An Introduction to Measure-Theoretic Probability

By

  • George Roussas, University of California, Davis, USA

An Introduction to Measure-Theoretic Probability, Second Edition, employs a classical approach to teaching students of statistics, mathematics, engineering, econometrics, finance, and other disciplines that measure theoretic probability. This book requires no prior knowledge of measure theory, discusses all its topics in great detail, and includes one chapter on the basics of ergodic theory and one chapter on two cases of statistical estimation. There is a considerable bend toward the way probability is actually used in statistical research, finance, and other academic and nonacademic applied pursuits. 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.
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Audience

Graduate students primarily in statistics, mathematics, electrical & computer engineering or other information sciences; mathematical economics/finance in departments of economics.

 

Book information

  • Published: March 2014
  • Imprint: ACADEMIC PRESS
  • ISBN: 978-0-12-800042-7


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 Sequences 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 rth Mean and its Implications
7. The Hahn-Jordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and The Radon-Nikodym 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
16. Two Cases of Statistical Inference: Estimation of a Real-Valued Parameter, Nonparametric Estimation of a Probability Density Function
Appendix A Brief Review of Chapters 1-16
Appendix B Brief Review of Riemann-Stieltjes Integral
Appendix C Notation and Abbreviations
Index
Revised Answers Manual to an Introduction to Measure-Theoretic Probability (online)