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December 1988 Entropy: An Inequality
J.-P. ALLOUCHE, M. MENDÈS FRANCE, G. TENENBAUM
Tokyo J. Math. 11(2): 323-328 (December 1988). DOI: 10.3836/tjm/1270133978

Abstract

We show that the classical Hölder inequality between means of order $\alpha$, $0<\alpha\leqq 1$, can be improved on the assumption that the terms are not too often of comparable size. As an application, we derive a general, optimal bound for the entropy of a probability distribution.

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J.-P. ALLOUCHE. M. MENDÈS FRANCE. G. TENENBAUM. "Entropy: An Inequality." Tokyo J. Math. 11 (2) 323 - 328, December 1988. https://doi.org/10.3836/tjm/1270133978

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Published: December 1988
First available in Project Euclid: 1 April 2010

zbMATH: 0685.28010
MathSciNet: MR976568
Digital Object Identifier: 10.3836/tjm/1270133978

Rights: Copyright © 1988 Publication Committee for the Tokyo Journal of Mathematics

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Vol.11 • No. 2 • December 1988
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