Let X be a supermartingale. The function $t \mapsto E\{X_t\} $is right continuous iff there is exists a modification Y of X which is cadlag. Such a modification is unique.
I just beagn reading the book on Stochastic Integration by Protter and was looking for the proof of Theorem 9 which is stated above. Can somebody point me to a book or a place where I could find it? Thank you