More on Kakeya Conditions for Achievement Sets

Author:

Miska PiotrORCID,Prus-Wiśniowski FranciszekORCID,Ptak JolantaORCID

Abstract

AbstractWe 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.

Funder

Narodowe Centrum Nauki

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Mathematics (miscellaneous)

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