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Ergodic theorem on B-structures

In the paper the extended individual ergodic theorem for B-structures with a state is presented. The classical ergodic theorem is formulated for ergodic mapping on Ω , where (Ω , S, P ) is a probability space and ξ : Ω → R is an integrable random variable. In our case S is replaced by a B-structure B and integrable random variable is replaced by an integrable observable.