عنوان

Probabilistic metric spaces /

(Number (ISBN

0486143759

(Number (ISBN

1306493803

(Number (ISBN

9780486143750

(Number (ISBN

9781306493802

Erroneous ISBN

0486445143

Erroneous ISBN

9780486445144

Publisher's Number

MWT11604497

Title Proper

Probabilistic metric spaces /

General Material Designation

[Book]

First Statement of Responsibility

B. Schweizer, A. Sklar.

Place of Publication, Distribution, etc.

Mineola, N.Y. :

Name of Publisher, Distributor, etc.

Dover Publications,

Date of Publication, Distribution, etc.

2005.

Specific Material Designation and Extent of Item

1 online resource (xvi, 313 pages) :

Other Physical Details

illustrations

Text of Note

Originally published: New York : North Holland, ©1983, in series: North Holland series in probability and applied mathematics. With new pref.

Text of Note

Includes bibliographical references (pages 253-266).

Text of Note

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.

Text of Note

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.

Text of Note

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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8

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Text of Note

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.

Source for Acquisition/Subscription Address

MIL

Stock Number

580631

Title

Probabilistic metric spaces

International Standard Book Number

0486445143

Metric spaces.

Probabilities.

MATHEMATICS-- Applied.

Metric spaces.

Probabilities.

Number

Edition

Class number

Book number

Schweizer, B., (Berthold)

Sklar, A., (Abe)

Date of Transaction

20200822114350.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y