Includes bibliographical references (pages 391-392) and index.

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.

"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"--