\begin{definition}[Definition:L1 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:
:$\ds \forall f, g \in S: \map {d_1} {f, g} := \int_a^b \size {\map f t - \map g t} \rd t$
Then $d_1$ is the '''$L^1$ metric''' on $\closedint a b$.
\end{definition}