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We discuss the structure of one-loop counterterms for the two-dimensionaltheory of gravitation in the covariant scheme and study the effect of quantumreparametrizations. Some of them are shown to be equivalent to the introductionof $2+\epsilon$-dimensional terms into the initially 2-dimensional theory. Wealso argue that the $\beta$-function for the Einstein constant has anon-trivial ultraviolet stable point beyond two dimensions.Comment: 16 page

Quantum reparametrizations in the two-dimensional gravity: a look from (2+ɛ) dimensions