  Starting from the De Witt supermetric and limiting ourselves to a family of
geometries characterized by a finite number of geometric invariants we extract
the unique integration measure. Such a measure turns out to be a geometric
invariant, i.e. independent of the gauge fixed metric used for describing the
geometries. The measure is also invariant in form under an arbitrary change of
parameters describing the geometries. The additional functional integration on
the conformal factor makes the measure independent of the free parameter
intervening in the De Witt supermetric. The differences between the case D=2
and $D>2$ are evidenced.
