\begin{definition}[Definition:Distribution]
Let $\map \DD {\R^d}$ be a test function space.
Let $\phi, \psi \in \map \DD {\R^d}$ be test functions.
Let $\alpha \in \C$ be a complex number.
Let $\sequence {\phi_n}_{n \mathop \in \N} \in \map \DD {\R^d}$ be a convergent sequence with the limit $\phi \in \map \DD {\R^d}$.
Suppose a mapping $T : \map \DD {\R^d} \to \C$ is linear and continuous:
:$\forall \psi, \phi \in \map \DD {\R^d} : \map T {\phi + \psi} = \map T \phi + \map T \psi$
:$\forall \phi \in \map \DD {\R^d} : \forall \alpha \in \C : \map T {\alpha \cdot \phi} = \alpha \cdot \map T \phi$
:$\paren {\phi_n \stackrel \DD {\longrightarrow} \phi} \implies \paren {\map T {\phi_n} \to \map T \phi}$
Then $T$ is a '''distribution'''.
\end{definition}