<abstract xmlns="http://www.w3.org/1999/xhtml">

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

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.

The Family of Central Cantor Sets with Packing Dimension Zero

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"The Family of Central Cantor Sets with Packing Dimension Zero"}

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...

The Family of Central Cantor Sets with Packing Dimension Zero

Published Online: Jan 01, 2022

Page range: 1 - 8

Received: Oct 12, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0001

Keywords
central Cantor sets, Baire category, product measure, sets of packing dimension zero

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

The Family of Central Cantor Sets with Packing Dimension Zero

Published Online: Jan 01, 2022

Page range: 1 - 8

Received: Oct 12, 2020

DOI: https://doi.org/10.2478/tmmp-2021-0001

Keywordscentral Cantor sets, Baire category, product measure, sets of packing dimension zero

© 2021 Mathematical Institute, Slovak Academy of Sciences

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
central Cantor sets, Baire category, product measure, sets of packing dimension zero