Is $\bigcup_{i = 1}^\infty \mathcal{A}_i$ necessarily a $\sigma$-algebra?

Asked Jul 20 '16 at 04:55

Active Jul 20 '16 at 04:55

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Suppose $\mathcal{A}_1 \subset \mathcal{A}_2 \subset \ldots$ are $\sigma$-algebras consisting of subsets of a set $X$. Is $\bigcup_{i = 1}^\infty \mathcal{A}_i$ necessarily a $\sigma$-algebra? If not, what is a counterexample?

edited Jul 20 '16 at 04:55

Em.

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asked Jul 20 '16 at 04:55

Is $\bigcup_{i = 1}^\infty \mathcal{A}_i$ necessarily a $\sigma$-algebra?

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