Consider a sequence of complex valued measures \mu_{n} in the euclidean space \R^d which converges weakly to some compactly supported measure \mu. The weak convergence is in the sens that \int_{\R^d} \psi d\mu_n converges to \int_{\R^d} \psi d\mu for each smooth function with compact support $\psi$.

My problem is I want to know if there is a way to extend this convergence to polynomials knowing that polynomials are integrable with respect \mu_n for each n.