On the Cantor series

Tibor Šalát

Czechoslovak Mathematical Journal (1968)

  • Volume: 18, Issue: 1, page 25-56
  • ISSN: 0011-4642

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Šalát, Tibor. "Über die Cantorschen Reihen." Czechoslovak Mathematical Journal 18.1 (1968): 25-56. <http://eudml.org/doc/12391>.

@article{Šalát1968,
author = {Šalát, Tibor},
journal = {Czechoslovak Mathematical Journal},
keywords = {Cantor series},
language = {ger},
number = {1},
pages = {25-56},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Über die Cantorschen Reihen},
url = {http://eudml.org/doc/12391},
volume = {18},
year = {1968},
}

TY - JOUR
AU - Šalát, Tibor
TI - Über die Cantorschen Reihen
JO - Czechoslovak Mathematical Journal
PY - 1968
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 18
IS - 1
SP - 25
EP - 56
LA - ger
KW - Cantor series
UR - http://eudml.org/doc/12391
ER -

References

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  1. G. Cantor, Über die einfache Zahlensysteme, Zeitschrift für Math. und Physik 14 (1869). 
  2. A. Rényi, A számjegyek eloszlása valós számok Cantor-féle elöállításaiban, Mat. Lap. VII (1956), 77-100. (1956) MR0099968
  3. O. Perron, Irrationalzahlen, Berlin-Leipzig, 1921. (1921) 
  4. H. G. Eggleston, Sets of fractional dimensions which occur in some problems of number theory, Proc. Lond. Math. Soc. 54 (1951), 42-93. (1951) Zbl0045.16603MR0048504
  5. T. Šalát, О мере Хаусдорфа линейных множеств, Czechosl. Math. J. 11 (86) (1961), 24- 56. (1961) MR0153802
  6. А. А. Бухштаб, Теория чисел, Москва, 1960. (1960) Zbl1004.90500
  7. T. Šalát, Cantorsche Entwicklungen der reellen Zahlen und das Hausdorffsche Mass, Publ. Math. Inst. Hung. Acad. Sci. VI (1961), 15-41. (1961) MR0147465
  8. E. Best, 10.1112/plms/s2-47.1.436, Proc. Lond. Math. Soc. 47 (1942), 436-454. (1942) MR0008421DOI10.1112/plms/s2-47.1.436
  9. A. Gierl, Über das Hausdorffsche Mass gewisser Punktmengen in der Zifferntheorie, Jour. rein. u. angew. Math. 202 (1959), 183-195. (1959) Zbl0095.26405MR0150253
  10. T. Šalát, Eine metrische Eigenschaft der Cantorschen Entwicklungen der reellen Zahlen und Irrationalitätskriterien, Czechosl. Math. J. 14 (89), (1964), 254-266. (1964) MR0168527
  11. F. Erdös A. Rényi, On Cantor’s series with convergent ( 1 q n ) , Ann Univ. Sci. Budap. de Roi. Eötvös nom. II (1959), 93-109. (1959) 
  12. Н. H. Ostmann, Additive Zahlentheorie I, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956. (1956) Zbl0072.03101
  13. T. Šalát, A remark on normal numbers, Revue roumaine de math. pures et appl. XI (1966), 53-56. (1966) MR0201386
  14. K. Kuratowski, Topologie I, Warszawa, 1958. (1958) 
  15. P. Erdös A.Renyi, Some futher statistical properties of the digits in Cantor's series, Acta math. acad. sci. Hung. X (1959), 21-29. (1959) MR0107631
  16. T. Šalát, Über die Hausdorffsche Dimension der Menge der Zahlen mit beschränkten Folgen von Ziffern in Cantorschen Entwicklungen, Czechosl. Math. J. 15 (90), (1965), 540-552. (1965) MR0188187

Citations in EuDML Documents

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  1. Hendrik Gerrit Meijer, Tibor Šalát, On a class of arithmetical sets
  2. Fritz Schweiger, Ergodische Theorie der Engelschen und Sylvesterschen Reihen
  3. Tibor Šalát, Remarks on Steinhaus’ property and ratio sets of sets of positive integers
  4. M. Dindoš, Tibor Šalát, Vladimír Toma, Statistical convergence of infinite series
  5. Władysław Narkiewicz, Tibor Šalát, A theorem of H. Steinhaus and ( R ) -dense sets of positive integers
  6. Tibor Šalát, Zu einigen Fragen der Gleichverteilung (mod 1)
  7. Tibor Šalát, Zur metrischen Theorie der Lürothschen Entwicklungen der reellen Zahlen
  8. Martin Máčaj, Tibor Šalát, Statistical convergence of subsequences of a given sequence
  9. Martin Máčaj, Milan Paštéka, Tibor Šalát, Marek Žabka, On difference sets of sets of positive integers

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