A Radon–Nikodym approach to measure information

We consider a decision maker facing uncertainty which behaves as a subjective expected utility maximizer. The value of information is traditionally captured as a greater expected utility the decision maker can achieve by selecting a best strategy as information arrives. We deal with the limit process of being better informed, and introduce an information density function depending solely on the states that gives an exact least upper bound to being more informed. This information density function is given by a Radon–Nikodym-type theorem for set functions and is explicitly computed for the countable case.