Let $I_\alpha\subset[0,1]$ be an [$\alpha$-Cantor set][1] of Lebesgue measure $\alpha$ and let $I=I_\alpha+\{1\}=\{1+x:x\in I_\alpha\}$.

**Q1.** What is the Lebesgue measure of the set $\{\frac{t}{s}:t,s\in I\}$? 

**Q2**. How is $\mu(\{\frac{t}{s}:t,s\in I\}\})$ (where $\mu$ is the Lebesgue measure)  compared to $\alpha$?

**Context:** These two questions have to do the growth and  Følner sequences in $(\mathbb R^*,\times)$?


  [1]: https://en.wikipedia.org/wiki/Smith%E2%80%93Volterra%E2%80%93Cantor_set