## Probabilistic Metric SpacesThis distinctly nonclassical treatment focuses on developing aspects that differ from the theory of ordinary metric spaces, working directly with probability distribution functions rather than random variables. |

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### Contents

Introduction and Historical Survey | 1 |

Preliminaries | 18 |

Metric and Topological Structures | 30 |

Copyright | |

14 other sections not shown

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addition Archimedean associative binary operation C-space closed closure complete composition consequence consider contains continuous convergence convolution copula Corollary defined Definition denote determined direction distance distinct distribution functions E-space element equal equivalent established example exist extended fact fixed follows function f Furthermore given Hence holds identity immediate implies independent inequality integer interval introduced Lemma margins Math measure Menger space metric space n-copula natural nondecreasing normed Note obtain pair particular PM space points positive probabilistic metric spaces probability probability space Problem PROOF properties pseudometrically random variables respect satisfies Schweizer sense sequence shows Similarly simple space statistical strict strong topology structure studied subset Suppose t-norm Theorem theory tion transform triangle function TT.L unique Wald whence yields