Before revision: We fully characterize discrete-time dynamic convex expectations (\mathcal{E }  upper semianalytic functions - in particular we work without a reference measure and do not assume essential suprema to exist. It is shown that \mathcal{E } (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
After revision: We fully characterize discrete-time dynamic convex expectations (\mathcal{E } upper semianalytic functions from U } (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.