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Here's a question I got as a homework assignment:

Let $\{A_i\}_{i=1,\ldots,\infty}$ a sequence of events in the probability space $(\Omega,F,\mathbb{P})$. Show that if $\mathbb{P}(A_i)=1$ for all $i$ then $\mathbb{P}(\bigcap_{i-1}^{\infty}A_i)=1$

So, as the equation is very obvious, I don't know how to prove it.

Any suggestions?

Thanks!

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    I switched the tag from Probability to Probability theory2012-11-04
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    It may seem obvious, but it really does depend on the fact that you’re considering only countably many events. If there were uncountably many events, the probability of their intersection could even be $0$.2012-11-04

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