How to prove the natural parameter space of an exponential model is convex without using Holders inequality and other complex theories?
Here is the original question.
Let A be the natural parameter space for an Exponential model f(u; phi) = exp{ (phi-transpose) * u - k(phi)}*h(u).
Give an elementary proof that A is convex.
Note: Please prove without using Holders inequality and other complex theories. Please let me know a simple way to prove that the natural parameter space A is convex.