More on Kakeya Conditions for Achievement Sets.

We identify an incorrect estimate in the proof of one of principal theorems from Marchwicki and Miska (Results Math, 2021. ) 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. [ABSTRACT FROM AUTHOR]