Some characterization theorems for generalized measures of uncertainty and information

Summary Some characterization theorems are given for the various generalized measures of information and uncertainty by using two types of functional inequalities. This paper unifies several existing results on the various measures of information and some special cases of interest are mentioned at appropriate places.The work of this paper was done while the author was a visiting postdoctoral fellow with the University of Waterloo. This paper was presented at the Meeting on Information Measures held at the University of Waterloo, Waterloo, Ontario, Canada from April 10–14, 1970.