For the question to be more understandable, here is a link for a screenshot:
Using the definition from below the to be proven statement, I have come to the following conclusion:
$\limsup_{n\to \infty} A_n = \cap_{n\ge 1} (\cup_{k\ge n} A_k) = (A_1 \cup ... \cup A_n) \cap (A_2 \cup ... \cup A_n) \cap ... \cap (A_n \cup A_n) = A_n$ therefore $P(\limsup_{n\to \infty} A_n) = 0$ only if $P(A_n) = 0$.
Is that correct or have I made some logical error here, it doesn't say anywhere in the exercise that $P(A_n) = 0$.
I'd be very glad if one of you could help me with this and also send me some formatting cheat sheet for this website so the questions can get easier to read.