Originally Posted by

**surjective** I have a function defined as:

$\displaystyle \begin{displaymath}f(x) = \left\{\begin{array}{lr}\frac{1}{k} & : x \in [0,k]\\0 & : x \notin [0,k]\end{array}\right.\end{displaymath} $

I am asked to show that $\displaystyle f_{k} \to 0$ in $\displaystyle L^{\infty}(\mathbb{R})$ as $\displaystyle k \to \infty$

To be honest, I don't understand the question completely. When I make a skecth of the first few functions it's clear that $\displaystyle f_{k} \to 0$. It's the "in $\displaystyle L^{\infty}(\mathbb{R})$" which is confusing me.

Could someone clarify?

Thanks a bunch.