Prove that the Lebesgue measure of a particular set is zero. I am doing revision and got extremely stuck with the following exercise, which appeared in an exam from the previous year.
Consider the measure space $(\mathbb R, \mathbb B, \lambda)$ where $\mathbb B$ is the Borel sigma algebra and $\lambda$ the Lebesgue measure. Let $\delta > 0$ and 
\begin{align*}
V := \left\{x \in \mathbb R: \exists \text{ infinitely many } p \in \mathbb Z, \,  q \in \mathbb N \text{ where } \left|x - \frac{p}{q}\right| \le \frac{1}{q^{2+\delta}}\right\}.
\end{align*}
Show that $\lambda(V) = 0$.
I wish I had an attempt for this, but unfortunately I don't know how to start, I'm afraid. 
Please help me.

The set $V$ appears to be the set of rational numbers, which has measure zero.
