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## Random Averaging in Ergodic Theorem and Boundary Deformation Rate in Symbolic Dynamics

Moscow Mathematical Journal. 2019. Vol. 19. No. 1. P. 77-88.
Gurevicha B. M., S.A. Komech, Tempelman A. A.

For some symbolic dynamical systems we study the value of the boundary deformation for a small ball in the phase space during a period of time depending on the center and radius of the ball. For actions of countable Abelian groups, a version of the Mean Ergodic theorem with averaging over random sets is proved and used in the proof of the main theorem on deformation rate.