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

• Main Authors: Pierpaolo Angelini, Angela De Sanctis
• Format: Article
• Language: English
• Published: Accademia Piceno Aprutina dei Velati 2018-07-01
• Series: Ratio Mathematica
• Subjects: metric; collinearity; vector subspace; convex set; linear dependence
• Online Access: http://eiris.it/ojs/index.php/ratiomathematica/article/view/401

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.