Probability Measures on Metric Spaces

K. R. Parthasarathy, Z. W. Birnbaum, E. Lukacs

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9781483200224
• eBook ISBN: 9781483225258
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Probability Measures on Metric Spaces presents the general theory of probability measures in abstract metric spaces. This book deals with complete separable metric groups, locally impact abelian groups, Hilbert spaces, and the spaces of continuous functions. Organized into seven chapters, this book begins with an overview of isomorphism theorem, which states that two Borel subsets of complete separable metric spaces are isomorphic if and only if they have the same cardinality. This text then deals with properties such as tightness, regularity, and perfectness of measures defined on metric spaces. Other chapters consider the arithmetic of probability distributions in topological groups. This book discusses as well the proofs of the classical extension theorems and existence of conditional and regular conditional probabilities in standard Borel spaces. The final chapter deals with the compactness criteria for sets of probability measures and their applications to testing statistical hypotheses. This book is a valuable resource for statisticians.

Table of contents

• Fron Cover
• Probability Measures on Metric Spaces
• Copyright Page
• Table of Contents
• Preface
• Chapter I. The Borel Subsets of a Metric Space
• Chapter II. Probability Measures in a Metric Space
• Chapter III. Probability Measures in a Metric Group
• Chapter VI. Probability Measures in Locally Compact Abelian Groups
• Chapter V. The Kolmogorov Consistency Theorem and Conditional Probability
• Chapter VI. Probability Measures in a Hilbert Space
• Chapter VII. Probability Measures on C[0, 1] and D[0, 1]
• Bibliographical Notes
• Bibliography
• List of Symbols
• Author Index
• Subject Index