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In mathematics, probabilistic metric spaces are a generalization of metric spaces where the distance no longer takes values in the non-negative real numbers R ≥ 0, but in distribution functions.
Let D+ be the set of all probability distribution functions F such that F = 0 such that max = 1].
Then given a non-empty set S and a function F: S × S → D+ where we denote F by Fp,q for every ∈ S × S, the ordered pair is said to be a probabilistic metric space if:
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