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**albi** Frankly speaking I was working on some probability theory theorem when this problem occured. I'm 99% sure $\displaystyle R_1$ 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 $\displaystyle R_1$ is closed under finite intersections. Than I take complement of set that belongs to $\displaystyle R_1$ and I get finite intersection - the only problem is to find a simple proof that the "intersected" sets belong to $\displaystyle R_1$ .