On Modification Theorems
Murali Rao · Transactions of the American Mathematical Society · 1972
Given a right continuous family ${F_t}$ of complete $\sigma$-fields and a bounded right continuous family ${X_t}$ of random variables, we show in this paper that it is possible to modify the conditional expectations $E({X_t}|{F_t})$ to be right continuous. When ${X_t} = X$, this reduces to a result of J. L. Doob.