Functional Integrals of Quantum 2D Gravity

A class of functional Integrals measures quasiinvariant under the actions groups of diffeomorfisms is proposed. The common feature of the measures consists in the existence of nonlinear nonlocal substitutions that transform the measures to the Wiener one. The method is applied to calculation of path integrals in quantum 2d gravity models, including Schwarzian and some other path integrals.