Doob Sequence Definition (Doob sequence): The Doob sequence of a function f with respect to a sequence X1,...,Xn is Yi=E[f(X1,...,Xn)X1,...,Xi] Yo=E[f(X1,.…,Xn)】->Yn=f(X1,.,Xn)Definition (Doob sequence): Yi = E[f (X1,...,Xn) | X1,...,Xi] The Doob sequence of a function f with respect to a sequence X1,...,Xn is Y0 = E[f (X1,...,Xn)] Yn = f (X1,...,Xn) Doob Sequence