Cauchy transform and uniform approximation by polynomial modules

For a compact subset K of the complex plane C, let C(K) denote algebra continuous functions on K. an open U?K, A(K,U)?C(K) be that are analytic in U. We show there exists ??A(K,U) so each f?A(K,U) can uniformly approximated by {pn+qn?} K, where pn and qn polynomials z. In particular, ? chosen as Cauchy transform finite positive measure ? compactly supported C?U. Recent developments capacity provide us useful tools our proofs.