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You are not logged in. #1 20080731 10:48:15
#2 20080731 21:10:20
#5 20080928 09:42:00
Re: σalgebraThe concept of a sigma algebra is particularly useful in analysis. It can actually be quite difficult to prove that any explicit set is (Lebesgue) measurable. However, the set of measurable sets forms a sigma algebra. Using this fact, we can get a whole lot of sets by simply proving that all open and closed sets are measurable. In particular, given those facts any Borel set is indeed measurable. "In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..." #6 20081001 07:29:06
Re: σalgebraAnd indeed, sigmaalgebras are a kind of introduction to measure theory (Borel and Lebesgue measures in particular) Last edited by TooT (20081001 07:29:26) 