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Representations for real numbers and their ergodic properties

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Bibliography

  1. B. H. Bissinger, A generalization of continued fractions,Bulletin of the Amer. Math. Soc.,50 (1944), pp. 868–876.

    Google Scholar 

  2. C. I. Everett, Representations for real numbers,Bulletin of the Amer. Math. Soc.,52 (1946), pp. 861–869.

    Google Scholar 

  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.

  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. É. Borel, Les probabilités dénombrables et leurs applications arithmétiques,Rendiconti del Circ. Mat. di Palermo,27 (1909), pp. 247–271.

    Google Scholar 

  6. D. Raikoff, On some arithmetical properties of summable functions,Mat. Sbornik,1 (1936), pp. 377–384.

    Google Scholar 

  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. P. Lévy,Théorie de l'addition des variables aléatoires (Paris, 1954), Ch. IX, pp. 290.

  9. A. Khintchine, Metrische Kettenbruchprobleme,Comp. Math.,1 (1935), pp. 359–382.

    Google Scholar 

  10. A. Khintchine, Zur metrischen Kettenbruchtheorie,Comp. Math.,3 (1936), pp. 276–285.

    Google Scholar 

  11. A. Khintchine,Kettenbrüche (Leipzig, 1956).

  12. C. Ryll-Nardzewski, On the ergodic theorems. II. Ergodic theory of continued fractions,Studia Math.,12 (1951), pp. 74–79.

    Google Scholar 

  13. S. Hartman E. Marczewski C. Ryll-Nardzewski, Théorèmes ergodiques et leurs applications,Coll. Math.,2 (1951), pp. 109–123.

    Google Scholar 

  14. S. Hartman, Quelques propriétés ergodiques des fractions continues,Studia Math.,12 (1951), pp. 271–278.

    Google Scholar 

  15. F. Riesz, Sur la théorie ergodique,Commentarii Math. Helv.,1 (1944–45), pp. 221–239.

    Google Scholar 

  16. A. Rényi, Valós számok előállítására szolgáló algoritmusokról,MTA Mat. és. Fiz. Oszt. Közl.,7 (1957), pp. 265–293.

    Google Scholar 

  17. N. Dunford andD. S. Miller, On the ergodic theorem,Trans. Amer. Math. Soc.,60 (1946), pp. 538–549.

    Google Scholar 

  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. K. Knopp, Mengentheoretische Behandlung einiger. Probleme der diophantischen Approximationen und der transfiniten. Wahrscheinlichkeiten,Math. Annalen,95 (1926), pp. 409–426.

    Google Scholar 

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Rényi, A. Representations for real numbers and their ergodic properties. Acta Mathematica Academiae Scientiarum Hungaricae 8, 477–493 (1957). https://doi.org/10.1007/BF02020331

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