A stability result concerning the Shannon entropy

• Autores: Alessando Morando
• Localización: Aequationes mathematicae, ISSN 0001-9054, Vol. 62, Nº. 3, 2001, págs. 286-296
• Idioma: inglés
• DOI: 10.1007/pl00000154
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• Resumen

  • We are concerned with a well-known characterization of the Shannon entropy by Faddeev, suitably re-examined in the frame of Ulam--Hyers "stability" of functional equations. By use of some results about number theoretical functions, we give a sufficient condition that the solutions of a suitable system of countably many functional inequalities approximate the Shannon entropy uniformly.