Probability help/sigma-algebras

[FTaylor244]

Let (S, ε, P) be a probability space and let A be an element of ε with P(A)>0. Let F={AπE :E is an element of ε }
-Prove that F is a sigma-algebra on A.


Not sure even where to go with this really. I know that to be a sigma-algebra has to be closed under complementation and countable unions. I'm not very good with proofs, and just a push in the right direction would help me out a ton. Thanks!

 

[disregardthat]

So you will need to show that:

- A is in F
- The complement of A cap E is in F
- A countable union U_i A cap E_i is in F.

All you need to know are the properties of sets and that epsilon is a sigma algebra. Try it and show what you have tried.

 

[FTaylor244]

Oh, I was under the impression I had to do it the other way around, such that F is in A, etc..maybe that's why I'm having such a hard time here.

Ok so...

A is in F because F=A intersect E, and since an intersect of A is in F, then all of A has to be in F (not sure how to write this properly)
F=AnE is the same as F=(A^c U E^c)^c (^c=complement)
not really sure how to go about the last one

 

[disregardthat]

A is in F because F=A intersect E, and since an intersect of A is in F, then all of A has to be in F (not sure how to write this properly)
F=AnE is the same as F=(A^c U E^c)^c (^c=complement)
not really sure how to go about the last one

F is a set of subsets of A, namely the set of A cap E for E in the sigma algebra. Check the definition of a sigma algebra. Try again keeping that in mind.