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To show that sets made up of single points are Borel sets, it is enough to say that:

There exist a sample space A = {a1, a2,..., an} n = 1, 2,...

then Bn = {an}; where Bn belongs to A.

Then Bn is closed, and its complement must be open.

So the sigma algebra geberated by A is a orel field because it is formed by finite unions and intersections of open sets?

I am some confused here...