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.
Set with different fractal dimensions
原文：http://www.cnblogs.com/jinjun/p/4909862.html