The Radon–Nikodym theorem states that,
given a measurable space $(X,\Sigma)$, if a $\sigma$-finite measure $\nu$ on $(X,\Sigma)$ is absolutely continuous with respect to a $\sigma$-finite measure $\mu$ on $(X,\Sigma)$, then there is a measurable function $f$ on $X$ and taking values in $[0,\infty)$, such that
$$\nu(A) = \int_A f \, d\mu$$
for any measurable set $A$.
$f$ is called the Radon–Nikodym derivative of $\nu$ wrt $\mu$.
I was wondering in what cases the concept of Radon–Nikodym derivative and the concept of derivative in real analysis can coincide and how?
Thanks and regards!