The Family of Central Cantor Sets with Packing Dimension Zero

Nowakowski, Piotr

doi:10.2478/tmmp-2021-0001

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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The Family of Central Cantor Sets with Packing Dimension Zero

Abstract

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