Fundamental metric expressions of a generic quadruple divided random quantity
After establishing a metric over the vector space of the bivariate random quantities
which are the components of a generic quadruple divided random quantity I
establish a metric over the vector space of the quadruple divided random quantities
in order to show that a coherent prevision of a generic bivariate random quantity
coincides with the notion of a-product. Therefore, metric properties of the notion
of a-product mathematically characterize the notion of coherent prevision of
a generic bivariate random quantity. I accept the principles of the theory of concordance
into the domain of subjective probability for this reason. 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. By
considering quadruple divided random quantities I realize that the notion of coherent
prevision of a generic bivariate random quantity can be used in order to obtain
fundamental metric expressions of quadruple divided random quantities.
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