Definition:Supremum Norm

Definition
Let $S$ be a set.

Let $\struct {X, \norm {\,\cdot\,} }$ be a normed vector space.

Let $\mathcal B$ be the set of bounded mappings $S \to X$.

For $f \in \mathcal B$ the supremum norm of $f$ on $S$ is defined as:


 * $\norm f_\infty = \sup \set {\norm {\map f x}: x \in S}$

Also known as
Other names include the sup norm, uniform norm or infinity norm.

Also see

 * Supremum Norm is Norm