Definition:L1 Metric

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Definition

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 $\closedint a b$.


Also see

  • Results about the $L^1$ metric can be found here.