Geometria métrica aleatória

Abstract

In looking for Professor Xavier and putting myself under his orientation to the monograph, he initially introduced me to his work "Contribution to the Study of Probabilistic Metric Spaces" for an initial reading; the subject very pleased me. We then began some geometric ideas of the Metric Spaces (Blumental (1953)), then going to Random Length of Arcs (Xavier (1979)). On the other hand, to clarify notions and ideas, we had to consult several other works included in the bibliography, between books and articles; of the latter, some have been studied by us in its entirety. So we can conclude and we are presenting this monograph dealing with some concepts about Probabilistic Metric Spaces (Chapter 1), on Random Length of Arcs (Chapter 2) and on Intermediarity (Chapter 3), that is, on how "one point is between two others ".