Set with different fractal dimensions

Given $0<s<u<v<1$ and $s<t<v$, one can construct a Cantor set $E\subset [0,1]$ such that $\dim_H E=s, \dim_P E=t, \underline{\dim}_B E=u$ and $\overline{\dim}_B E=v$, see Sets with different dimensions in $[0,1]$,Real Analysis Exchange by Donald W. Spear.

时间： 2024-10-12 18:18:21

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