Radon-Nikodym theorem

• Radon-Nikodym theorem
  Let $\mu$ and $\nu$ be $\sigma-$finite measures on some measurable space $(X, \mathcal{A})$. Then there exists a measurable function $$ f = \frac{d\nu}{d\mu} $$ if and only if $\nu$ is absolutely continuous with respect to $\mu$. This function $f$ is called the Radon–Nikodym derivative.