> [!definition] > > Let $(\Omega, \cf, \mu)$ be a [[Measure Space|measure space]] and $f \in L^+$ be a non-negative [[Measurable Function|measurable function]]. Define a measure $\mu f$ on $(\Omega, \cf)$ by setting > $ > \mu f(E) = \int_E f d\mu > $ > then $\mu f$ is a measure by the [[Dominated Convergence Theorem]]. If $\nu$ is another measure on $(\Omega, \cf)$ equal to $\mu f$, then $\nu$ has density $f$ with respect to $\mu$ (see [[Lebesgue-Radon-Nikodym Theorem|Radon-Nikodym derivative]]).