Mazur-Ulam theorem in probabilistic normed groups

In this paper, we give a probabilistic counterpart of  Mazur-Ulam theorem  in probabilistic normed groups. We show, under some conditions, that every surjective isometry between two probabilistic normed groups is a homomorphism.

کلیدواژه ها:

Probabilistic normed groups ، Invariant probabilistic metrics ، Mazur-Ulam Theorem