**AMS Chelsea Publishing**

Volume: 352;
1967;
276 pp;
Hardcover

MSC: Primary 60;

Print ISBN: 978-0-8218-3889-1

Product Code: CHEL/352.H

List Price: $46.00

Individual Member Price: $41.40

**Electronic ISBN: 978-1-4704-3028-3
Product Code: CHEL/352.H.E**

List Price: $46.00

Individual Member Price: $41.40

#### Supplemental Materials

# Probability Measures on Metric Spaces

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*K. R. Parthasarathy*

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.

#### Table of Contents

# Table of Contents

## Probability Measures on Metric Spaces

- Cover Cover11
- Title page iii4
- Preface v6
- Contents ix10
- The Borel subsets of a metric space 114
- Probability measures in a metric space 2639
- Probability measures in a metric group 5669
- Probability measures in locally compact abelian groups 7386
- The Kolmogorov consistency theorem and conditional probability 131144
- Probability measures in a Hilbert space 151164
- Probability measures on 𝐶[0,1] and 𝐷[0,1] 211224
- Bibliographical notes 268281
- Bibliography 270283
- List of symbols 273286
- Author index 274287
- Subject index 275288
- Back Cover Back Cover1290

#### Readership

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

#### Reviews

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