Mistake using Borel-Cantelli Lemma

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Ah, I see. In that case you are correct that [itex]P(\overline{X}_n < c \text{ e.v.})=0[/itex], but this is irrelevant, since we may have [itex]\liminf_{n\rightarrow \infty} \overline{X}_n < c[/itex] even if we do not have [itex]\overline{X}_n < c \text{ e.v.}[/itex]
 

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