After introducing the notion of weak solutions and the local Kato class associated with a regular Dirichlet form, the authors prove an estimate for the Green's function by using the assumed doubling property of the intrinsic balls. This estimate is used to extend the Evans-Vasilesco theorem on the continuity of the potential of a non-negative Radon measure to a general class of Dirichlet-Poincaré forms. The result is then applied to show that every diffuse Radon measure that charges no set of positive capacity admits a representation as the product of a Borel function and a Kato measure.