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https://open.uns.ac.rs/handle/123456789/9013
Title: | Some properties of Rényi entropy over countably infinite alphabets | Authors: | Kovačević, Marko Stanojević, Ivan Šenk, Vojin |
Issue Date: | 1-Apr-2013 | Journal: | Problems of Information Transmission | Abstract: | We study certain properties of Rényi entropy functionals H α(P) on the space of probability distributions over ℤ+. Primarily, continuity and convergence issues are addressed. Some properties are shown to be parallel to those known in the finite alphabet case, while others illustrate a quite different behavior of the Rényi entropy in the infinite case. In particular, it is shown that for any distribution P and any r ∈ [0,∞] there exists a sequence of distributions Pn converging to P with respect to the total variation distance and such that limn→∞ lim α→1+ H∞(Pn) = lim α→1+ limn→∞ H ∞(Pn) + r. © 2013 Pleiades Publishing, Ltd. | URI: | https://open.uns.ac.rs/handle/123456789/9013 | ISSN: | 329460 | DOI: | 10.1134/S0032946013020014 |
Appears in Collections: | FTN Publikacije/Publications |
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