Funciones con derivadas sucesivas grandes y pequeñas por doquier

• Autores: Luis Bernal González
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 38, Fasc. 2, 1987, págs. 117-122
• Idioma: español
• Títulos paralelos:
  • Functions with big and small successive derivatives everywhere
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• Resumen

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