A differentiability criterion for continuous functions

A generalization of the GGR conjecture

“…When n = 1, Theorem 0.2 is a tautology that does not even require the hypothesis that f is n − 1 times Peano differentiable at c; while Theorem 0.1 does not make sense. Proposition 0.3 is almost an extension of Theorem 0.1 for n = 1; it points in the direction of the result for higher n. A non-trivial generalization of the n = 1 case in Theorem 0.2, the problem of finding all exact first order generalized Riemann derivatives that imply the first (Peano) derivative for all continuous functions at c, is proved in [12].…”