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Show that Sobolev space is complete. I am trying

Than $L^p(\Omega)$ is complete then If $f_n \in L^p(\Omega)$ then $f_n \to f \in L^p(\Omega)$. But rest show that $D^{\alpha}f \in L^p(\Omega)$. How I will be able to show this?

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    If $f_n$ is Cauchy in sobolev space $W^{m,p}$, then for each $|\alpha|\le m$, $D^{\alpha}f_n$ is Cauchy in $L^p$ and converges to some $f_{\alpha}\in L^p$. The Crucial thing is to show $f_{\alpha}=D^{\alpha}f$.2012-11-08

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