Abstract
In this paper, we are going to study the capacity theory and exceptionality of hyperfinite Dirichlet forms. We shall introduce positive measures 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 study the properties of internal multiplicative functionals, subordinate semigroups and subprocesses. Moreover, we shall discuss transformation of hyperfinite Dirichlet forms.
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