While studying Sobolev spaces the following notion/fact comes up and I do not see the triviality. Perhaps someone can give some lines to this notion and in particular to this $L^p$-space notion:
Let $\Sigma_k = \{\alpha: \vert\alpha\vert \leq k\}$ and consider
$W^{k,p}(U) \ni f\rightarrow (f_\alpha)_{\vert\alpha \vert\leq k}\in L^p(U \times\Sigma_k)$
This should be a isometry for obvious reasons. Why?