Semnan University International Journal of Nonlinear Analysis and Applications 2008-6822 8 2 2017 12 27 Mazur-Ulam theorem in probabilistic normed groups 327 333 2786 10.22075/ijnaa.2017.1281.1318 EN Alireza Pourmoslemi Department of Mathematics, Payame Noor University, Tehran, Iran Kourosh Nourouzi Faculty of Mathematics, K.N. Toosi University of Technology, P.O. Box 16315-1618, Tehran, Iran Journal Article 2016 03 23 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. Probabilistic normed groups Invariant probabilistic metrics Mazur-Ulam Theorem https://ijnaa.semnan.ac.ir/article_2786_313d118769848a5d41636e321e9950d6.pdf