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| AN INTRODUCTION TO MEASURE-THEORETIC PROBABILITY
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To order this title, and for more information, click here
By
George Roussas, University of California, Davis
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.
Audience
Graduate students primarily in statistics, mathematics, electrical & computer engineering or other information sciences; mathematical economics/finance in departments of economics.
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
| Bibliographic details |
Hardbound, 462 pages, publication date: OCT-2004
ISBN-13: 978-0-12-599022-6
ISBN-10: 0-12-599022-7
Imprint: ACADEMIC PRESS
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| Price and Ordering |
Price:
GBP 76
USD 120
EUR 89.95
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Last update: 5 Sep 2009
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