Function to K/Supremum norm/Definition

Supremum norm

Let ${}T$ be a set, and let

$f\colon T\longrightarrow {\mathbb {K} }$

denote a function. Then

${}\Vert {f}\Vert :=\Vert {f}\Vert _{T}={\operatorname {sup} \,{\left(\vert {f(x)}\vert {|}x\in T\right)}}\,$

is called the supremum (or the supremum norm) of ${}f$. It is a nonnegative real number, or ${}\infty$.