$W_0^{m,p}(\Omega)$ is a proper closed subspace of $W^{m,p}(\Omega)$

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$W_0^{m,p}(\Omega)$ is a proper closed subspace of $W^{m,p}(\Omega)$

how to prove this one what is function which is in $W^{m,p}(\Omega)$ and not in $W_0^{m,p}(\Omega)$

is $|x|$ will works?