Funciones con derivadas sucesivas grandes y pequeñas por doquier

Abstract

In this paper we show that, given two double sequences of positive real numbers, α and β, the subset of all functions defined on an open real set which have big derivatives and small ones with respect to α and β, at every point, is residual in C∞. As a corollary, we derive that Baire-almost every function of C∞ has null radius of convergence at each point.