Definition:Limit of Sequence/Test Function Space

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Let $\map \DD {\R^d}$ be the test function space.

Let $\phi \in \map \DD {\R^d}$ be a test function.

Let $\sequence {\phi_n}_{n \mathop \in \N}$ be a sequence of test functions in $\map \DD {\R^d}$.

Let $\sequence {\phi_n}_{n \mathop \in \N}$ converge to $\phi$ in $\map \DD {\R^d}$.

Then $\phi$ is a limit of $\sequence {\phi_n}_{n \mathop \in \N}$ in $\map \DD {\R^d}$ as $n$ tends to infinity which is usually written:

$\phi_n \stackrel \DD {\longrightarrow} \phi$