What is a probabilistic metric space and why is it diffrent from a normal metric space?

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- Jan 25th 2006, 05:04 AMSkanderH?Probabilistic metric space?
What is a probabilistic metric space and why is it diffrent from a normal metric space?

- Jan 29th 2006, 05:34 PMrabeldinProbabilistic 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.

- Jan 29th 2006, 05:51 PMSkanderHProbabilistic metric space vs probability space?
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

Cheers

Skander - Jan 29th 2006, 05:56 PMrabeldinProbabilistic metric space
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.