On the metric theory of the Lüroth expansions of real numbers
Czechoslovak Mathematical Journal (1968)
- Volume: 18, Issue: 3, page 489-522
- ISSN: 0011-4642
Access Full Article
topHow to cite
topŠalát, 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
top- O. Perron, Irrationalzahlen, De Gruyter, Berlin-Leipzig, 1921. (1921) MR0115985
- A. Rényi, A számjegyek eloszlása valós számok Cantor-féle elöállításaiban, Mat. Lap. 7, (1956), 77-100. (1956) MR0099968
- P. Erdös A. Rényi, 10.1007/BF02063287, Acta math. acad. sci. Hung. X (1959), 21-29. (1959) MR0107631DOI10.1007/BF02063287
- P. Erdös A. Rényi, On Cantor’s series with convergent , Ann. Univ. Sci. Budap. de Rol. Eötvös nom. II (1959), 93-109. (1959) MR0126414
- 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
- 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
- Т. Šalát, Cantorsche Entwicklungen der reellen Zahlen und das Hausdorffsche Mass, Publ. Math. Inst. Hung. Acad. Sci. VI (1961), 15-41. (1961) MR0147465
- T. Šalát, Über die Cantorschen Reihen, Czechosl. Math. J. 18 (93) (1968), 25-56. (1968) MR0223305
- 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)
- T. Šalát, О мере Хаусдорфа линейных множеств, Czechosl. Math. J. II (86) (1961), 24-56. (1961)
- К. Knopp, 10.1007/BF01206618, Math. Ann. 95 (1926), 409-426. (1926) MR1512285DOI10.1007/BF01206618
- A. Rényi, Wahrscheinlichkeitsrechnung, VEB Deutscher Verlag der Wissenschaften, Berlin, 1962. (1962) MR0474442
- K. Knopp, Theorie und Anwendung der unendlichen Reihen, 1931. Zbl0842.40001
- A. Хинчин, Цепные дроби, Москва, 1961. (1961) Zbl1160.68305
- S. Hartman, Quelques propriétés ergodiques des fractions continues, Studia Math. ХII (1951), 271-278. (1951) Zbl0044.12402MR0046584
- T.Šalát, Remarks on the ergodic theory of the continued fractions, Mat. čas. SAV 17 (1967), 121-130. (1967) Zbl0166.05703MR0226244
- A. Chinčin, Metrische Kettenbruchprobleme, Comp. Math. I (1935), 361-382. (1935)
- W. Specht, Elementare Beweise der Primzahlsätze, VEB Deutscher Verlag der Wissenschaften, Berlin, 1956. (1956) Zbl0072.03103MR0086829
- V. Jarník, Zur metrischen Theorie der diophantischen Approximationen, Prace matem.- fizyczne XXXVI (1928-1929), 91-106. (1928)
- T. Šalát, A remark on normal numbers, Revue roumaine de math. pures et appl. XI (1966), 53-56. (1966) MR0201386
- К. Kuratowski, Topologie I, Warszawa, 1958. (1958)
- H. H. Ostmann, Additive Zahlentheorie I, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1956. (1956) Zbl0072.03101MR0098721
Citations in EuDML Documents
top- János Galambos, Some remarks on the Lüroth expansion
- Arnold Knopfmacher, John Knopfmacher, Metric properties of some special p-adic series expansions
- Luming Shen, Kui Fang, The fractional dimensional theory in Lüroth expansion
- Fritz Schweiger, Ergodische Theorie der Engelschen und Sylvesterschen Reihen
- Chunyun Cao, Jun Wu, Zhenliang Zhang, The efficiency of approximating real numbers by Lüroth expansion
- János Galambos, On infinite series representations of real numbers
- Jose Barrionuevo, Robert M. Burton, Karma Dajani, Cor Kraaikamp, Ergodic properties of generalized Lüroth series
NotesEmbed ?
topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.