Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gelfand-Yaglom-Perez Theorem for Generalized Relative Entropies   The 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.

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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-ex
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn