On a Geometric Representation of Probability Laws and of a Coherent Prevision-Function According to Subjectivistic Conception of Probability

Abstract

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 in an original way. We are the first in the world to do this kind of work: it is the foundation of our next and extensive study concerning the formulation of a geometric, wellorganized and original theory of random quantities.

Keywords

• metric
• collinearity
• vector subspace
• convex set
• linear dependence