A separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle

We prove constructively that every uniformly continuous convex function f:X→R+f:X→R+ has positive infimum, where X is the convex hull of finitely many vectors. Using this result, we prove that a separating hyperplane theorem, the fundamental theorem of asset pricing, and Markov's principle are constructively equivalent. This is the first time that important theorems are classified into Markov's principle within constructive reverse mathematics.