Here's a question I got as a homework assignment:
Let $\{A_i\}_{i=1,\ldots,\infty}$ a sequence of events in the probability space $(\Omega,F,\mathbb{P})$. Show that if $\mathbb{P}(A_i)=1$ for all $i$ then $\mathbb{P}(\bigcap_{i-1}^{\infty}A_i)=1$
So, as the equation is very obvious, I don't know how to prove it.
Any suggestions?
Thanks!