On the minimal members of convex expectations

In this paper, we show that for a convex expectation E [ ⋅ ] defined on L 1 ( Ω , F , P ) , the following statements are equivalent:(i) a minimal member of the set of all convex expectations defined on L 1 ( Ω , F , P ) ; linear; mensional Jensen inequality for E holds. dition, we prove a sandwich theorem for convex expectation and concave expectation.