Let $\Omega$ be any measurable ($\sigma$-finite, if necessary) space. let $1\leq p\leq\infty,x\in L^p(\Omega)$.
Then how to proof $\forall\varepsilon>0,\exists\delta>0$，so that for any $1\leq q\leq\infty$, if $|q-p|<\delta$, we have $x\in L^q(\Omega)$ and $\left| ||x||_p -||x||_q\right|<\varepsilon$