What is a probabilistic metric space and why is it diffrent from a normal metric space?
Begin with the definition of a metric space. Then define a probability measure on it. A probability measure is a function from the space of subsets of the metric space (intervals, regions, etc.) to the interval [0,1] such that the function obeys the axioms of probability.
Thanks for answering
I think what you just posted is the definition of a probability space in terms of a metric space, as opposed to a probabilistic metric space, which is something quite different.
Actually since I first posted this question, and got almost no answers, I had to go do it the hard way, by looking for the the definition in books and papers.
I am not completly sure yet, but I think I got the general idea:
A probabilistic metric space is a sapce S where the measure is not a mapping from S*S to positive real numbers, but from S*S to a space of probability distributions.
I haven't got all the details yet, but "triangle functions" and t-norms seem to be in close relation with probabilistic metric spaces.
More help is welcome
You may be right. There are too many variations in terminology based on local conditions, what textbook is in use, who is teaching the course, etc. A question like that one is like a question that asks "What do you mean when you say..." directed to the person who uses the phrase.