Why it mustn't be a sigma algebra?
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We have $(Omega, mathcal F, P)$ , some probability space. Let $mathcal F_1$ - some sub-algebra of $mathcal F$ and $forall n$ define $mathcal F_{n+1}$ as class of sets, which received by countable intersecting or countable union from $mathcal F_n$ . How to prove, that $cup_{n in mathbb N} mathcal F_n$ mustn't be even $sigma$ -algebra? Does it exists some counterexample?
probability-theory measure-theory
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asked Dec 3 '18 at 15:11
anykk anykk
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