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- W1659913825 abstract "Though Shannon entropy of a probability measure $P$, defined as $- int_{X} frac{ud P}{ud mu} ln frac{ud P}{udmu} ud mu$ on a measure space $(X, mathfrak{M},mu)$, does not qualify itself as an information measure (it is not a natural extension of the discrete case), maximum entropy (ME) prescriptions in the measure-theoretic case are consistent with that of discrete case. In this paper, we study the measure-theoretic definitions of generalized information measures and discuss the ME prescriptions. We present two results in this regard: (i) we prove that, as in the case of classical relative-entropy, the measure-theoretic definitions of generalized relative-entropies, R'{e}nyi and Tsallis, are natural extensions of their respective discrete cases, (ii) we show that, ME prescriptions of measure-theoretic Tsallis entropy are consistent with the discrete case." @default.
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- W1659913825 date "2006-01-18" @default.
- W1659913825 modified "2023-09-27" @default.
- W1659913825 title "On Measure Theoretic definitions of Generalized Information Measures and Maximum Entropy Prescriptions" @default.
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