<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

Data publikacji: 13 sty 2017

Zakres stron: 179 - 203

Otrzymano: 30 mar 2016

Przyjęty: 17 paź 2016

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

Słowa kluczowe
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

Data publikacji: 13 sty 2017

Zakres stron: 179 - 203

Otrzymano: 30 mar 2016

Przyjęty: 17 paź 2016

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

Słowa kluczoweLüroth 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.

Słowa kluczowe
Lüroth series, convergence in probability, convergence in distribution, iterated arithmetic means, iterated weighted means