On equivalence of predictable and natural stochastic processes

A new approach to study of predictable stochastic processes is suggested. This approach is based on the Doob proof of the Doleans-Dad theorem about equivalence of increasing predictable and natural stochastic processes. A generalization of the Doob theorem about uniform approximation of an indicator function is proved. With the help of this degeralization it is proved that the Doleans-Dad theorem is valid fot stochastic processes with integrable variation.