If $M$ is a smooth manifold and $\mu$ is a $1$-density thereon then we may define a Borel measure (on Borel sets $A$) on $M$ as: \begin{equation} \nu(A) = \int_M I_A \mu. \end{equation}

My question is does the converse hold also? Is not, then when would it.

That is, if $\nu$ is a measure on $M$ then when does there exist a $1$-density $\mu$ such that $\nu$ and $\mu$ are related as above.

In short is there a version of the Radon–Nikodym theorem relating densities and measures on manifolds?