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" An introduction to measure-theoretic probability / "
by George G. Roussas (Department of Statistics, University of California, Davis).
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BL
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| Record Number
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618072
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dltt
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| Main Entry
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Roussas, George G.
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| Title & Author
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An introduction to measure-theoretic probability /\ by George G. Roussas (Department of Statistics, University of California, Davis).
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| Edition Statement
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Second edition.
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| Page. NO
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xxiv, 401 pages :: illustrations ;; 25 cm
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| ISBN
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9780128000427
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: 0128000422
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| Notes
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Machine generated contents note: 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.
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Includes bibliographical references and index.
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| Abstract
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"In this introductory chapter, the concepts of a field and of a [sigma]-field are introduced, they are illustrated bymeans of examples, and some relevant basic results are derived.Also, the concept of a monotone class is defined and its relationship to certain fields and [sigma]-fields is investigated. Given a collection of measurable spaces, their product space is defined, and some basic properties are established. The concept of a measurable mapping is introduced, and its relation to certain [sigma]-fields is studied. Finally, it is shown that any random variable is the pointwise limit of a sequence of simple random variables"--
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Probabilities.
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Measure theory.
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| Parallel Title
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Introduction to measure theoretic probability
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