I am having a lot of problems trying to do this problem:
Prove that $\mathbb{R}^n$ can be decomposed into a countable union of the form $$\mathbb{R}^n = N \cup \bigcup_{k=1}^{\infty} B(x_k,r_k)^-$$ where $\lambda(N)=0$ and the closed balls $B(x_,r_k)^-$ are disjoint.
The only thing I have is Lebesgue Measure (in the exercise $\lambda(N)$). Please help.