A new meaning and role of the notion of coherent prevision of multiple random quantities

I accept the principles of the theory of concordance into the domain of subjective probability in order to construct an original, geometric and well-organized theory of multiple random quantities. This acceptance is well-founded because the definition of concordance is implicit as well as the one of prevision of a random quantity and in particular of probability of an event. I limit myself to considering no more than two random quantities in this paper. A coherent prevision of a bivariate random quantity coincides with the notion of a-product. Metric properties of the notion of a-product mathematically characterize the notion of coherent prevision of a bivariate random quantity.