Information in metric space

The idea of information, in the classic theories of Fisher and Wiener–Shannon, is a measure only of probabilistic and repetitiveness events. The idea of information is broader than the probability. The Wiener–Shannonʹs axioms are extended to the non-probabilistic and repetitiveness events. It is possible the introduction of a Theory of Information for events not connected to the probability therefore for non-repetitive events. On the basis of so called Laplaceʹs principle of insufficient knowledge, the MaxInf principle is defined for choose solutions in absence of knowledge. In this paper the value of information, as a measure of equality of data among a set of values, is applied in numeric analysis as method for approximation of data, as an example of application.