# Borel Sets

1. Feb 2, 2005

### jetoso

Question:
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...

2. Feb 2, 2005

### mathman

In order to define Borel sets, the open sets must be defined. Once you have that, Borel sets are the smallest collection containg open sets and closed under the operations of countable unions and intersections, as well as complements.

In your example, what are the open sets?

3. Feb 3, 2005