Probabilistic Metric Spaces (Dover Books on Mathematics)

Schweizer, B.; Sklar, A.

ISBN 10: 0486445143 / ISBN 13: 9780486445144

Editore: Dover Publications, 2011

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Dati bibliografici

• Titolo: Probabilistic Metric Spaces (Dover Books on Mathematics)
• Editore: Dover Publications
• Data di pubblicazione: 2011
• Lingua: Inglese
• ISBN 10: 0486445143
• ISBN 13: 9780486445144
• Rilegatura: Brossura
• Condizione: nuovo

Descrizione articolo

Riassunto

This 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. The two-part treatment begins with an overview that discusses the theory's historical evolution, followed by a development of related mathematical machinery. The presentation defines all needed concepts, states all necessary results, and provides relevant proofs.
The second part opens with definitions of probabilistic metric spaces and proceeds to examinations of special classes of probabilistic metric spaces, topologies, and several related structures, such as probabilistic normed and inner-product spaces. Throughout, the authors focus on developing aspects that differ from the theory of ordinary metric spaces, rather than simply transferring known metric space results to a more general setting.

Contenuti

Preface to Dover Edition Preface Special Symbols 1. Introduction and Historical Survey 2. Preliminaries 3. Metric and Topical Structures 4. Distribution Functions 5. Associativity 6. Copulas 7. Triangle Functions 8. Probabilistic Metric Spaces 9. Random Metric Spaces 10. Distribution-Generated Spaces 11. Transformation-Generated Spaces 12. The Strong Topology 13. Profile Functions 14. Betweenness 15. Supplements References Index Errata Notes Supplementary References