  We investigate the influence of the measure in the path integral for
Euclidean quantum gravity in four dimensions within the Regge calculus. The
action is bounded without additional terms by fixing the average lattice
spacing. We set the length scale by a parameter $\beta$ and consider a scale
invariant and a uniform measure. In the low $\beta$ region we observe a phase
with negative curvature and a homogeneous distribution of the link lengths
independent of the measure. The large $\beta$ region is characterized by
inhomogeneous link lengths distributions with spikes and positive curvature
depending on the measure.
