I'm trying to prove that for $\space \Omega \subset {\mathbb{R}}^{d}, \space$ $\Omega \in C^{0,1} \space$ there is a continuous embedding of the Sobolev space $W^{d,1}(\Omega)$ into $C(\overline{\Omega})$.
I was advised to prove it for cuboid domains first and then use the "fact" that lipschitz domain can be expressed as a countable union of disjoint open cuboids and possibly a zero measure set. However I have no idea where this "fact" comes from and I also don't see how to apply it.
I'll appreciate any help.