Definition
13
[10C] Given \(pβ[1,β]\), the norms \(\| x\| _ p\) are defined on \(β^ n\) with
\begin{equation} \| x\| _ p= \begin{cases} \sqrt[p]{β_{i=1}^ n|x_ i|^ p} & pβ β\\ \max _{i=1}^ n|x_ i| & p=β \end{cases} \label{eq:norme_ p_ R_ n} \end{equation}
14