6 papers
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.
Spectre operator, achievement sets and sets of P-sums in a hyperspace of compact sets
Piotr Nowakowski, Franciszek Prus-Wiśniowski, Filip Turoboś
Let be an Abelian metric group and . We investigate the spectre of a set , defined as the set of all elements such that for every either…
The Lebesgue measure of boundaries of multigeometric Cantorvals
Piotr Nowakowski, Franciszek Prus-Wiśniowski
We prove that the boundary of every multigeometric Cantorval is a null set, and extend this result to a larger class of standard achievable Cantorvals. In addition, we discuss the…
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…