Earlier I had posted question about Borel cantelli Lemma. Thanks to Nate and Shai for your kind response. Please see my profile for the earlier questions. As you can see I do not understand the lemma well. Here are some confusions I have. I hope someone will be kind enough to help me understand the following:
Is it true that P ([An i.o.]∩ A) = P [( A ∩ An) i.o.]. If so, how do we prove this? or is it trivial? And assuming that we know that P[An i.o.] =1 , can we establish that the sum {P(A ∩ An)} diverges (meaning = infinity) ?
Thanks