  We examine a possibility to introduce a non-trivial classical background
metric into the 2-d Liouville gravity theory. The classical background appears
as a part of the Weyl factor of the physical metric of 2-d surfaces with some
conformal dimension. On the other hand, the rest part of the factor corresponds
to the quantum fluctuating sector, having another conformal dimension such that
these two conformal dimensions sum up to just (1,1). Consequently we conclude
that, in the 2-d Liouville gravity, the target space dimensions D can be beyond
1.
