<abstract xmlns="http://www.w3.org/1999/xhtml"><p>There are various methods how to describe and characterize distribution of elements of sets of positive integers. One of the most interesting is that using the set of all distribution functions of the corresponding ratio block sequence introduced in [Strauch, O.—Tóth, J.T.: Publ. Math. Debrecen <bold>58</bold> (2001), no. 4, 751–778]. In the present paper we give some sufficient conditions under which this set is small in a metric sense. As a corollary we obtain a new characterization of the case of asymptotic distribution.</p></abstract>

There are various methods how to describe and characterize distribution of elements of sets of positive integers. One of the most interesting is that using the set of all distribution functions of the corresponding ratio block sequence introduced in [Strauch, O.—Tóth, J.T.: Publ. Math. Debrecen 58 (2001), no. 4, 751–778]. In the present paper we give some sufficient conditions under which this set is small in a metric sense. As a corollary we obtain a new characterization of the case of asymptotic distribution.

On Small Sets of Distribution Functions of Ratio Block Sequences

Department of Mathematics, University of Ostrava, 30. dubna 22, 701 03 Ostrava 1,

Uniform distribution theory

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On Small Sets of Distribution Functions of Ratio Block Sequences"}

There are various methods how to describe and characterize distribution of elements of sets of positive integers. One of the most interesting is that using the...

On Small Sets of Distribution Functions of Ratio Block Sequences

Publié en ligne: 13 janv. 2017

Pages: 165 - 174

Reçu: 14 janv. 2016

Accepté: 07 avr. 2016

DOI: https://doi.org/10.1515/udt-2016-0009

Mots clés
asymptotic distribution function, uniform distribution, block sequence

© 2016 David Krčmarský et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On Small Sets of Distribution Functions of Ratio Block Sequences

Publié en ligne: 13 janv. 2017

Pages: 165 - 174

Reçu: 14 janv. 2016

Accepté: 07 avr. 2016

DOI: https://doi.org/10.1515/udt-2016-0009

Mots clésasymptotic distribution function, uniform distribution, block sequence

© 2016 David Krčmarský et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Mots clés
asymptotic distribution function, uniform distribution, block sequence