And this relates to Probability and Statistics, how?
Edit: My bad. Sorry about that!
Frankly speaking I was working on some probability theory theorem when this problem occured. I'm 99% sure is algebra but the full proof seems bit too long.... If somebody knows a short proof, please post it.
PS I think I can prove that is closed under finite intersections. Than I take complement of set that belongs to and I get finite intersection - the only problem is to find a simple proof that the "intersected" sets belong to .