An introduction to measure-theoretic probability

George G. Roussas

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. The book features excellent exposition marked by a clear, coherent and logical devleopment of the subject. It is easy to understand, with detailed discussion of material and complete proofs.

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  • 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

「Nielsen BookData」より


書名 An introduction to measure-theoretic probability
著作者等 Roussas, George G.
Roussas George
出版元 Elsevier Academic Press
刊行年月 c2005
ページ数 xviii, 443 p.
大きさ 24 cm
ISBN 0125990227
NCID BA69278802
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言語 英語
出版国 オランダ