1. The problem statement, all variables and given/known data http://i.imgur.com/tjpka.png (the actual problem is the third part down) 2. Relevant equations the first two parts are the definition of borel sets,and the second part is a relevant theorem. 3. The attempt at a solution so I'm new to Borel sets. And I feel like I'm missing something big, because this exercise seems to contradict a lot of statistics I've learned. I have a feeling once I get what I'm missing, it should be relatively easy to prove this stuff, but if someone could help me find out what it is I'm missing, it would be greatly appreciated. For example: (i) from the exercise. This seems to be true if and only if A and B are disjoint, but nowhere are we told this is so. (ii) seems to imply that AUB = 1 (following from (iv) of the theorem), but again, we are not told this. (iii) seems to imply that A⊆C, or C⊆A, but nowhere are we told this is so. (iv) I haven't started yet, but I'm not worried about that one; at first glance it just looks like letting AUB equal one set, and then using the theorem. But the first 3 are proving a big conceptual block for me. again, I think I'm missing exactly what a Borel set is, and how it is different than a usual set. Any help with that would be awesome. Thanks.