عنوان

An introduction to measure-theoretic probability /

(Number (ISBN

0128000422

(Number (ISBN

9780128000427

Number

dltt

Title Proper

An introduction to measure-theoretic probability /

General Material Designation

[Book]

First Statement of Responsibility

by George G. Roussas (Department of Statistics, University of California, Davis).

Edition Statement

Second edition.

Specific Material Designation and Extent of Item

xxiv, 401 pages :

Other Physical Details

illustrations ;

Dimensions

25 cm

Text of Note

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.

Text of Note

Includes bibliographical references and index.

Text of Note

"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"--

Parallel Title

Introduction to measure theoretic probability

Measure theory.

Probabilities.

Roussas, George G.

Date of Transaction

20140617043000.0

Cataloguing Rules (Descriptive Conventions))

rda

Electronic name

[Book]

Y