Relaxation for Dirichlet problems involving a Dirichlet form

For a fixed Dirichlet form, we study the space of positive Borel measures ( possibly infinite) which do not charge polar sets. We prove the density in this space of the set of the measures which represent varying domains. Our method is constructive. For the Laplace operator, the proof was based on a pavage of the space. Here, we substitute this notion by that of homogeneous covering in the sense of Coiffman and Weiss.