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,

It follows from countable sub additivity of the outer measure and the fact a single point set is null. This comes from the fact it can be covered by a single interval (x - r , x + r) for x being the element of the set, r being any positive number.
