  We use bounded cohomology to define a notion of volume of an SO(n,1)-valued
representation of a lattice SO(n,1) and, using this tool, we give a complete
proof of the volume rigidity theorem of Francaviglia and Klaff in this setting.
Our approach gives in particular a proof of Thurston's version of Gromov's
proof of Mostow Rigidity (also in the non-cocompact case), which is dual to the
Gromov--Thurston proof using the simplicial volume invariant.}
