Extension of the renormalizability criterion to the case of arbitrary unperturbed Lagrangian

Extension of the renormalizability criterium of the perturbation theory is generalized in the case, when an unperturbed lagrangian is not a lagrangian of free fields L0. The derivating functional of the Green function, written in the form of a function integral is disintegrated by the perturbed lagrangian L1 when building the perturbation theory. Described are ultraviolet divergences and possibilities of their elimination in eucledian space. The criterion permits to state extension renormalizability of the perturbation theory for eVery point L0 and the direction L1 assigned in this point in linear space of different lagrangians. According to the Weinberg theorem the grade asymptotics of Green functions is not changed at slight shift from the initial point in the supernormalized direction. For any point and any direction the extension of the perturbation theory is supernormalized in this space