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Abstract
Measures of information based on fuzzy sets (possibility distributions) had been defined only for finite domains of discourse. This paper presents a method of defining such information functions on a continuous universe of discourse—a domain which is a measurable space of measure 1. The method is based on the concept of “rearangement” of a function, used in lieu of sorting discrete possibility values. For technical reasons, it is preferred to express information value as information distance to the most “uninformed” (constant possibility 1) distribution. The final form of the information for possibility distribution f is
The paper then discusses related information distances and approximations using discrete information functions.