On weighted polynomial approximation

Let $\Phi :{\mathbb{R}}^n\to [1,\mathrm{\infty })$ 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 $C_{\Phi }({\mathbb{R}}^n)$.