\begin{definition}[Definition:Convolution of Measurable Function and Measure]
Let $\mu$ be a measure on the Borel $\sigma$-algebra $\BB^n$ on $\R^n$.
Let $f: \R^n \to \R$ be a $\BB^n$-measurable function such that for all $x \in \R^n$:
:$\ds \int_{\R^n} \map f {x - y} \rd \map \mu y$
is finite.
The '''convolution of $f$ and $\mu$''' is the mapping $f * \mu: \R^n \to \R$ defined as:
:$\ds \forall x \in \R^n: \map {f * \mu} x := \int_{\R^n} \map f {x - y} \rd \map \mu y$
\end{definition}