Probabilistic Metric Spaces [NOOK Book]

Overview

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.
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Probabilistic Metric Spaces

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Overview

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.
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Product Details

  • ISBN-13: 9780486143750
  • Publisher: Dover Publications
  • Publication date: 10/14/2011
  • Sold by: Barnes & Noble
  • Format: eBook
  • Pages: 336
  • File size: 15 MB
  • Note: This product may take a few minutes to download.

Table of Contents

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
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