- #1
Zaare
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I'm supposed to answer the question "Can a sigma-algebra be infinite and countable?"
I think I can show that if it has a countable number of disjoint subsets, then it can't be countable considering the possible combinations of the subsets.
Now I need to show that if a sigma-algebra consists of an infinite number of subsets, then it has a countable number of disjoint subsets.
Any ideas on how I can do this?
I think I can show that if it has a countable number of disjoint subsets, then it can't be countable considering the possible combinations of the subsets.
Now I need to show that if a sigma-algebra consists of an infinite number of subsets, then it has a countable number of disjoint subsets.
Any ideas on how I can do this?