Acta Mathematica Academiae Scientiarum Hungarica

, Volume 8, Issue 3–4, pp 477–493

Representations for real numbers and their ergodic properties

  • A. Rényi
Article

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Bibliography

  1. [1]
    B. H. Bissinger, A generalization of continued fractions,Bulletin of the Amer. Math. Soc.,50 (1944), pp. 868–876.Google Scholar
  2. [2]
    C. I. Everett, Representations for real numbers,Bulletin of the Amer. Math. Soc.,52 (1946), pp. 861–869.Google Scholar
  3. [3]
    W. Bolyai,Tentamen iuventutem studiosam in elementa matheseos purae elementaris ac sublimioris methodo intuitiva evidentiaque huic propria introducendi, ed. sec. (Budapest, 1897), Vol. I.Google Scholar
  4. [4]
    Gy. Farkas, A Bolyai-féle algoritmus,Értekezések a matematikai tudományok köréből,8 (1881), pp. 1–8, further seeP. Veres, A Bolyai-féle algoritmus,Mennyiségtani és Term. Tud. Didaktikai Lapok,1 (1943), pp. 57–62.Google Scholar
  5. [5]
    É. Borel, Les probabilités dénombrables et leurs applications arithmétiques,Rendiconti del Circ. Mat. di Palermo,27 (1909), pp. 247–271.Google Scholar
  6. [6]
    D. Raikoff, On some arithmetical properties of summable functions,Mat. Sbornik,1 (1936), pp. 377–384.Google Scholar
  7. [7]
    R. O. Kuzmin, Sur un problème de Gauss,Atti del Congresso Internazionale del Matematici Bologna, (1928), Vol. VI, pp. 83–89.Google Scholar
  8. [8]
    P. Lévy,Théorie de l'addition des variables aléatoires (Paris, 1954), Ch. IX, pp. 290.Google Scholar
  9. [9]
    A. Khintchine, Metrische Kettenbruchprobleme,Comp. Math.,1 (1935), pp. 359–382.Google Scholar
  10. [10]
    A. Khintchine, Zur metrischen Kettenbruchtheorie,Comp. Math.,3 (1936), pp. 276–285.Google Scholar
  11. [11]
    A. Khintchine,Kettenbrüche (Leipzig, 1956).Google Scholar
  12. [12]
    C. Ryll-Nardzewski, On the ergodic theorems. II. Ergodic theory of continued fractions,Studia Math.,12 (1951), pp. 74–79.Google Scholar
  13. [13]
    S. Hartman E. Marczewski C. Ryll-Nardzewski, Théorèmes ergodiques et leurs applications,Coll. Math.,2 (1951), pp. 109–123.Google Scholar
  14. [14]
    S. Hartman, Quelques propriétés ergodiques des fractions continues,Studia Math.,12 (1951), pp. 271–278.Google Scholar
  15. [15]
    F. Riesz, Sur la théorie ergodique,Commentarii Math. Helv.,1 (1944–45), pp. 221–239.Google Scholar
  16. [16]
    A. Rényi, Valós számok előállítására szolgáló algoritmusokról,MTA Mat. és. Fiz. Oszt. Közl.,7 (1957), pp. 265–293.Google Scholar
  17. [17]
    N. Dunford andD. S. Miller, On the ergodic theorem,Trans. Amer. Math. Soc.,60 (1946), pp. 538–549.Google Scholar
  18. [18]
    F. Riesz, On a recent generalization of G. D. Birkhoff's ergodic theorem,Acta Sci. Math. Szeged,11 (1948), pp. 193–200.Google Scholar
  19. [19]
    K. Knopp, Mengentheoretische Behandlung einiger. Probleme der diophantischen Approximationen und der transfiniten. Wahrscheinlichkeiten,Math. Annalen,95 (1926), pp. 409–426.Google Scholar

Copyright information

© Akadémiai Kiadó 1957

Authors and Affiliations

  • A. Rényi
    • 1
  1. 1.Budapest

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