Abstract:The theory of risk measurement based on the theory of classical probability measurement has already had a lot of research results,but there are many nonadditive risks in the financial and insurance markets,therefore, it is of great theoretical and practical significance to analyze the theory of risk measurement based on nonadditive measure.First, we propose one measure of variability based on the Choquet integral theory, and prove that this measure is a coherent and comonotonical additive measure of variability.Then, we give one representation and comonotonical additive measures of variability in chance space.These conclusions extend the theory of measure of variability to the nonadditive condition.