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I just started a prob theory class and i'm a total beginner. I can't find the definition of the following anywhere:

1) What does it mean for a set to be generated by the singletons? In other words, how do I show a certain set is generated by the singletons

2) Similarly, what does it mean to be generated by a collection of sets?

My guess: A set generated by the singletons (or a collection of sets) means that that set can be formed by taking all the singletons and unioning them and complementing them, which leads us to a borel field?