# Thread: Sigma algebra of infinite sets.

1. ## Sigma algebra of infinite sets.

I'm having trouble with this problem, please help:

Let Ω be a uncountable set. Let S be the collection of subsets of Ω given by: AS if and only if A is finite or infinite countable or A complement is finite or infinite countable. Show that S is a σ-algebra

2. Originally Posted by LAINHELL
I'm having trouble with this problem, please help:

Let Ω be a uncountable set. Let S be the collection of subsets of Ω given by: AS if and only if A is finite or infinite countable or A complement is finite or infinite countable. Show that S is a σ-algebra
Note that $\emptyset,\Omega\in S$ (Why? Hint: see the definition of $S$).

Now, if $A\in S$, is $A^c\in S$? (To show this, you just mess around with the definition of $S$.)

Last, you want to show that if $\{A_i\}$ is a collection of sets in $S$, then $\bigcup A_i\in S$ (what have you tried?)

Please show some work so we can have a better idea of where to help you.

Does this makes sense?