\begin{definition}[Definition:L2 Metric/Closed Real Interval]
Let $S$ be the set of all real functions which are continuous on the closed interval $\closedint a b$.
Let the real-valued function $d: S \times S \to \R$ be defined as:
:$\ds \forall f, g \in S: \map d {f, g} := \paren {\int_a^b \paren {\map f t - \map g t}^2 \rd t}^{\frac 1 2}$
Then $d$ is the '''$L^2$ metric''' on $\closedint a b$.
\end{definition}