On Measure Theoretic definitions of Generalized Information Measures and Maximum Entropy Prescriptions
| dc.creator | Dukkipati, Ambedkar | |
| dc.creator | Murty, M Narasimha | |
| dc.creator | Bhatnagar, Shalabh | |
| dc.date | 2006-01-18 | |
| dc.date.accessioned | 2026-07-07T08:15:51Z | |
| dc.date.available | 2026-07-07T08:15:51Z | |
| dc.description | Though Shannon entropy of a probability measure $P$, defined as $- \int_{X} \frac{\ud P}{\ud μ} \ln \frac{\ud P}{\udμ} \ud μ$ on a measure space $(X, \mathfrak{M},μ)$, 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 measure-theoretic 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. | |
| dc.identifier | https://arxiv.org/abs/cs/0601080 | |
| dc.identifier | http://arxiv.org/abs/cs/0601080 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/133586 | |
| dc.subject | Information Theory | |
| dc.title | On Measure Theoretic definitions of Generalized Information Measures and Maximum Entropy Prescriptions | |
| dc.type | text |