  We study the semiclassical expansion of the effective action for a Regge
state-sum model and its dependence on the choice of the path-integral measure
and the spectrum of the edge lengths. If the positivity of the edge lengths is
imposed in the effective action equation, we find that the semiclassical
expansion is not possible for the power-law measures, while the exponential
measures allow the semiclassical expansion. Furthermore, a slightly generalized
exponential measure can generate the cosmological term in the effective action
as a quantum correction, with a naturally small value of the cosmological
constant. We also find that in the case of a discrete length spectrum, the
semiclassical expansion is allowed only if the spectrum gap is much smaller
than the Planck length.
