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Probability Measures on Metric Spaces
 
Front Cover for Probability Measures on Metric Spaces
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Available Formats:
Hardcover ISBN: 978-0-8218-3889-1
Product Code: CHEL/352.H
276 pp 
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $44.10
Electronic ISBN: 978-1-4704-3028-3
Product Code: CHEL/352.H.E
276 pp 
List Price: $46.00
MAA Member Price: $41.40
AMS Member Price: $41.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $73.50
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Front Cover for Probability Measures on Metric Spaces
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Probability Measures on Metric Spaces
AMS Chelsea Publishing: An Imprint of the American Mathematical Society
Available Formats:
Hardcover ISBN:  978-0-8218-3889-1
Product Code:  CHEL/352.H
276 pp 
List Price: $49.00
MAA Member Price: $44.10
AMS Member Price: $44.10
Electronic ISBN:  978-1-4704-3028-3
Product Code:  CHEL/352.H.E
276 pp 
List Price: $46.00
MAA Member Price: $41.40
AMS Member Price: $41.40
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $73.50
MAA Member Price: $66.15
AMS Member Price: $66.15
  • Book Details
     
     
    AMS Chelsea Publishing
    Volume: 3521967
    MSC: Primary 60;

    Having been out of print for over 10 years, the AMS is delighted to bring this classic volume back to the mathematical community.

    With this fine exposition, the author gives a cohesive account of the theory of probability measures on complete metric spaces (which he views as an alternative approach to the general theory of stochastic processes). After a general description of the basics of topology on the set of measures, he discusses regularity, tightness, and perfectness of measures, properties of sampling distributions, and metrizability and compactness theorems. Next, he describes arithmetic properties of probability measures on metric groups and locally compact abelian groups. Covered in detail are notions such as decomposability, infinite divisibility, idempotence, and their relevance to limit theorems for "sums" of infinitesimal random variables. The book concludes with numerous results related to limit theorems for probability measures on Hilbert spaces and on the spaces \(C[0,1]\).

    The Mathematical Reviews comments about the original edition of this book are as true today as they were in 1967. It remains a compelling work and a priceless resource for learning about the theory of probability measures.

    The volume is suitable for graduate students and researchers interested in probability and stochastic processes and would make an ideal supplementary reading or independent study text.

    Readership

    Graduate students and research mathematicians interested in probability and stochastic processes.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. The Borel subsets of a metric space
    • Chapter 2. Probability measures in a metric space
    • Chapter 3. Probability measures in a metric group
    • Chapter 4. Probability measures in locally compact abelian groups
    • Chapter 5. The Kolmogorov consistency theorem and conditional probability
    • Chapter 6. Probability measures in a Hilbert space
    • Chapter 7. Probability measures on $C[0,1]$ and $D[0,1]$
  • Reviews
     
     
    • From a review of the original edition:

      A very readable book which should serve as an excellent source from which a student could learn the subject ... a convenient reference for the specialist for theorems which must by now be regarded as basic to the subject.

      Mathematical Reviews
  • Request Review Copy
  • Get Permissions
Volume: 3521967
MSC: Primary 60;

Having been out of print for over 10 years, the AMS is delighted to bring this classic volume back to the mathematical community.

With this fine exposition, the author gives a cohesive account of the theory of probability measures on complete metric spaces (which he views as an alternative approach to the general theory of stochastic processes). After a general description of the basics of topology on the set of measures, he discusses regularity, tightness, and perfectness of measures, properties of sampling distributions, and metrizability and compactness theorems. Next, he describes arithmetic properties of probability measures on metric groups and locally compact abelian groups. Covered in detail are notions such as decomposability, infinite divisibility, idempotence, and their relevance to limit theorems for "sums" of infinitesimal random variables. The book concludes with numerous results related to limit theorems for probability measures on Hilbert spaces and on the spaces \(C[0,1]\).

The Mathematical Reviews comments about the original edition of this book are as true today as they were in 1967. It remains a compelling work and a priceless resource for learning about the theory of probability measures.

The volume is suitable for graduate students and researchers interested in probability and stochastic processes and would make an ideal supplementary reading or independent study text.

Readership

Graduate students and research mathematicians interested in probability and stochastic processes.

  • Chapters
  • Chapter 1. The Borel subsets of a metric space
  • Chapter 2. Probability measures in a metric space
  • Chapter 3. Probability measures in a metric group
  • Chapter 4. Probability measures in locally compact abelian groups
  • Chapter 5. The Kolmogorov consistency theorem and conditional probability
  • Chapter 6. Probability measures in a Hilbert space
  • Chapter 7. Probability measures on $C[0,1]$ and $D[0,1]$
  • From a review of the original edition:

    A very readable book which should serve as an excellent source from which a student could learn the subject ... a convenient reference for the specialist for theorems which must by now be regarded as basic to the subject.

    Mathematical Reviews
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