# ?Probabilistic metric space?

• Jan 25th 2006, 05:04 AM
SkanderH
?Probabilistic metric space?
What is a probabilistic metric space and why is it diffrent from a normal metric space?
• Jan 29th 2006, 05:34 PM
rabeldin
Probabilistic 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 PM
SkanderH
Probabilistic metric space vs probability space?

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 PM
rabeldin
Probabilistic 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.