  Let $\varPhi:{\mathbb R}^n \to [1, \infty)$ be a semi-continuous from below
function such that $\lim \limits_{x \to \infty} \displaystyle \frac {\ln
\varPhi(x)} {\Vert x \Vert} = +\infty$. It is shown that polynomials are dense
in $C_{\varPhi}({\mathbb R}^n)$.
