Weak Convergence of Measures

Probability and Mathematical Statistics: A Series of Monographs and Textbooks

Harald Bergström, Z. W. Birnbaum, E. Lukacs

• Publisher: Academic Press
• Year: 2014
• Print ISBN:
  9780120910809
• eBook ISBN:
  9781483191454
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

Weak Convergence of Measures provides information pertinent to the fundamental aspects of weak convergence in probability theory. This book covers a variety of topics, including random variables, Hilbert spaces, Gaussian transforms, probability spaces, and random variables. Organized into six chapters, this book begins with an overview of elementary fundamental notions, including sets, different classes of sets, different topological spaces, and different classes of functions and measures. This text then provides the connection between functionals and measures by providing a detailed introduction of the abstract integral as a bounded, linear functional. Other chapters consider weak convergence of sequences of measures, such as convergence of sequences of bounded, linear functionals. This book discusses as well the weak convergence in the C- and D-spaces, which is reduced to limit problems. The final chapter deals with weak convergence in separable Hilbert spaces. This book is a valuable resource for mathematicians.

Table of contents

• Front Cover
• Weak Convergence of Measures
• Copyright Page
• Table of Contents
• PREFACE
• CHAPTER I. SPACES, MAPPINGS, AND MEASURES
• CHAPTER II. INTEGRALS, BOUNDED, LINEAR FUNCTIONALS, AND MEASURES
• CHAPTER III. WEAK CONVERGENCE IN NORMAL SPACES
• CHAPTER IV. WEAK CONVERGENCE ON R(k)
• CHAPTER V. WEAK CONVERGENCE ON THE C- AND D-SPACES
• CHAPTER VI. WEAK CONVERGENCE IN SEPARABLE HILBERT SPACES
• APPENDIX: A PRODUCT-SUM IDENTITY
• NOTES AND COMMENTS
• BIBLIOGRAPHY
• INDEX