Sorry for my bad english.
Let $(E,A,\mu)$ be a measured space. Let $(A_n)_{n \geq 1}$ be a sequence of sets of $A$.
Let $\epsilon > 0$ be a real number. For $q$ an integer $\geq 1$, we consider in $\mathbb{R}$ :
$A_q = [0,1] \bigcap \bigcup_{p=0}^q [p/q-1/q^{2+\epsilon},p/q+1/q^{2+\epsilon}]$.
We want to prove that $\mu(A_q) \leq 2/q^{1+\epsilon}$ and $\sum_{q=1}^{\infty} \mu(A_q) < \infty$.
I really don't know how to do it, especially the first point... Someone could help me ? Thank you in advance...