4 papers · 1 filter
A characterization of uniqueness of purely atomic finite measures with central Cantor set range
Piotr Nowakowski, Franciszek Prus-Wiśniowski
We study purely atomic measures whose range is a central Cantor set and characterize those central Cantor sets that are the range of exactly one such measure. Next, we extend the c…
Achievement sets -- current results and open problems
Szymon Głąb, Franciszek Prus-Wiśniowski
We survey recent developments in the theory of achievement sets and present a substantial collection of open problems.
Achievable Cantorvals almost without reversed Kakeya conditions
Franciszek Prus-Wiśniowski, Jolanta Ptak
Examples of achievable Cantorvals are constructed with reversed Kakeya conditions only on a set of asymptotic density zero which answers in positive the Problem 5.2 from Marchwicki…
Algebraic sums of achievable sets involving Cantorvals
Jacek Marchwicki, Piotr Nowakowski, Franciszek Prus-Wiśniowski
In this paper we look at the topological type of algebraic sum of achievement sets. We show that there is a Cantorval such that the algebraic sum of its copies is still a Canto…