Prove that every finite set has measure zero.
Let X be a finite set $\displaystyle X=\{x_1, x_2, ..., x_n\}$.
Let $\displaystyle \epsilon >0$ and choose a cover for X,
$\displaystyle \{(x_i - \frac{\epsilon}{3n}, x_i + \frac{\epsilon}{3n})\}_{i=1}^n$
Then $\displaystyle \sum_{i=1}^{n}[(x_i + \frac{\epsilon}{3n})- (x_i - \frac{\epsilon}{3n})] = n \frac{2 \epsilon}{3n}= \frac{2\epsilon}{3} < \epsilon$
Thus X is of measure zero.