Abstract:

 A class of capacity was induced by the nonlinear expectations, and the properties of this capacity were studied. In order to better describe the characteristics of capacity, the notion of weak-2-alternating was proposed. Then the weak-2-alternating, sub-2-alternating and 2-alternating of capacity were respectively studied  by using the properties of nonlinear expectations. Final, a theorem of the odd nonlinear expectations operator was obtained, which makes these three properties to be equivalent.

Key words: nonlinear expectations; capacity; 2-alternating; sub-2-alternating; weak-2-alternating