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Probability methods in the theory of distributions modulo one. (English) Zbl 0201.37701

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References:
[1] Cassels, J.W.S. [1] An extension of the law of the iterated logarithm , Proc. Cambridge Philos. Soc. 47 (1951) 55-64. · Zbl 0042.13704
[2] Cigler, J. [2] Asymptotische Verteilung reeller Zahlen mod 1 , Monatshefte für Math. 64 (1960) 201-225. · Zbl 0111.25301 · doi:10.1007/BF01361535 · eudml:177097
[3] Cigler, J. [8] Der Individuelle Ergodensatz in der Theorie der Gleichverteilung mod 1 , J. reine angew. Math. 205 (1960) 91-100. · Zbl 0131.29301 · doi:10.1515/crll.1960.205.91 · resolver.sub.uni-goettingen.de · eudml:150454
[4] Cigler, J. [4] Über eine Verallgemeinerung des Hauptsatzes der Theorie der Gleichverteilung , J. reine angew. Math. 210 (1962) 141-147. · Zbl 0117.28402 · doi:10.1515/crll.1962.210.141 · crelle:GDZPPN00217975X · eudml:150539
[5] Cigler, J. und Helmberg, J. [5] Neuere Entwicklungen der Theorie der Gleichverteilung , Jahresber. Deutschen Math. Ver. 64 (1961) 1- 50. · Zbl 0109.03404 · eudml:146486
[6] Corput, J. G. Van Der [6] Diophantische Ungleichungen I, Zur Gleichverteilung Modulo Eins , Acta Math. 56 (1981) 373-456. · Zbl 0001.20102 · doi:10.1007/BF02545780
[7] Doob, J. [7] Stochastic processes , John Wiley and Sons, New York, 1958. · Zbl 0696.60003
[8] Feller, W. [8] The general form of the so-called law of the iterated logarithm , Trans. Amer. Math. Soc. 54 (1948) 373-402. · Zbl 0063.08417 · doi:10.2307/1990253
[9] Hlawka, E. [9] Zur formalen Theorie der Gleichverteilung in kompakten Gruppen , Rend. Circ. Mat. Palermo Ser. II, 4 (1955) 1-15. · Zbl 0065.26402 · doi:10.1007/BF02846027
[10] Hlawka, E. [10] Folgen auf kompakten Räumen , Abh. math. Sem. Univ. Hamburg 20 (1956) 228-241. · Zbl 0072.05701 · doi:10.1007/BF03374560
[11] Kac, M. [11] Probability methods in some problems of analysis and number theory , Bull. Amer. Math. Soc. 55 (1949) 641-665. · Zbl 0036.30502 · doi:10.1090/S0002-9904-1949-09242-X
[12] Kemperman, J.H.B. [12] On the distribution of a sequence in a compact group , this journal. · Zbl 0131.27004 · numdam:CM_1964__16__138_0 · eudml:88885
[13] Kesten, H. , [18] Uniform distribution mod 1 , Annals Math. 71 (1960) 445-471. · Zbl 0101.03803 · doi:10.2307/1969938
[14] Kesten, H. [14] Uniform distribution mod 1, II , Acta Arith. 7 (1961) 855-860. · Zbl 0113.27004 · eudml:207019
[15] Khintchin, A.I. [15] Mathematical foundations of information theory , Dover Publ., New York, 1957. · Zbl 0088.10404
[16] Loève, M. [16] Probability Theory , 2nd ed., D. van Nostrand Co., Princeton, 1960. · Zbl 0095.12201
[17] Lorentz, G.G. [17] A contribution to the theory of divergent series , Acta Math. 80 (1948) 167-190. · Zbl 0031.29501 · doi:10.1007/BF02393648
[18] Pyateckii-Šapiro, I.I. [18] On the laws of distribution of the fractional parts of an exponential function , Izv. Akad. Nauk SSSR Ser. Mat. 15 (1951) 47-52. · Zbl 0042.04902
[19] Stapleton, J.H. [19] Asymptotic distributions modulo 1 and its extension to abstract spaces , Thesis, Purdue University, 1957.
[20] Wall, D.D. [20] Normal numbers, Thesis , University of California, Berkeley, 1949.
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