Abstract: Assuming g_1, g_2, ..., g_k are measure preserving transformations on a probability space X, we require that a function f from X to a measurable space Y satisfies that f(x) is in F(x, f(g_1 x), .... f(g_k x) ) almost everywhere for an upper semi continuous correspondence F defined on X x Y^k. If there exists such functions however NONE of them are measurable with respect to any finitely additive extension of the probability measure for which the g_i are still measure preserving, we say that the correspondence F is paradoxical. We demonstrate some paradoxical correspondences that are also convex valued and nowhere empty. We are curious if there are applications beyond optimization and economics. Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006) The Operator Algebra Seminar schedule is here: https://sites.google.com/view/oastorvergata/home-page