A Note on Weighted Polynomial Approximation with Varying Weights

It is shown that if weighted polynomialswnPnwith deg Pn⩽nconverge uniformly on the support of the extremal measure associated withw, then they converge to 0 everywhere else. It is also shown that uniform approximation on the support can always be characterized by a closed subsetZhaving the property that a function can be approximated if and only if it vanishes onZ.