We deal with conditional decomposable information measures, directly defined as functions on a suitable set of conditional events satisfying a class of axioms. For these general measures we introduce a notion of independence and study its main properties in order to compare it with classical definitions present in the literature. The particular case of Wiener-Shannon information measure is taken in consideration and the links between the provided independence for information measures and the independence for the underlying probability are analyzed.
INDEPENDENCE AND CONDITIONAL DECOMPOSABLE INFORMATION MEASURES / Busanello, Giuseppe; Giulianella, Coletti; Vantaggi, Barbara. - In: INTERNATIONAL JOURNAL OF UNCERTAINTY, FUZZINESS AND KNOWLEDGE BASED SYSTEMS. - ISSN 0218-4885. - STAMPA. - 18:3(2010), pp. 225-246. [10.1142/s0218488510006519]
INDEPENDENCE AND CONDITIONAL DECOMPOSABLE INFORMATION MEASURES
BUSANELLO, GIUSEPPE;VANTAGGI, Barbara
2010
Abstract
We deal with conditional decomposable information measures, directly defined as functions on a suitable set of conditional events satisfying a class of axioms. For these general measures we introduce a notion of independence and study its main properties in order to compare it with classical definitions present in the literature. The particular case of Wiener-Shannon information measure is taken in consideration and the links between the provided independence for information measures and the independence for the underlying probability are analyzed.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
