[en] It is shown that the account of the reggeon production thresholds xi⁰=ln(M₂/S⁰) approximately 2 in the Reggeon field theory results in the fact that the epsilon-expansion becomes analytical at epsilon=2 and the simultaneous limiting transition to epsilon → 2 and E → 0 becomes possible which is consistent with the physical space dimension in the asymptotic energy region. The introduction of thresholds facilitates the accomplishment of perturbation theory calculations at D=2 eliminating the ultraviolet divergences of theory and proves useful for the accomplishment of smooth matching of the perturbation theory and asymptotic solutions