Skip to content
Licensed Unlicensed Requires Authentication Published by De Gruyter February 28, 2017

Sequences of cantor type and their expressibility

Jaroslav Hančl and Jan Šustek
From the journal Mathematica Slovaca


This paper deals with a criterion for sequences of Cantor type to have an expressible set with zero Lebesgue measure.

MSC 2010: 11K55

(Communicated by Stanislav Jakubec)


[1] Erdös, P.: Some problems and results on the irrationality of the sum of infinite series. J. Math. Sci. 10 (1975), 1–7.Search in Google Scholar

[2] Hančl, J.: Expression of real numbers with the help of infinite series. Acta Arith. 2 (1991), 97–104.Search in Google Scholar

[3] Hančl, J.—Nair, R.—Novotný, L.—Šustek, J.: On the Hausdorff dimension of the expressible set of certain sequences. Acta Arith. 155 (2012), 85–90.Search in Google Scholar

[4] Hančl, J.—Nair, R.—Šustek, J.: On the Lebesgue measure of the expressible set of certain sequences. Indag. Math., N.S., 17 (2006), 567–581.Search in Google Scholar

[5] Khinchin, A. Y.: Continued Fractions. Chicago Univ. Press, Chicago, 1964.Search in Google Scholar

Received: 2012-12-3
Accepted: 2015-2-17
Published Online: 2017-2-28
Published in Print: 2017-2-1

© 2017 Mathematical Institute Slovak Academy of Sciences