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.
After revision: We fully characterize discrete-time dynamic convex expectations (\mathcal{E } V) and \mathcal{L upper semianalytic functions - in particular we work without a reference measure and do not assume essential suprema to exist.