Three-Diffeomorphism Conformal Space over Lorentzian Manifold

Through making use of a Borel measure and a piecewise-Riemannian inner scalar product, it is shown that over a Lorentzian manifold every three diffeomorphisms generate a conformal space, whose elements are smooth vector-valued functions equipped with compact supports. Few examples, in particular a diffeoinvariant measure, are provided with respect to an arbitrary smooth function introduced as into consideration as a multiplier to a local scale factor.