i need some help with stopping time and martingales:
let $M=(M_n)_n\ge0$ a martingale such that $0<a<|M_n-M_n-1|\le K$, and let $T$ be a stopping time $T=\inf\{n:M_n>\lambda\}$, how can i demonstrate that T is not integrable?
I have to demonstrate that using Doob theorem, in particular i already showed that if $\tau$ was integrable $M^{\tau}$ is uniformly integrable (which is point 1 of the exercise), but i can't understand how to go on.
Thanks in advance!