The conversation between human and AI assistant.
How do I solve the following problem in measure theory ?
I see. So we just need to show that each $\bigcap\limits_{j=1}^{\infty} F_{j,n}$ is measurable?
Exactly. But note that $\bigcap\limits_{j=1}^{n} F_{j,n} = F_{n,n} = \bigcap\limits_{j=1}^{n} E_j$, so each $F_{j,n}$ is decreasing as $n$ increases.