\begin{definition}[Definition:Delta Sequence]
Let $\sequence {\map {\delta_n} x}_{n \mathop \in \N}$ be a sequence of continuous real-valued functions.
Let $\phi \in \map {\CC^\infty} \R$ be a smooth function with a compact support.
Suppose:
:$\ds \lim_{n \mathop \to \infty} \int_{-\infty}^\infty \map {\delta_n} x \map \phi x = \map \phi 0$
Then $\sequence {\map {\delta_n} x}_{n \mathop \in \N}$ is called the '''delta sequence'''.
{{Research|Need to check whether conditions on the sequence, $\phi$, and normalization can be relaxed.}}
\end{definition}