The generalized (also called extended) transfer principles as introduced in two earlier papers by Egghe and Rousseau are known to be stronger properties than the classical transfer principle of Dalton. Hence, functions satisfying one of these generalized principles are very good concentration measures. This paper studies the following non-trivial problem: how many different generalized transfer principles can a function satisfy? We show that a function can, at most, satisfy one generalized transfer principle. This also shows that a further generalization of transfer principles, comprising the generalized ones, is not possible. The proof of this result involves the solution of a norm problem in mathematical analysis and analytical geometry.