  The gravitational measure on an arbitrary topological three-manifold is
constructed. The nontrivial dependence of the measure on the conformal factor
is discussed. We show that only in the case of a compact manifold with boundary
the measure acquires a nontrivial dependence on the conformal factor which is
given by the Liouville action. A nontrivial Jacobian (the divergent part of it)
generates the Einstein-Hilbert action. The Hartle-Hawking wave function of
Universe is given in terms of the Liouville action. In the gaussian
approximation to the Wheeler-DeWitt equation this result was earlier derived by
Banks et al. Possible connection with the Chern-Simons gravity is also
discussed.
