On the Geometric Generalization of Entropy

A new approach to the notion of a probability space is proposed. A stochastically measurable space is equipped with a geometric structure by introducing distances between elementary events. The probabilistic proximity space (in the discrete case) is used to generalize the notion of entropy. Entropy thus geometrized is shown to preserve all the former properties and also to acquire a previously unknown useful quality. This opens new possibilities in the area of information disciplines.