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

Rita Giuliano

doi:10.1515/udt-2016-0020

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

Uniform distribution theory

Volume 11 (2016): Issue 2 (December 2016)

By: Rita Giuliano

Open Access

|Jan 2017

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.

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Articles in this issue

DOI: https://doi.org/10.1515/udt-2016-0020 | Journal eISSN: 2309-5377 | Journal ISSN: 1336-913X

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Language: English

Page range: 179 - 203

Submitted on: Mar 30, 2016

Accepted on: Oct 17, 2016

Published on: Jan 13, 2017

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

Lüroth series,

convergence in probability,

convergence in distribution,

iterated arithmetic means,

iterated weighted means

Related subjects:

Mathematics,

Algebra and number theory,

Discrete mathematics,

Probability and statistics,

Numerical and computational mathematics

© 2017 Rita Giuliano, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 11 (2016): Issue 2 (December 2016)