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Folland question #1.2.5

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Here is the question I am starring at:

If $\mathcal{M}$ is the $\sigma$-algebra generated by $\epsilon,$ then $\mathcal{M}$ is the union of $\sigma$-algebras generated by $\mathcal{F}$ as $\mathcal{F}$ ranges over all countable subsets of $\epsilon.$(Hint: Show that the latter object is a $\sigma$-algebra.)

I do not understand what this question is teaching us, I do not understand its statement, could anyone explain it to me please?

I also do not understand why the hint will prove the required.Could anyone explain it to me please?


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