The family of central Cantor sets with packing dimension zero

Year, pages: 2021, 1 - 8

As in the recent article of M. Balcerzak, T. Filipczak and P. Nowakowski, we identify the family $\mathcal{CS}$ of central Cantor subsets of $[0,1]$ with the Polish space $X:=(0,1)^{\mathbb{N}}$ equipped with the probability product measure $μ $. We investigate the size of the family $\mathcal{P}₀$ of sets in $\mathcal{CS}$ with packing dimension zero. We show that $\mathcal{P}₀$ is meager and of $μ$ measure zero while it is treated as the corresponding subset of $X$. We also check possible inclusions between $\mathcal{P}₀$ and other subfamilies of $\mathcalCS$ consisting of small sets.

Nowakowski, P. 2021. The family of central Cantor sets with packing dimension zero. In Tatra Mountains Mathematical Publications, vol. 78, no.1, pp. 1-8. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0001

Nowakowski, P. (2021). The family of central Cantor sets with packing dimension zero. Tatra Mountains Mathematical Publications, 78(1), 1-8. 1210-3195. DOI: https://doi.org/10.2478/tmmp-2021-0001

Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava

https://creativecommons.org/licenses/by-nc-nd/4.0/