Abstract
The equivalence between non-extensive C. Tsallis entropy and the extensive entropy introduced by Alfréd Rényi is discussed. The Rényi entropy is studied from the perspective of the geometry of the Lebesgue and generalised, exotic Lebesgue spaces. A duality principle is established. The Rényi entropy for the Lévy distribution, in the domain when the nunerical methods fails, is approximated by asymptotic expansion for the large values of the Rényi parameter.
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