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Probability Measures on Metric Spaces
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AMS Chelsea Publishing
1967; 276 pp; hardcover
Volume: 352
ISBN-10: 0-8218-3889-X
ISBN-13: 978-0-8218-3889-1
List Price: US$43 Member Price: US$38.70
Order Code: CHEL/352.H

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.

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

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

• The Borel subsets of a metric space
• Probability measures in a metric space
• Probability measures in a metric group
• Probability measures in locally compact abelian groups
• The Kolmogorov consistency theorem and conditional probability
• Probability measures in a Hilbert space
• Probability measures on $$C[0,1]$$ and $$D[0,1]$$
• Bibliographical notes
• Bibliography
• List of symbols
• Author index
• Subject index