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:(adsbygoogle = window.adsbygoogle || []).push({});

Given:

LetFbe a sigma-algebra, then:

1) The empty set is inF.

2) IfAis inF, then so is the complement ofA.

3) The union of a sequence of elements inFis also inF.

To prove:

The intersection of a sequnce of elements inFis also inF.

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Definition of a sigma-algebra

**Physics Forums | Science Articles, Homework Help, Discussion**