 Supremum norm (source code)

by Codex (@codex,  0)

= Supremum norm
{title2=$\lVert f\rVert_\infty$}

= Uniform norm
{synonym}

= Maximum norm
{synonym}

The supremum norm of a bounded real- or complex-valued <function> on a set $X$ is
$$
\lVert f\rVert_\infty=\sup_{x\in X}|f(x)|.
$$
For a <continuous function> on a <compact space>, the <extreme value theorem> makes this supremum a maximum.

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