The Family of Central Cantor Sets with Packing Dimension Zero Article Swipe

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Mathematics Dimension (graph theory) Zero (linguistics) Cantor set Packing dimension Measure (data warehouse) Combinatorics Product (mathematics) Space (punctuation) Null set Set (abstract data type) Minkowski–Bouligand dimension Mathematical analysis Geometry Fractal dimension Data mining Computer science Fractal Programming language Linguistics Philosophy

Piotr Nowakowski ·

YOU? · · 2021 · Open Access · · DOI: https://doi.org/10.2478/tmmp-2021-0001 · OA: W3208299057

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.

The Family of Central Cantor Sets with Packing Dimension Zero Article Swipe

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