Before revision:  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. \rho(-|f|)) .
After revision:  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|) =0. We also apply our results to the case of uncertain volatility .