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Remarks on Rényi versions of conditional entropy and mutual information

We examine the analogue of Arimoto’s definition of conditional Rényi entropy and Rényi mutual information for abstract alphabets. Despite being dependent on the reference measure, these notions have useful properties similar to those known in the discrete setting. Moreover, we explore relationships between the families of mutual informations defined by Sibson, Csiszár, and Lapidoth-Pfister. In particular, we show that various notions of Rényi capacity and center coincide, extending results of Csiszár and Nakiboğlu.