In 1942 Karl Menger defined statistical metric spaces by generalizing metric spaces by replacing the distance d(p, q) between two points p and q by a distribution function Fp,q. Here the value Fp,q(x) at the point x can be interpreted as the probability that the distance between the two points p and q be less than x. Later ? Sestnev generalized statistical metric spaces defined by Menger. Further these spaces are these days known as ? Sestnev probabilistic normed spaces. ? Sestnev also considered probabilistic normed spaces, probabilistic normed spaces as defined by ? Sestnev despite the simplicity of their definition had tittle program perhaps mainly due to its technical difficult. this motivated Alsina, Schweizer and Sklar to reconsider the definition of probabilistic normed spaces and coming up with a redefinition of probabilistic normed spaces. A new, wider, definition of a PN space was introduced in 1993 by Alsina, Schweizer and Sklar. Their definition quickly became the standard one, and, to the best of the authors knowledge, it has been adopted by all the researchers who, after them, have investigated the properties, the uses or the applications of PN spaces.Alsina, Schweizer and Sklar generalized the definition of probabilistic normed spaces still further to define the probabilistic inner product spaces. The every surjective isometry between normed spaces is Affine. This theorem has been proved by Mazur and Ulam in 1932. D. Mushtari proved in 1968 the same result in the case of probabilistic normed spaces in the sense of A. Sherstnev. The purpose of this thesis is to prove the theorem in the probabilistic setting as defined by Alsina, schweizer and Sklar.