Before revision:  It is shown that \mathcal{E } (\cdot|U)}\colon }\to(U) be a sublinear increasing functional which leaves L(U) invariant.
After revision:  It is shown that \mathcal{E } (\cdot|U)}\colon }\to\mathcal{L(U) be a sublinear increasing functional which leaves L(U) invariant.