Before revision:  Furthermore{\cal   the convex risk measure admits a dual representation in terms of a weakly relatively compact set of probability measures absolutely continuous with respect to some probability measure belonging to the canonical c_{\rho .
After revision:  Furthermore{\cal _b(\Omega). We prove that the convex risk measure admits a dual representation in terms of a weakly relatively compact set of probability measures absolutely continuous with respect to some probability measure belonging to the canonical c_{\rho .