suppose you have a sequence of random variables $\displaystyle (X_n)_{n \geq 0}$. Then what does $\displaystyle sup_n E[X_n]$ mean? it does not make sense to me since if n is fixed then $\displaystyle E[X_n]$ is a constant. Is it the same thing as $\displaystyle lim sup_{n-> \infty} E[X_n]$?