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We identify an incorrect estimate in the proof of one of principal theorems from Marchwicki and Miska (Results Math, 2021. https://doi.org/10.1007/s00025-021-01479-2 ) and demonstrate that the original construction of a special series with unique subsums remains valid when using a weaker estimate th...

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Bibliographic Details
Published inResultate der Mathematik Vol. 78; no. 3
Main Authors Miska, Piotr, Prus-Wiśniowski, Franciszek, Ptak, Jolanta
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.06.2023
Subjects
Mathematics
Mathematics and Statistics
cantor set
cantorval
semi-fast convergent series
40A05
Achievement set
set of subsums
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Summary:We identify an incorrect estimate in the proof of one of principal theorems from Marchwicki and Miska (Results Math, 2021. https://doi.org/10.1007/s00025-021-01479-2 ) and demonstrate that the original construction of a special series with unique subsums remains valid when using a weaker estimate that we prove to be true. Additionally, we present a weaker version—without the uniqueness of subsums—of the Thm. 2.1 from Marchwicki and Miska (2021), but with a very simple proof based on the concept of semi-fast convergent series.
ISSN:1422-6383
1420-9012
DOI:10.1007/s00025-023-01890-x