An Introduction To Measure-theoretic Probability

Hardcover | March 24, 2014

byGeorge G. RoussasEditorGeorge G. Roussas

not yet rated|write a review
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. 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 non-mathematical settings in academic, research and corporate/finance pursuits.

Pricing and Purchase Info

$155.63 online
$186.69 list price (save 16%)
In stock online
Ships free on orders over $25

From the Publisher

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,...

From the Jacket

An Introduction to Measure-theoretic Probability , Second Edition, employs a classical approach to teaching students of statistics, mathematics, engineering, econometrics, finance, and other disciplines measure-theoretic probability. This book requires no prior knowledge of measure theory, discusses all its topics in great detail, and ...

George G. Roussas earned a B.S. in Mathematics with honors from the University of Athens, Greece, and a Ph.D. in Statistics from the University of California, Berkeley. As of July 2014, he is a Distinguished Professor Emeritus of Statistics at the University of California, Davis. Roussas is the author of five books, the author or co-au...

other books by George G. Roussas

Introduction to Probability
Introduction to Probability

Kobo ebook|Nov 27 2013

$138.00

An Introduction To Probability And Statistical Inference
An Introduction To Probability And Statistical Inferenc...

Hardcover|Sep 25 2014

$162.15 online$194.06list price(save 16%)
see all books by George G. Roussas
Format:HardcoverDimensions:426 pages, 9.41 × 7.24 × 0.98 inPublished:March 24, 2014Publisher:Academic PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0128000422

ISBN - 13:9780128000427

Look for similar items by category:

Customer Reviews of An Introduction To Measure-theoretic Probability

Reviews

Extra Content

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

Editorial 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 Measure-Theoretic Probability  "This second edition employs a classical approach to teaching students of statistics, mathematics, engineering, econometrics, finance, and other disciplines measure-theoretic 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 1287-1 "...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