Gelfand-Yaglom-Perez Theorem for Generalized Relative Entropies

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dc.creatorDukkipati, Ambedkar
dc.creatorBhatnagar, Shalabh
dc.creatorMurty, M Narasimha
dc.date2006-01-18
dc.date.accessioned2026-07-07T06:58:24Z
dc.date.available2026-07-07T06:58:24Z
dc.descriptionThe measure-theoretic definition of Kullback-Leibler relative-entropy (KL-entropy) plays a basic role in the definitions of classical information measures. Entropy, mutual information and conditional forms of entropy can be expressed in terms of KL-entropy and hence properties of their measure-theoretic analogs will follow from those of measure-theoretic KL-entropy. These measure-theoretic definitions are key to extending the ergodic theorems of information theory to non-discrete cases. A fundamental theorem in this respect is the Gelfand-Yaglom-Perez (GYP) Theorem (Pinsker, 1960, Theorem. 2.4.2) which states that measure-theoretic relative-entropy equals the supremum of relative-entropies over all measurable partitions. This paper states and proves the GYP-theorem for Renyi relative-entropy of order greater than one. Consequently, the result can be easily extended to Tsallis relative-entropy.
dc.identifierhttps://arxiv.org/abs/math-ph/0601035
dc.identifierhttp://arxiv.org/abs/math-ph/0601035
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/107340
dc.subjectMathematical Physics
dc.titleGelfand-Yaglom-Perez Theorem for Generalized Relative Entropies
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