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Sequences of cantor type and their expressibility

  • Jaroslav Hančl and Jan Šustek
Published/Copyright: February 28, 2017
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Abstract

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

MSC 2010: 11K55

This paper was supported by grant ME09017. The authors would like to thank Professor Radhakrishnan Nair from the Department of Mathematical Sciences, University of Liverpool, for his help with the presentation of the paper.



(Communicated by Stanislav Jakubec)


References

[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), 97–104.10.4064/aa-59-2-97-104Search 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), 85–90.10.4064/aa155-1-8Search 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), 567–581.10.1016/S0019-3577(06)81034-7Search in Google Scholar

[5] Khinchin, A. Y.: Continued Fractions. Chicago Univ. Press, Chicago, 1964.10.1063/1.3051235Search in Google Scholar

Received: 2012-12-03
Accepted: 2015-02-17
Published Online: 2017-02-28
Published in Print: 2017-03-01

© 2017 Mathematical Institute Slovak Academy of Sciences

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