On the Measure of the Midpoints of the Cantor Set in $\mathbb{R}$

Enrique Alvarado, Yunfeng Hu

In this paper, we are going to discuss the following problem: Let $T$ be a fixed set in ${\mathbb{R}}^n$. And let $S$ and $B$ he two subsets in ${\mathbb{R}}^n$ such that for any $x$ i…