Let $f(x) = x^{-1/2}$ for $ x \in (0,1)$ and zero otherwise.
Let $F(x) = \sum 2^{-n} f(x - r_{n})$ where $ {r_{n}} $ is an enumeration of rationals.
1) Prove that $F(x)$ is integrable and thus its series is convergent almost everywhere.
(I did this part)
2) Prove that any function $G$, where $G$ agrees with $F$ almost everywhere, is unbounded in any interval.
I'm stuck on part 2.
Thank you for any help