Vitali Covering theorem, countable sub-collection?
Solution 1:
Note $\mathcal G$ is a collection of disjoint balls. As every ball in $\mathbb R^n$ contains a rational point, there cannot be more than countably many of them.
Note $\mathcal G$ is a collection of disjoint balls. As every ball in $\mathbb R^n$ contains a rational point, there cannot be more than countably many of them.