Entropy and monotonicity

Abstract

Measuring the information provided by the observation of events has been a challenge for seventy years, since the simultaneous inception of entropy by Claude Shannon and Norbert Wiener in 1948. Various definitions have been proposed, depending on the context, the point of view and the chosen knowledge representation. We show here that one of the most important common feature in the choice of an entropy is its behavior with regard to the refinement of information and we analyse various definitions of monotonicity.