I have a little problem with this Lemma. I have to show:
Let be X nonnegative Supermartingale, then
$$E(U_{a,b}(X))≤\frac{a}{(b-a)}$$
$\forall a,b\in\mathbb{R}$ and $0 ≤ a < b$, while $U_{a,b}(X)$ called the number of upcrossing of [a,b]
Thank you very much in advance for your answer!