  We are concerned with sets of generic points for shift-invariant measures in
the countable symbolic space. We measure the sizes of the sets by the
Billingsley-Hausdorff dimensions defined by Gibbs measures. It is shown that
the dimension of such a set is given by a variational principle involving the
convergence exponent of the Gibbs measure and the relative entropy dimension of
the Gibbs measure with respect to the invariant measure. This variational
principle is different from that of the case of finite symbols, where the
convergent exponent is zero and is not involved. An application is given to a
class of expanding interval dynamical systems.
