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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Common terms and phrases
addition Archimedean associative binary operation C-space closed closure complete composition consequence consider contains continuous convergence convolution copula Corollary corresponding defined Definition denote determined direction distance distinct distribution functions E-space element equal equivalent established example exist extended fact Figure fixed follows function f Furthermore given Hence holds identity immediate implies independent inequality integer interval introduced Lemma Let S,F margins measure Menger space metric space n-copula natural neighborhood system nondecreasing Note obtain pair particular PM space points positive probabilistic probability probability space Problem PROOF properties pseudometrically Ran f random variables respect satisfies Schweizer sense sequence shows Similarly simple space strict strong topology structure studied subset Suppose t-norm Theorem theory topology transform triangle function unique Wald whence yields
Bibliographic information
| Title | Probabilistic Metric Spaces North Holland series in probability and applied mathematics Volume 5 of Probability and Applied Mathematics Series |
| Authors | Berthold Schweizer, Abe Sklar |
| Edition | illustrated |
| Publisher | North Holland, 1983 |
| Original from | the University of Michigan |
| Digitized | 5 Feb 2010 |
| ISBN | 0444006664, 9780444006660 |
| Length | 275 pages |
| Export Citation | BiBTeX EndNote RefMan |