A mixed theory of information. X: Information functions and information measures
[For Part IX by \textit{B. Ebanks} and \textit{W. Sander} see Util. Math. 30, 63-78 (1986; Zbl 0576.94010).] In a new, mixed theory of information the measures of information are assumed to depend on both the probabilities and the events. The author characterizes measures depending upon an n-tuple of events and upon a finite number of n-ary complete discrete probability distributions by a recursivity and a weak symmetry condition. The result contains a special case many characterization theorems for some well-known information measures like the Shannon entropy, the entropy of degree \(\alpha\), the inaccuracy, the directed divergence and the information improvement. There is a generalization of this result found by \textit{B. Ebanks}, \textit{P. L. Kannappan} and \textit{C. T. Ng} [Recursive inset entropies of multiplicative type on open domains; Manuscript]. For a survey of all important results about weakly symmetric and generalized recursive information measures we refer to a survey article of the present author [The fundamental equation of information and its generalizations, Aequationes Math. 33, 150-182 (1987)].
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