## Probability of tail event using Kolmogorov’s 0-1 law

If $X_1,X_2,… $ are independent random variables and $X=\sup_nX_n$ then $P(X<\infty)$ is either 0 or 1. I think that if we prove the event to be a tail event then the result will follow. But I just don’t know how to prove it to be a tail event. Answer Observe that for each $n$, $\{X<\infty\} … Read more