In the framework of Generalized Information Theory of J. Kampé de Fériet, a system of axioms for the conditional information is studied without assuming additivity.
@article{urn:eudml:doc:38836, title = {Sur les informations conditionnelles sans F-composabilit\'e.}, journal = {Stochastica}, volume = {4}, year = {1980}, pages = {81-88}, zbl = {0444.94005}, mrnumber = {MR0573727}, language = {fr}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38836} }
Valverde, Llorenç. Sur les informations conditionnelles sans F-composabilité.. Stochastica, Tome 4 (1980) pp. 81-88. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38836/