  We explore an extended coupling constant space of 4d regularized Euclidean
quantum gravity, defined via the formalism of dynamical triangulations. We add
a measure term which can also serve as a generalized higher curvature term and
determine the phase diagram and the geometries dominating in the various
regions. A first order phase transition line is observed, but no second order
transition point is located. As a consequence we cannot attribute any continuum
physics interpretation to the so-called crinkled phase of 4d dynamical
triangulations.
