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…
Dominated sets, microscopic sets and Hausdorff measures
Ondřej Zindulka, Piotr Nowakowski
Let be a family of sequences of positive numbers that decrease to 0, let be a metric space and . is said to be -dominated if, for every , a coun…
The algebraic difference of a Cantor set and its complement
Piotr Nowakowski, Cheng-Han Pan
Let be a Cantor set. In the classical problems, modifying the ``size'' of has a magnified effect on $\mathcal{…
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…