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" Probabilistic metric spaces / "
B. Schweizer, A. Sklar.
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BL
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878476
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| Main Entry
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Schweizer, B., (Berthold)
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| Title & Author
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Probabilistic metric spaces /\ B. Schweizer, A. Sklar.
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| Publication Statement
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Mineola, N.Y. :: Dover Publications,, 2005.
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1 online resource (xvi, 313 pages) :: illustrations
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| ISBN
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0486143759
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: 1306493803
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: 9780486143750
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: 9781306493802
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0486445143
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9780486445144
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| Notes
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Originally published: New York : North Holland, ©1983, in series: North Holland series in probability and applied mathematics. With new pref.
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| Bibliographies/Indexes
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Includes bibliographical references (pages 253-266).
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| Contents
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Cover; Title Page; Copyright Page; Contents; Preface to the Dover Edition; Preface; Special Symbols; Chapter 1. Introduction and Historical Survey; 1.0. Introduction; 1.1. Beginnings; 1.2. Menger, 1942; 1.3. Wald, 1943; 1.4. Developments, 1956-1960; 1.5. Some Examples; 1.6. Šerstnev, 1962; 1.7. Random Metric Spaces; 1.8. Topologies; 1.9. Tools; 1.10. Postscript; Chapter 2. Preliminaries; 2.1. Sets and Functions; 2.2. Functions on Intervals; 2.3. Probabilities, Integrals, Random Variables; 2.4. Binary Operations; Chapter 3. Metric and Topological Structures; 3.1. Metric and Related Spaces.
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10.1. Introduction10.2. Consistency, Triangle Inequalities; 10.3. C-Spaces; 10.4. Homogeneous and Semihomogeneous C-Spaces; 10.5. Moments and Metrics; 10.6. Normal C-Spaces; 10.7. Moments in Normal C-Spaces; 10.8. Open Problems; Chapter 11. Transformation-Generated Spaces; 11.1. Transformation-Generated Spaces; 11.2. Measure-Preserving Transformations; 11.3. Mixing Transformations; 11.4. Recurrence; 11.5. E-Processes: The Case of Markov Chains; 11.6. Open Problems; Chapter 12. The Strong Topology; 12.1. The Strong Topology and Strong Uniformity.
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3.2. Isometries, Homotheties, Metric Transforms3.3. Betweenness; 3.4. Minkowski Metrics; 3.5. Topological Structures; Chapter 4. Distribution Functions; 4.1. Spaces of Distribution Functions; 4.2. The Modified Lévy Metric; 4.3. The Space of Distance Distribution Functions; 4.4. Quasi-Inverses of Nondecreasing Functions; Chapter 5. Associativity; 5.1. Associative Binary Operations; 5.2. Generators and Ordinal Sums; 5.3. Associative Functions on Intervals; 5.4. Representation of Archimedean Functions; 5.5. Triangular Norms, Additive and Multiplicative Generators; 5.6. Examples.
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| Abstract
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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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Metric spaces.
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Probabilities.
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MATHEMATICS-- Applied.
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Metric spaces.
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Probabilities.
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| Dewey Classification
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514/.325
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| LC Classification
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QA611.28.S38 2005eb
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| Added Entry
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Sklar, A., (Abe)
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