Let $I_\alpha\subset[0,1]$ be an $\alpha$-Cantor set 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 $(\mathbb R^*,\times)$?

Let $I_\alpha\subset[0,1]$ be an $\alpha$-Cantor set 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 with the growth and Følner sequences in $(\mathbb R^*,\times)$?

Let $I_\alpha\subset[0,1]$ be an $\alpha$-Cantor set 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) is compared to $\alpha$?

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

Let $I_\alpha\subset[0,1]$ be an $\alpha$-Cantor set 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 $(\mathbb R^*,\times)$?