Let $\displaystyle n_1,n_2,n_3,...$ be an increasing sequence of positive integers. Let $\displaystyle E = \{x \in [0,2\pi] : lim_{k \to \infty} sin (n_k x)\}$ exists. Prove that $\displaystyle E$ is Lebesgue measurable and evaluate $\displaystyle m(E)$.

Hey this is something really new. How do I approach the question? Have been thinking for quite long and still couldn't get an idea on how to start.

Thank you in advance.