Uniqueness of the representation for G - martingales with finite variation ∗

Letting {δn} be a refining sequence of Rademacher functions on the interval [0, T ], we introduce a functional on processes in the G-expectation space by d(K) = lim sup n Ê[ ∫ T 0 δn(s)dKs]. We prove that d(K) > 0 if Kt = ∫ t 0 ηsd〈B〉s with nontrivial η ∈ M G(0, T ) and that d(K) = 0 if Kt = ∫ t 0 ηsds with η ∈ M G(0, T ). This implies the uniqueness of the representation for G-martingales with finite variation, which is the main purpose of this article.