Rational Numbers Null Set under Lebesgue Measure

Theorem
Let $\lambda$ be $1$-dimensional Lebesgue measure on $\R$.

Let $\Q$ be the set of rational numbers.

Then:
 * $\map \lambda \Q = 0$

that is, $\Q$ is a $\lambda$-null set.

Proof
We have that the Rational Numbers are Countably Infinite.

The result follows from Countable Set is Null Set under Lebesgue Measure.