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Probabilistic metric spaces
http://planetmath.org/probabilisticmetricspace
When I tried to read the book with that title by Schweizer and Sklar a few years ago, it did not resonate with me at all. This time I like it much more, and I particularly like it that Šerstnev's formalism actually makes them a function with a traditional triangle-like inequality (unlike what one sees when ppl use T-norms), so it is not all that different from other "multivalued distances", e.g. those valued in (dual) quantales.
When I tried to read the book with that title by Schweizer and Sklar a few years ago, it did not resonate with me at all. This time I like it much more, and I particularly like it that Šerstnev's formalism actually makes them a function with a traditional triangle-like inequality (unlike what one sees when ppl use T-norms), so it is not all that different from other "multivalued distances", e.g. those valued in (dual) quantales.