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 : = (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.