Borel Cantelli Exercise 2019

I intend to post this for a Borel-Cantelli lemma exercise on Math.SE.

The target event is ${\exists i_0 \in \Bbb{N} : \forall i \ge i_0, X_i = 1}$, whose complement is

$\{\forall i_0 \in \Bbb{N} : \exists i \ge i_0, X_i > = 0\} = \limsup_i \{X_i = 0\}.$

To apply Borel-Cantelli, one has to determine whether $\sum_i P(X_i = 0)<+\infty$.

1 comment

Test PR 289Jul 2, 2019 22:51:28

Test multiline table in PR/MR body.

Can you speak English? Equation like $1 + 1 = 3 - 1$ or

$$f + g = h?$$