Some properties of support functionals

The author considers convex functionals $f_t$ defined on the open convex subset $G$ of real $B$-space $X$ and continuous at $x_0\in G$. All linear functionals on $X$ which are support functionals of form $\int_Tf_t(x)\mu(dt)$ and $\max\limits_{t\in T}f_t(x)$ at $x_0$ are described.