Abstract
Recently, H. P. Chen, J. M. Fraser, and H. Yu proved that the popcorn set is of Assouad dimension 2 and box-counting dimension 4/3 by using inequalities from number theory and probability. In the present paper, we introduce logarithm density and β-condition for subsets of N, by which we give upper and lower bounds of box-counting dimensions of some popcorn subsets.
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