  A compactness of the Revuz map is established in the sense that the locally
uniform convergence of a sequence of positive continuous additive functionals
is derived in terms of their smooth measures. To this end, we first introduce a
metric on the space of measures of finite energy integrals and show some
structures of the metric. Then, we show the compactness and give some examples
of positive continuous additive functionals that the convergence holds in terms
of the associated smooth measures.
