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# An Introduction To Measure-theoretic Probability

## byGeorge G. RoussasEditorGeorge G. Roussas

### Hardcover | March 24, 2014

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$186.69

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### about

*An Introduction to Measure-Theoretic Probability, Second Edition*, employs a classical approach to teaching the basics of measure theoretic probability. 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.

This edition requires no prior knowledge of measure theory, covers 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. Topics range from the basic properties of a measure to modes of convergence of a sequence of random variables and their relationships; the integral of a random variable and its basic properties; standard convergence theorems; standard moment and probability inequalities; the Hahn-Jordan Decomposition Theorem; the Lebesgue Decomposition T; conditional expectation and conditional probability; theory of characteristic functions; sequences of independent random variables; and ergodic theory. There is a considerable bend toward the way probability is actually used in statistical research, finance, and other academic and nonacademic applied pursuits. Extensive exercises and practical examples are included, and all proofs are presented in full detail. Complete and detailed solutions to all exercises are available to the instructors on the book companion site.

This text will be a valuable resource for graduate students primarily in statistics, mathematics, electrical and computer engineering or other information sciences, as well as for those in mathematical economics/finance in the departments of economics.

- 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.

### Details & Specs

The following ISBNs are associated with this title:

ISBN - 10:0128000422

ISBN - 13:9780128000427

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### Extra Content

Table of Contents

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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