Description
An Introduction to MeasureTheoretic 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.
Key Features
 Provides in a concise, yet detailed way, the bulk of probabilistic tools essential to a student working toward an advanced degree in statistics, probability, and other related fields
 Includes extensive exercises and practical examples to make complex ideas of advanced probability accessible to graduate students in statistics, probability, and related fields
 All proofs presented in full detail and complete and detailed solutions to all exercises are available to the instructors on book companion site

Considerable bend toward the way probability is used in statistics in nonmathematical settings in academic, research and corporate/finance pursuits.
Readership
Table of Contents
 Dedication
 Pictured on the Cover
 Carathéodory, Constantine (1873–1950)
 Preface to First Edition
 Preface to Second Edition
 Chapter 1. Certain Classes of Sets, Measurability, and Pointwise Approximation
 Abstract
 1.1 Measurable Spaces
 1.2 Product Measurable Spaces
 1.3 Measurable Functions and Random Variables
 Chapter 2. Definition and Construction of a Measure and its Basic Properties
 Abstract
 2.1 About Measures in General, and Probability Measures in Particular
 2.2 Outer Measures
 2.3 The Carathéodory Extension Theorem
 2.4 Measures and (Point) Functions
 Chapter 3. Some Modes of Convergence of Sequences of Random Variables and their Relationships
 Abstract
 3.1 Almost Everywhere Convergence and Convergence in Measure
 3.2 Convergence in Measure is Equivalent to Mutual Convergence in Measure
 Chapter 4. The Integral of a Random Variable and its Basic Properties
 Abstract
 4.1 Definition of the Integral
 4.2 Basic Properties of the Integral
 4.3 Probability Distributions
 Chapter 5. Standard Convergence Theorems, The Fubini Theorem
 Abstract
 5.1 Standard Convergence Theorems and Some of Their Ramifications
 5.2 Sections, Product Measure Theorem, the Fubini Theorem
 Chapter 6. Standard Moment and Probability Inequalities, Convergence in the rth Mean and its Implications
 Abstract
 6.1 Moment and Probability Inequalities
 6.2 Convergence in the rth Mean, Uniform Continuity, Uniform Integrability, and their Relationships
 Chapter 7. The Hahn–Jordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and the Radon–Nikodym Theorem
 Abstract
 7.1 The
Details
 No. of pages:
 426
 Language:
 English
 Copyright:
 © 2014
 Published:
 24th March 2014
 Imprint:
 Academic Press
 Electronic ISBN:
 9780128002902
 Print ISBN:
 9780128000427
About the author
George Roussas
Reviews
"...a very thorough discussion of many of the pillars of the subject, showing in particular how 'measure theory with total measure one' is just the tip of the iceberg...It’s quite a book."MAA.org, An Introduction to MeasureTheoretic Probability
"This second edition employs a classical approach to teaching students of statistics, mathematics, engineering, econometrics, finance, and other disciplines measuretheoretic probability…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."Zentralblatt MATH 12871
"...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 wellwritten 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 fundam