<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In the present paper we extend two classic asymptotic results concerning convergence in probability and convergence in distribution for the denominators of the Lüroth series and obtain new theorems concerning the same two kinds of convergence for the <italic>r</italic>-iterated arithmetic means of such denominators. These results are extended to <italic>r</italic>-iterated weighted means.</p></abstract>

In the present paper we extend two classic asymptotic results concerning convergence in probability and convergence in distribution for the denominators of the Lüroth series and obtain new theorems concerning the same two kinds of convergence for the r-iterated arithmetic means of such denominators. These results are extended to r-iterated weighted means.

Convergence Results for <italic>r</italic>-Iterated Means of the Denominators of the Lüroth Series

Uniform distribution theory

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

Convergence Results for -Iterated Means of the Denominators of the Lüroth Series

In the present paper we extend two classic asymptotic results concerning convergence in probability and convergence in distribution for the denominators of the...

Convergence Results for r-Iterated Means of the Denominators of the Lüroth Series

Publié en ligne: 13 janv. 2017

Pages: 179 - 203

Reçu: 30 mars 2016

Accepté: 17 oct. 2016

DOI: https://doi.org/10.1515/udt-2016-0020

Mots clés
Lüroth series, convergence in probability, convergence in distribution, iterated arithmetic means, iterated weighted means

© 2016 Rita Giuliano, published by De Gruyter Open

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

Convergence Results for r-Iterated Means of the Denominators of the Lüroth Series

Publié en ligne: 13 janv. 2017

Pages: 179 - 203

Reçu: 30 mars 2016

Accepté: 17 oct. 2016

DOI: https://doi.org/10.1515/udt-2016-0020

Mots clésLüroth series, convergence in probability, convergence in distribution, iterated arithmetic means, iterated weighted means

© 2016 Rita Giuliano, published by De Gruyter Open

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

Mots clés
Lüroth series, convergence in probability, convergence in distribution, iterated arithmetic means, iterated weighted means