  Let $\mathcal{V}$ be the set of all combinations of expected value of finite
objective functions from designing information. I showed that $\mathcal{V}$ is
a compact and convex set implemented by signal structures with finite support
when unknown states are finite. Moreover, $\mathcal{V}(\mu)$ as a
correspondence of prior is continuous. This result can be applied to develop a
concavification method of Lagrange multipliers that works with general
constrained optimization. It also provides tractability to a wide range of
information design problems.
