  We work out the constraints imposed by SL(2C) invariance for sphere topology
and modular invariance for torus topology, on the discretized form of Liouville
action in Polyakov's non local covariant form. These are sufficient to
completely fix the discretized action except for the overall normalization
constant and a term which in the continuum limit goes over to a topological
invariant. The treatment can be extended to the supersymmetric case.
