I am going through the text 'Fractal Geometry: Mathematical Foundations and Applications' and came the following exercise:
Give a set $B\subset\mathbb{R}$ that has Hausdorff dimension $s=\frac{\log2}{\log3}$ but has $H^s(B)=\infty$.
My thoughts:
Now, when I see $\frac{\log2}{\log3}$ the first thing that comes to mind is the cantor set $C$, but the $H^s(C)$ is finite. I feel as though I am missing a lemma or theorem. Is there some relation of the Hausdorff dimension of a set constructed by countable unions?