\begin{definition}[Definition:Multiplication of Distribution by Smooth Function]
Let $d \in \N$ be a natural number.
Let $\alpha \in \map {\CC^\infty} {\R^d}$ be a smooth function.
Let $T \in \map {\DD'} {\R^d}$ be a distribution.
Then the '''multiplication of a distribution by a smooth function''' $\alpha T$ is defined by:
:$\alpha \map T \phi := \map T {\alpha \phi}$
where $\phi \in \map \DD {\R^d}$ is a test function.
\end{definition}