POTENTIAL-THEORY OF HYPERFINITE DIRICHLET FORMS

In this paper, we are going to study the capacity theory and exception ality of hyperfinite Dirichlet forms. We shall introduce positive meas ures of hyperfinite energy integrals and associated theory. Fukushima' s decomposition theorem will be established on the basis of discussing hyperfinite additive functionals and hyperfinite measures. We shall s tudy the properties of internal multiplicative functionals, subordinat e semigroups and subprocesses. Moreover, we shall discuss transformati on of hyperfinite Dirichlet forms.