Kachurovskii, A. G. 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. Reviewer: E.Petrisor (Timişoara) MSC: 28D05 Measure-preserving transformations 28E05 Nonstandard measure theory Keywords:internal set theory; Birkhoff-Khinchin theorem; fluctuation ergodic theorem; nonstandard analysis × Cite Format Result Cite Review PDF