Let $(E,\mathcal E)$ be a measurable space, let $\mu$ be a $\sigma$-finite positive measure, and let $\nu:\mathcal E\to\mathbb C$ be a finite complex measure. If $\nu\ll\mu$, then there exists $g\in L^1(E,\mathcal E,\mu)$ such that for every $A\in\mathcal E$, \begin{align*} \nu(A)=\int_A g\,d\mu. \end{align*} The function $g$ is unique up to equality $\mu$-a.e.