\begin{definition}[Definition:Convolution of Measures]
Let $\mu$ and $\nu$ be measures on the Borel $\sigma$-algebra $\BB^n$ on $\R^n$.
The '''convolution of $\mu$ and $\nu$''', denoted $\mu * \nu$, is the measure defined by:
:$\ds \mu * \nu: \BB^n \to \overline \R, \map {\mu * \nu} B := \int_{\R^n} \map {\chi_B} {x + y} \map {\rd \mu} x \map {\rd \nu} y$
where $\chi_B$ is the characteristic function of $B$.
\end{definition}