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Let S be a fixed set.

1. What is the difference between an algebra on S and a sigma-algebra on S?

2. Why do we require an event space to be a sigma algebra instead of an algebra?

3. Find a set S and an algebra A on S such that A is not a sigma-algebra on S.

Also, I have a proof that I could use some hints on how to start and the general form in which I should go about it.

Prove that every sigma-algebra on S is an algebra on S.

Thanks.