Bernardo Lafuerza Guillén, Panackal Harikrishnan; Probabilistic normed spaces, Imperial College Press, London 2014, World Scientific, London-Singapore-Hong Kong 2014, xi+220 pp, ISBN 978-1-78326-468-1/hbk; 978-1-78326-470-4/ebook.

Abstract

Probabilistic metric (PM) spaces are spaces on which there is a "distance function" taking as values distribution functions - the "distance" between two points p; q is a distribution function (in the sense of probability theory) F(p; q) , whose value F(p; q)(t) at t 2 R can be interpreted as the probability that the distance between p and q be less than t. Probabilistic metric spaces were first considered by K. Menger in 1942, who made important contributions to the subject, followed almost immediately by A. Wald in 1943. A good presentation of results up to 1983 is given in the book by B. Schweizer and A. Sklar, Probabilistic metric spaces, North Holland, Amsterdam 1983 (reprinted and updated by Dover Publications, New York 2012).