Convergence of discrete Dirichlet forms to continuous Dirichlet forms on fractals

It is well known that a Dirichlet form on a fractal structure can be defined as the limit of an increasing sequence of discrete Dirichlet forms, defined on finite subsets which fill the fractal. The initial form is defined on V-(0), which is a sort of boundary of the fractal, and we have to require that it is an eigenform, i.e., an eigenvector of a particular nonlinear renormalization map for Dirichlet forms on V-(0). In this paper, I prove that, provided an eigenform exists, even if the form on V-(0) is not an eigenform, the corresponding sequence of discrete forms converges to a Dirichlet form on all of the fractal, both pointwise and in the sense of Gamma-convergence (but these two limits can be different). The problem of Gamma-convergence was first studied by S. Kozlov on the Gasket.