Suppose f , g ? L?(0, 1); let F1 , . . . , FN be ?-algebras of Borel sets in [0, 1].
Put f0 = f and fj = E(f{j ?1} |Fj ), j = 1, 2, . . . , N . The function f is transformable into g, if for any ? > 0 there exist N and such ?-algebras F1 , . . . , FN that fN ? g