On a geometric representation of probability laws and of a coherent prevision-function according to subjectivistic conception of probability

We distinguish the two extreme aspects of the logic of certainty by identifying their corresponding structures into a linear space. We extend probability laws P formally admissible in terms of coherence to random quantities. We give a geometric representation of these laws P and of a coherent prevision-function P which we previously defined. This work is the foundation of our next and extensive study concerning the formulation of a geometric, well-organized and original theory of random quantities.