Definition:Supremum Norm

Definition
Let $S$ be a set.

Let $(X,\| \cdot \|)$ be a normed vector space.

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

This is a vector space.

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


 * $\| f \|_{\infty} = \sup\{\|f(x)\| : x \in S \}$

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

Also see

 * Supremum Norm is Norm