Before revision:  To get these results we study the topological properties of the dual of the Banach space L^1(c) associated to some capacity cand we prove a representation Theorem for convex risk measures on L^1(c). As applications, we obtain that every G-expectation \E (resp. in case of uncertain volatility every sublinear risk measure \rho), admits a representation with a numerable family of probability measures absolutely continuous with respect to some P belonging to the canonical c-class, with c(f )=  \E(|f|) , (resp.
After revision:  To get these results we study the topological properties of the dual of the Banach space L^1(c) associated to a capacity c. As application we obtain that every G-expectation \E (resp. in case of uncertain volatility every sublinear risk measure \rho), admits a representation with a numerable family of probability measures absolutely continuous with respect to some P belonging to the canonical c-class, with c(f )= \E(|f|) , (resp.