Definition of a sigma-algebra

1. Apr 21, 2005

Zaare

Given the definition of a sigma-algebra, I need to show that the intersection of a sequence of elements in a sigma-algebra is in the sigma-algebra:

Given:
Let F be a sigma-algebra, then:
1) The empty set is in F.
2) If A is in F, then so is the complement of A.
3) The union of a sequence of elements in F is also in F.

To prove:
The intersection of a sequnce of elements in F is also in F.

I'm quite stuck and seem to go around in circles. Any help on how to attack this problem would be appreciated.

2. Apr 21, 2005

matt grime

Take an intersection AnBnC... what is its complement?

3. Apr 21, 2005

Zaare

Right, the intersection is the union of the complements. And since the complements, and therefore the union, are in F, the intersection must also be in F.