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- W1987459102 abstract "In this paper we study certain properties of R'{e}nyi entropy functionals $H_alpha(mathcal{P})$ on the space of probability distributions over $mathbb{Z}_+$. Primarily, continuity and convergence issues are addressed. Some properties shown parallel those known in the finite alphabet case, while others illustrate a quite different behaviour of R'enyi entropy in the infinite case. In particular, it is shown that, for any distribution $mathcal P$ and any $rin[0,infty]$, there exists a sequence of distributions $mathcal{P}_n$ converging to $mathcal{P}$ with respect to the total variation distance, such that $lim_{ntoinfty}lim_{alphato{1+}} H_alpha(mathcal{P}_n) = lim_{alphato{1+}}lim_{ntoinfty} H_alpha(mathcal{P}_n) + r$." @default.
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- W1987459102 date "2013-04-01" @default.
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- W1987459102 title "Some properties of Rényi entropy over countably infinite alphabets" @default.
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- W1987459102 doi "https://doi.org/10.1134/s0032946013020014" @default.
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