Is the Intersection of a Sequence in a Sigma-Algebra Also in the Sigma-Algebra?

[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.

 

[matt grime]

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

 

[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.