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Fluctuation of means in the Birkhoff-Khinchin ergodic theorem. (English. Russian original) Zbl 0855.28007

Sib. Adv. Math. 3, No. 2, 103-144 (1993); translation from Tr. Inst. Mat. SO RAN 21, 52-86 (1992).
The author proves a refinement of the classical Birkhoff-Khinchin theorem in ergodic theory. His version is called fluctuation ergodic theorem. In his approach, he uses results and the formalism of nonstandard analysis.

MSC:

28D05 Measure-preserving transformations
28E05 Nonstandard measure theory