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Remarks on the remainder in Birkhoff’s ergodic theorem. (English) Zbl 0336.28005

MSC:
28D05 Measure-preserving transformations
11K06 General theory of distribution modulo \(1\)
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References:
[1] M. Smorodinsky,Ergodic Theory, Entropy. Lecture Notes in Mathematics 214, Springer Verlag.
[2] E. Hecke, Analytische Funktionen und die Verteilung von Zahlen mod. eins,Abh. Math. Semin. Hamburg Univ.,1 (1922), 54–76. · JFM 48.0197.03 · doi:10.1007/BF02940580
[3] H. Kesten, On a conjecture of Erdos and Szüsz related to uniform distribution mod 1,Acta Arithm. XII (1966), 193–212. · Zbl 0144.28902
[4] H. Furstenberg, H. Keynes andL. Shapiro, Prime flows in topological dynamics,Israel J. Math.,14(1) (1973), 26–38. · Zbl 0264.54030 · doi:10.1007/BF02761532
[5] Vera T. Sós, On the distribution of the sequence (n\(\alpha\)),Tagungsbericht, Math. Inst. Oberwolfach,28 (1972).
[6] S. Kakutani, Induced measure preserving transformations,Proc. Imp. Acad. Tokyo,19 (1943), 635–641. · Zbl 0060.27406 · doi:10.3792/pia/1195573248
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