M-Cantorvals of Ferens type-Reference-Cited by-同舟云学术

M-Cantorvals of Ferens type

Published:2017-07-14 Issue:4 Volume:67 Page:907-918
ISSN:0139-9918
Container-title:Mathematica Slovaca
language:en
Short-container-title:

Author:

Banakiewicz Michał¹,Prus-Wiśniowski Franciszek²

Affiliation:

1. Studium of Mathematics West Pomeranian University of Technology Al. Piastów 48 PL-70-311 Szczecin Poland

2. Instytut Matematyki Uniwersytet Szczeciński ul. Wielkopolska 15 PL-70-453 Szczecin Poland

Abstract

Abstract A special family of multigeometric series is considered from the point of view of behaviour of their sets of subsums. A sufficient condition for their sets of subsums to be M-Cantorvals is proven. The Lebesgue measure of those special M-Cantorvals is computed and it is shown to be equal to the sum of lengths of all component intervals of the M-Cantorvals. A new sufficient condition for the set of subsums of a series to be a Cantor set is formulated and it is used to demonstrate that the discussed multigeometric series always have Cantor sets as their sets of subsums for sufficiently small ratios of the series.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/ms-2017-0019/pdf

Reference17 articles.

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