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## Main Question or Discussion Point

- what is the difference between algebra and sigma algebra?
- How to construct the smallest algebra generated by a given collection of sets?
- How to check that a given collection of sets is an algebra?
- How to check that a given collection is the smallest algebra containing a collection of sets?
- How to construct the smallest sigma-algebra generated by a given collection of sets, especially a collection of singletons?
- How to check that a given collection of sets is a sigma-algebra?
- How to prove that the sigma-algebra generated by two different collections of sets is the same. sigma-algebra?
- How to check that a given collection is the smallest sigma-algebra containing a collection of sets?

Could you please give me some hints, for solve these kind of problems?

Thanks