On Measure Theoretic definitions of Generalized Information Measures and Maximum Entropy Prescriptions

X dP dμ ln dP dμ dμ on a measure space (X,M, μ), 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 measuretheoretic definitions of generalized relative-entropies, Rényi 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.