In many books, a martingale (roughly speaking) is defined as a process X1,X2,... satisfying:
which is equivalent to
While the latter is understandable to me, I interpret the former in this sense: "expectation is equal to a random variable", which is absurd to me.
Now, I am sure this is a stupid question but: how should I interpret the former?
Maybe that X_tn is no more a random variable but a number (because at time tn is known)? If so, why don't textbook put that symbol in lower case as usual... ?