A representation theorem for real convex functions
Roy Rakestraw · Pacific Journal of Mathematics · 1975
The Krein-Milman theorem is used to prove the following result.A nonnegative function / on [0,1] is convex if, and only if, there exist nonnegative Borel measures μ x and μ 2 on [0,1] such that for every x E [0,1].An example is given for which the representation is not unique.