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References
V. V. Ivanov, “Fluctuations of means in the ergodic theorem,” Dokl. RAN (1995) (to appear).
F. Riesz and B. Sz.-Nagy, Lectures on Functional Analysis [Russian translation], Mir, Moscow (1979).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1972).
E. Bishop, “An upcrossing inequality with applications,” Michigan Math. J.,13, No. 1, 1–13 (1966).
N. Wiener, “The ergodic theorem,” Duke Math. J.,5, 1–18 (1939).
I. P. Kornfel'd, Ya. G. Sinaî, and S. V. Fomin, Ergodic Theory [in Russian], Nauka, Moscow (1980).
P. R. Halmos, Lectures on Ergodic Theory [Russian translation], Izdat. Inostr. Lit., Moscow (1959).
A. A. Borovkov, Probability Theory [in Russian], Nauka, Moscow (1986).
A. N. Shiryaev, Probability [in Russian], Nauka, Moscow (1989).
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Dedicated to the memory of my teacher Gleb Pavlovich Akilov.
Translated fromSibirskiî Matematicheskiî Zhurnal, Vol. 37, No. 1, pp. 117–150, January–February, 1996.
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Ivanov, V.V. Geometric properties of monotone functions and probabilities of random fluctuations. Sib Math J 37, 102–129 (1996). https://doi.org/10.1007/BF02104763
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DOI: https://doi.org/10.1007/BF02104763