In this work we provide a characterization of Ck,1 functions on Rn (that ik K times differentiable with locally Lipschitz k-th derivatives) by means of (k+1)-th divided differences and Riemann derivatives. In particular we prove that the class of Ck,1 functions is equivalent to the class of functions with bounded (K+1)-th divided difference. From this result we deduce a Taylor's formula for this class of functions and a characterization through Riemann derivatives.
