Abstract We study the density of polynomials in H2 ( E , φ ) , the space of square integrable functions with respect to e−φdm and holomorphic on the interior of E in C, where φ is a subharmonic function and d m is a measure on E . We give a result where E is the union of a Lipschitz graph and a Carathéodory domain, which we state as a weighted L2-version of the Mergelyan theorem. We also prove a weighted L 2 -version of the Carleman theorem.