The family of central Cantor sets with packing dimension zero

0553967 - MÚ 2022 RIV SK eng J - Článek v odborném periodiku
Nowakowski, Piotr
The family of central Cantor sets with packing dimension zero.
Tatra Mountains Mathematical Publications. Roč. 78, č. 1 (2021), s. 1-8. ISSN 1210-3195
Institucionální podpora: RVO:67985840
Klíčová slova: Baire category * central Cantor sets * product measure * sets of packing dimension zero
Obor OECD: Pure mathematics
Způsob publikování: Open access
https://doi.org/10.2478/tmmp-2021-0001

As in the recent article of M. Balcerzak, T. Filipczak and P. Nowakowski, we identify the family CS of central Cantor subsets of [0, 1] with the Polish space X: = (0, 1)N equipped with the probability product measure μ. We investigate the size of the family P0 of sets in CS with packing dimension zero. We show that P0 is meager and of μ measure zero while it is treated as the corresponding subset of X. We also check possible inclusions between P0 and other subfamilies CS consisting of small sets.
Trvalý link: http://hdl.handle.net/11104/0328629