Radon–Nikodym derivative

Summary

The Radon–Nikodym derivative $d\nu / d\mu$ is the density of one measure $\nu$ with respect to another measure $\mu$. It exists when both measures are σ-finite and $\nu$ is absolutely continuous with respect to $\mu$, by the Radon–Nikodym theorem. It turns integrals against $\nu$ into integrals against $\mu$. Probability densities, likelihood ratios and conditional expectations are all Radon–Nikodym derivatives.