Category:Definitions/L1 Metric

This category contains definitions related to $L^1$ metric.
Related results can be found in Category:L1 Metric.

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 $\closedint a b$.