\begin{definition}[Definition:Measure with Density]
Let $\struct {X, \Sigma, \mu}$ be a measure space.
Let $f: X \to \overline \R_{\ge 0}$ be a positive $\mu$-measurable function.
Then the '''measure with density $f$ with respect to $\mu$''', denoted $f \mu$, is defined by:
:$\map {f \mu} E := \ds \int_E f \rd \mu$
where $\ds \int_E f \rd \mu$ is the $\mu$-integral of $f$ over $E$.
\end{definition}