The Family of Central Cantor Sets with Packing Dimension Zero

Piotr Nowakowski

doi:10.2478/tmmp-2021-0001

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The Family of Central Cantor Sets with Packing Dimension Zero

Tatra Mountains Mathematical Publications

Volume 78 (2021): Issue 1 (October 2021)

By: Piotr Nowakowski

Open Access

|Jan 2022

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.

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2021-0001 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 1 - 8

Submitted on: Oct 12, 2020

Published on: Jan 1, 2022

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

central Cantor sets,

Baire category,

product measure,

sets of packing dimension zero

Related subjects:

Mathematics,

General mathematics

© 2022 Piotr Nowakowski, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 78 (2021): Issue 1 (October 2021)