Let $U,V \subset \mathbb{R}^n$ be open sets. Let $\rho_0: U \to (0,\infty)$ and $\rho_1: V \to (0,\infty)$ be continuous probability densities with respect to [Lebesgue measure](/page/Lebesgue%20Measure), and define Borel probability measures $\mu$ on $U$ and $\nu$ on $V$ by