Let $\displaystyle n,q \in \mathbb{N}$ such that $\displaystyle q \leq n$ and let $\displaystyle E_1,E_2,...,E_n$ be measurable subsets of $\displaystyle [0,1]$. Suppose that for each point $\displaystyle x \in [0,1]$, there are at least $\displaystyle q$ sets in $\displaystyle \{E_1,E_2,...,E_n\}$ that contain $\displaystyle x$. Prove that there exists $\displaystyle 1 \leq i \leq n$ such that $\displaystyle m(E_i) \geq \frac{q}{n}$.