The Family of Central Cantor Sets with Packing Dimension Zero-Reference-Cited by-同舟云学术

The Family of Central Cantor Sets with Packing Dimension Zero

Published:2021-10-01 Issue:1 Volume:78 Page:1-8
ISSN:1338-9750
Container-title:Tatra Mountains Mathematical Publications
language:en
Short-container-title:

Author:

Nowakowski Piotr¹²

Affiliation:

1. Institute of Mathematics , Łódź University of Technology , Łódź , POLAND

2. Institute of Mathematics , Czech Academy of Sciences , Prague , CZECH REPUBLIC

Abstract

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 P 0 of sets in CS with packing dimension zero. We show that 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 P 0 and other subfamilies CS consisting of small sets.

Publisher

Walter de Gruyter GmbH

Link

https://www.sciendo.com/pdf/10.2478/tmmp-2021-0001

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