Before revision:  Furthermore, we explore the relations existing between mathematical and financial properties attributable to an acceptance set on the one hand , and the corresponding properties of the induced measure on the other . Dual characterizations in terms of polar sets and support functionals are provided.
After revision:  Furthermore, we explore the relations existing between mathematical and financial properties attributable to an acceptance set on the one hand , and the corresponding properties of the induced measure . Hence, we fill the gap that is the lack of an acceptance set for deviation measures . Dual characterizations in terms of polar sets and support functionals are provided.