Mistake using Borel-Cantelli Lemma

logarithmic · 2012-05-15

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

Thread starter logarithmic
Start date May 15, 2012

May 18, 2012

Citan Uzuki

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]