Any finite set is a null-set How can we prove that a finite set is a null-set? Maybe would it be easier to prove that the outer measure of a finite set is $0$? any ideas on how to tackle this problem?
thanks,

You can just as easily prove that a countably infinite set $\{a_1,a_2,a_3,\dots\}$ is null by putting an interval of width $\frac{\epsilon}{2^n}$ about $a_n$. 
The above paragraph assumed we were working in the reals, but a similar idea works for $\mathbb{R}^n$. 
