On the metric theory of the Lüroth expansions of real numbers

Tibor Šalát

Czechoslovak Mathematical Journal (1968)

  • Volume: 18, Issue: 3, page 489-522
  • ISSN: 0011-4642

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Šalát, Tibor. "Zur metrischen Theorie der Lürothschen Entwicklungen der reellen Zahlen." Czechoslovak Mathematical Journal 18.3 (1968): 489-522. <http://eudml.org/doc/12427>.

@article{Šalát1968,
author = {Šalát, Tibor},
journal = {Czechoslovak Mathematical Journal},
keywords = {metric theory; Lüroth expansions of real numbers; Hausdorff dimension},
language = {ger},
number = {3},
pages = {489-522},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Zur metrischen Theorie der Lürothschen Entwicklungen der reellen Zahlen},
url = {http://eudml.org/doc/12427},
volume = {18},
year = {1968},
}

TY - JOUR
AU - Šalát, Tibor
TI - Zur metrischen Theorie der Lürothschen Entwicklungen der reellen Zahlen
JO - Czechoslovak Mathematical Journal
PY - 1968
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 18
IS - 3
SP - 489
EP - 522
LA - ger
KW - metric theory; Lüroth expansions of real numbers; Hausdorff dimension
UR - http://eudml.org/doc/12427
ER -

References

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  4. P. Erdös A. Rényi, On Cantor’s series with convergent ( 1 q n ) , Ann. Univ. Sci. Budap. de Rol. Eötvös nom. II (1959), 93-109. (1959) MR0126414
  5. P. Erdös A. Rényi P. Szüsz, On Engel's and Sylvester's series, Ann. Univ. Sci. Budap. de Roi. Eötvös nom. I (1958), 7-- 32. (1958) MR0102496
  6. A. Rényi, A new approach to the theory of Engel's series, Ann. Univ. Sci. Budap. de Rol. Eötvös nom. V (1962), 25-32. (1962) MR0150123
  7. Т. Šalát, Cantorsche Entwicklungen der reellen Zahlen und das Hausdorffsche Mass, Publ. Math. Inst. Hung. Acad. Sci. VI (1961), 15-41. (1961) MR0147465
  8. T. Šalát, Über die Cantorschen Reihen, Czechosl. Math. J. 18 (93) (1968), 25-56. (1968) MR0223305
  9. L. Holzer, Zur Bestimmung des Lebesgueschen Masses linearer Punktmengen, deren Elemente durch systematische Entwicklungen gegeben sind, Sitzungsberichte Akad. der Wissensch. in Wien, Mat.-naturwis. Klasse, Abl. IIa, 137 (1928), 1, 421-453. (1928) 
  10. T. Šalát, О мере Хаусдорфа линейных множеств, Czechosl. Math. J. II (86) (1961), 24-56. (1961) 
  11. К. Knopp, 10.1007/BF01206618, Math. Ann. 95 (1926), 409-426. (1926) MR1512285DOI10.1007/BF01206618
  12. A. Rényi, Wahrscheinlichkeitsrechnung, VEB Deutscher Verlag der Wissenschaften, Berlin, 1962. (1962) MR0474442
  13. K. Knopp, Theorie und Anwendung der unendlichen Reihen, 1931. Zbl0842.40001
  14. A. Хинчин, Цепные дроби, Москва, 1961. (1961) Zbl1160.68305
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  16. T.Šalát, Remarks on the ergodic theory of the continued fractions, Mat. čas. SAV 17 (1967), 121-130. (1967) Zbl0166.05703MR0226244
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Citations in EuDML Documents

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  1. János Galambos, Some remarks on the Lüroth expansion
  2. Arnold Knopfmacher, John Knopfmacher, Metric properties of some special p-adic series expansions
  3. Luming Shen, Kui Fang, The fractional dimensional theory in Lüroth expansion
  4. Chunyun Cao, Jun Wu, Zhenliang Zhang, The efficiency of approximating real numbers by Lüroth expansion
  5. Fritz Schweiger, Ergodische Theorie der Engelschen und Sylvesterschen Reihen
  6. János Galambos, On infinite series representations of real numbers
  7. Jose Barrionuevo, Robert M. Burton, Karma Dajani, Cor Kraaikamp, Ergodic properties of generalized Lüroth series

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