International Journal of Mathematics and Mathematical Sciences
Volume 18 (1995), Issue 4, Pages 649-652

Completion of probabilistic normed spaces

Bernardo Lafuerza Guillén,1 José Antonio Rodríguez Lallena,1 and Carlo Sempi2

1Departamento de Matemática, Aplicada Universidad de Almeria, Almeria 04120, Spain
2Dipartimento di Matematica, Universitá di Lecce, Lecce 73100, Italy

Received 6 December 1993; Revised 28 January 1994

Copyright © 1995 Bernardo Lafuerza Guillén et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We prove that every probabilistic normed space, either according to the original definition given by Šerstnev, or according to the recent one introduced by Alsina, Schweizer and Sklar, has a completion.