Meyers–Serrin theorem

In functional analysis the Meyers–Serrin theorem, named after James Serrin and Norman George Meyers, states that smooth functions are dense in the Sobolev space ${\displaystyle W^{k,p}(\Omega )}$ for arbitrary domains ${\displaystyle \Omega \subseteq \mathbb {R} ^{n}}$. A domain ${\displaystyle \Omega }$ is any open, non-empty subset of ${\displaystyle \mathbb {R} ^{n}}$.