In [16] K. Menger proposed the probabilistic concept of distance by replacing the number d(p, q), as the distance between points p, q, by a distribution function Fp,q. This idea led to development of probabilistic analysis [3], [11] [18]. In this paper, generalized probabilistic 2-normed spaces are studied and topological properties of these spaces are given. As an example, a space of random va...

One proves that the Mazur-Ulam theorem can be extended in the framework of metric spaces as long as a well behaved concept of midpoint is available. This leads to the new concept of Mazur-Ulam space. Besides the classical case of real normed spaces, other examples such as Sym++(n,R), the space of all n × n dimensional positive definite matrices, appear as cones attached to suitable Euclidean Jo...