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Entropy 2014, 16(7), 3732-3753; doi:10.3390/e16073732
Article

On the Connections of Generalized Entropies With Shannon and Kolmogorov–Sinai Entropies

Received: 17 May 2014 / Revised: 19 June 2014 / Accepted: 30 June 2014 / Published: 3 July 2014
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Abstract

We consider the concept of generalized Kolmogorov–Sinai entropy, where instead of the Shannon entropy function, we consider an arbitrary concave function defined on the unit interval, vanishing in the origin. Under mild assumptions on this function, we show that this isomorphism invariant is linearly dependent on the Kolmogorov–Sinai entropy.
Keywords: dynamical entropy; Kolmogorov–Sinai entropy dynamical entropy; Kolmogorov–Sinai entropy
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Falniowski, F. On the Connections of Generalized Entropies With Shannon and Kolmogorov–Sinai Entropies. Entropy 2014, 16, 3732-3753.

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