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On a Geometric Generalization of Entropy

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Abstract

A new approach to the notion of a probability space is proposed. A stochastically measurable space is equipped with a geometric structure by introducing distances between elementary events. The probabilistic proximity space (in the discrete case) is used to generalize the notion of entropy. Entropy thus geometrized is shown to preserve all the former properties and also to acquire a previously unknown useful quality. This opens new possibilities in the area of information disciplines.

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  5. Leus, V.A., On the Geometric Generalization of Entropy, Trudy konf., posvyashchennoi 90-letiyu so dnya rozhdeniya A.A. Lyapunova (Proc. Conf. Dedicated to the 90th Anniv. since the Birth of A.A. Lyapunov), Novosibirsk, 2001. Available from http://www.ict.nsc.ru/ws/Lyap2001/2243.

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  1. Sobolev Institute of Mathematics, Siberian Branch of the RAS, Novosibirsk

    V. A. Leus

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  1. V. A. Leus
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Leus, V.A. On a Geometric Generalization of Entropy. Problems of Information Transmission 39, 170–177 (2003). https://doi.org/10.1023/A:1025196104258

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  • DOI: https://doi.org/10.1023/A:1025196104258

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