Hi there,

I'm faced with two questions concerning sigma algebras but i believe my problem is with the interpretation of the sets themselves!

1.F = {A subset Omega : A is finite} . Is F always a sigma algebra?

The way I'm reading this is that F contains only the set A so that would mean the complement of A (i.e. A') isn't inside F and hence won't fulfil the condition of "closed under complements" for a sigma algebra right away, right?

2. Omega = R (real line)

F = {A subset R : A is finite or A' is finite}. Is F a sigma algebra?

This is where my suspicion about my interpretation grew. I mean, there wouldn't be a need to mention A' if it isn't even in F right? So, the question is, what exactly is contained in F in both cases?