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- Probabilistic_metric_space abstract "A probabilistic metric space is a generalization of metric spaces where the distance is no longer valued in positive real numbers, but instead is valued in distribution functions.Let D+ be the set of all probability distribution functions F such that F(0) = 0: F is a nondecreasing, left continuous mapping from the real numbers R into [0, 1] such thatsup F(x) = 1where the supremum is taken over all x in R.The ordered pair (S,d) is said to be a probabilistic metric space if S is a nonempty set andd: S×S →D+In the following, d(p, q) is denoted by dp,q for every (p, q) ∈ S × S and is a distribution function dp,q(x). The distance-distribution function satisfies the following conditions:du,v(x) = 1 for all x > 0 ⇔ u = v (u, v ∈ S).du,v(x) = dv,u(x) for all x and for every u, v ∈ S.du,v(x) = 1 and dv,w(y) = 1 ⇒ du,w(x + y) = 1 for u, v, w ∈ S and x, y ∈ R.".
- Probabilistic_metric_space wikiPageExternalLink ProbabilisticMetricSpace.html..
- Probabilistic_metric_space wikiPageID "3891878".
- Probabilistic_metric_space wikiPageRevisionID "552309139".
- Probabilistic_metric_space hasPhotoCollection Probabilistic_metric_space.
- Probabilistic_metric_space subject Category:Metric_geometry.
- Probabilistic_metric_space subject Category:Theory_of_probability_distributions.
- Probabilistic_metric_space comment "A probabilistic metric space is a generalization of metric spaces where the distance is no longer valued in positive real numbers, but instead is valued in distribution functions.Let D+ be the set of all probability distribution functions F such that F(0) = 0: F is a nondecreasing, left continuous mapping from the real numbers R into [0, 1] such thatsup F(x) = 1where the supremum is taken over all x in R.The ordered pair (S,d) is said to be a probabilistic metric space if S is a nonempty set andd: S×S →D+In the following, d(p, q) is denoted by dp,q for every (p, q) ∈ S × S and is a distribution function dp,q(x). ".
- Probabilistic_metric_space label "Probabilistic metric space".
- Probabilistic_metric_space sameAs m.0b5d_7.
- Probabilistic_metric_space sameAs Q7246858.
- Probabilistic_metric_space sameAs Q7246858.
- Probabilistic_metric_space wasDerivedFrom Probabilistic_metric_space?oldid=552309139.
- Probabilistic_metric_space isPrimaryTopicOf Probabilistic_metric_space.