Probability Measures on Metric Spaces

K.R. Parthasarathy

ISBN 10: 082183889X / ISBN 13: 9780821838891

Published by American Mathematical Society, US, 2005

About this Item

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.

Seller Inventory # LU-9780821838891

Bibliographic Details

• Title: Probability Measures on Metric Spaces
• Publisher: American Mathematical Society, US
• Publication Date: 2005
• Language: English
• ISBN 10: 082183889X
• ISBN 13: 9780821838891
• Binding: Hardback
• Condition: New

About this title

Synopsis

Parthasarathy builds far in advance of the general theory of stochastic processes as the theory of probability measures in complete separable metric spaces. He begins with the Borel subsets of a metric space and proceeds to explain 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, and probability measures on C[0,1] and D[0,1]. Parthasarathy includes a comprehensive bibliography and bibliographic notes. Annotation ©2006 Book News, Inc., Portland, OR (booknews.com)