$f : X \to [0, \infty]$ is an D5610: Unsigned basic Borel function on $M$

Then $f$ is a Radon-Nikodym derivative of $\mu$ with respect to $\nu$ if and only if \begin{equation} \forall \, E \in \mathcal{F} : \mu(E) = \int_E f \, d \nu \end{equation}