An Introduction to Measure-theoretic Probability

An Introduction to Measure-theoretic Probability

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Description

This book provides in a concise, yet detailed way, the bulk of the probabilistic tools that a student working toward an advanced degree in statistics,
probability and other related areas, should be equipped with. The approach is classical, avoiding the use of mathematical tools not necessary for carrying out the discussions. All proofs are presented in full detail.
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Product details

  • Hardback | 462 pages
  • 147.3 x 228.6 x 30.5mm | 861.84g
  • Academic Press Inc
  • San Diego, United States
  • English
  • black & white illustrations
  • 0125990227
  • 9780125990226

Review quote

"...provides basic tools in measure theory and probability.... A well-written book. Highly recommended."
-CHOICE

"Based on the material presented in the manuscript, I would without any hesitation adopt the published version of the book. The topics dealt are essential to the understanding of more advanced material; the discussion is deep and it is combined with the use of essential technical details. It will be an extremely useful book. In addition it will be a very popular book."
- Madan Puri, Indiana University

"Would likely use as one of two required references when I teach either Stat 709 or Stat 732 again. Would also highly recommend to colleagues. The author has written other excellent graduate
texts in mathematical statistics and contiguity and this promises to be another. This book could well
become an important reference for mathematical statisticians.
- Richard Johnson, University of Wisconsin

"The author has succeeded in making certain deep and fundamental ideas of probability and measure theory accessible to statistics majors heading in the direction of graduate studies in
statistical theory. "
-Doraiswamy Ramachandran, California State University
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About George G. Roussas

George G. Roussas received his B.A. in Mathematics at the University of Athens, Greece, and his Ph.D. in Statistics at the University of California, Berkeley. Roussas is currently Professor and Associate Dean of Statistics at the University of California, Davis. His teaching career began at the University of Wisconsin, Madison. Then he was a Professor of Applied Mathematics at the University of Patras, Greece, and also served as the Dean of the College of Sciences and as Chancellor of that University. At the University of Crete, Greece, Roussas served as Vice President of Academic Affairs. Roussas has published several books, and had more than 65 research papers published in refereed journals. He is a Fellow of the Institute of Mathematical Statistics, the American Statistical Association, and the Royal Statistical Society, and is an elected member of the International Statistical Institute. Finally, Roussas is the Associate Editor of two journals, Statistics and Probability Letters, and Nonparametric Statistics.
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Table of contents

Preface
1. Certain Classes of Sets, Measurability, Pointwise Approximation
2. Definition and Construction of a Measure and Its Basic Properties
3. Some Modes of Convergence of a Sequence of Random Variables and Their Relationships
4. The Integral of a Random Variable and Its Basic Properties
5. Standard Convergence Theorems, The Fubini Theorem
6. Standard Moment and Probability Inequalities, Convergence in the r-th Mean and Its Implications
7. The Hahn-Jordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and The Radon-Nikcodym Theorem
8. Distribution Functions and Their Basic Properties, Helly-Bray Type Results
9. Conditional Expectation and Conditional Probability, and Related Properties and Results
10. Independence
11. Topics from the Theory of Characteristic Functions
12. The Central Limit Problem: The Centered Case 13. The Central Limit Problem: The Noncentered Case
14. Topics from Sequences of Independent Random Variables
15. Topics from Ergodic Theory
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Review Text

"...provides basic tools in measure theory and probability, in the classical spirit, relying heavily on characteristic functions as tools without using martingale or empirical process methods. A well-written book. Highly recommended [for] graduate students; faculty."
-CHOICE

"Based on the material presented in the manuscript, I would without any hesitation adopt the published version of the book. The topics dealt are essential to the understanding of more advanced material; the discussion is deep and it is combined with the use of essential technical details. It will be an extremely useful book. In addition it will be a very popular book."
- Madan Puri, Indiana University

"Would likely use as one of two required references when I teach either Stat 709 or Stat 732 again. Would also highly recommend to colleagues. The author has written other excellent graduate
texts in mathematical statistics and contiguity and this promises to be another. This book could well
become an important reference for mathematical statisticians.
- Richard Johnson, University of Wisconsin

"The author has succeeded in making certain deep and fundamental ideas of probability and measure theory accessible to statistics majors heading in the direction of graduate studies in
statistical theory. "
-Doraiswamy Ramachandran, California State University
show more