### Journals Information

**
Mathematics and Statistics Vol. 6(4), pp. 50 - 60 DOI: 10.13189/ms.2018.060402 Reprint (PDF) (164Kb) **

## Probabilities Obtained by Means of Hyperhomographies into a Quadruple Random Quantity

**Pierpaolo Angelini ^{*}**

Department of Statistical Sciences, Sapienza University of Rome, Italy

**ABSTRACT**

I realized that it is possible to construct an original and well-organized theory of multiple random quantities by accepting the principles of the theory of concordance into the domain of subjective probability. A very important point relevant to such a construction is consequently treated in this paper by showing that a coherent prevision of a bivariate random quantity coincides with the notion of -product of two vectors while a coherent prevision of a quadruple random quantity coincides with the notion of -product of two affine tensors. Metric properties of the notion of -product mathematically characterize both the notion of coherent prevision of a generic bivariate random quantity and the notion of coherent prevision of a generic quadruple random quantity. Coherent previsions of bivariate and quadruple random quantities can be used in order to obtain fundamental metric expressions of bivariate and quadruple random quantities.

**KEYWORDS**

Hyperhomography, Translation, Affine Tensor, Antisymmetric Tensor, -product, -norm

**Cite This Paper in IEEE or APA Citation Styles**

(a). IEEE Format:

[1] Pierpaolo Angelini , "Probabilities Obtained by Means of Hyperhomographies into a Quadruple Random Quantity," Mathematics and Statistics, Vol. 6, No. 4, pp. 50 - 60, 2018. DOI: 10.13189/ms.2018.060402.

(b). APA Format:

Pierpaolo Angelini (2018). Probabilities Obtained by Means of Hyperhomographies into a Quadruple Random Quantity. Mathematics and Statistics, 6(4), 50 - 60. DOI: 10.13189/ms.2018.060402.