\begin{definition}[Definition:Dirac Delta Distribution]
Let $a \in \R^d$ be a real vector.
Let $\phi \in \map \DD {\R^d}$ be a test function.
Let $\delta_a \in \map {\DD'} {\R^d}$ be a distribution.
Suppose $\delta_a$ is such that:
:$\map {\delta_a} \phi = \map \phi a$
Then $\delta_a$ is known as the '''Dirac delta distribution'''.
{{Research|For $d \ge 2$ this works in Euclidean space with Cartesian coordinates. Change of coordinates and integration measure may affect this somewhat}}
\end{definition}