Let ((X, mathscr{A}, mu)) be a probability space and assume that (|u|_{q} 0). Show that (lim _{p

Let \((X, \mathscr{A}, \mu)\) be a probability space and assume that \(\|u\|_{q}<\infty\) for some \(q>0\). Show that \(\lim _{p ightarrow 0}\|u\|_{p}=\exp \left(\int \log |u| d \muight)\) (we set \(e^{-\infty}:=0\) ).