The Resource An introduction to measure-theoretic probability, by George G. Roussas, Department of Statistics, University of California, Davis

An introduction to measure-theoretic probability, by George G. Roussas, Department of Statistics, University of California, Davis

Label
An introduction to measure-theoretic probability
Title
An introduction to measure-theoretic probability
Statement of responsibility
by George G. Roussas, Department of Statistics, University of California, Davis
Creator
Author
Subject
Language
eng
Summary
"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"--
Assigning source
Provided by publisher
Cataloging source
DLC
http://library.link/vocab/creatorName
Roussas, George G
Index
index present
LC call number
QA273
LC item number
.R864 2014
Literary form
non fiction
Nature of contents
bibliography
http://library.link/vocab/subjectName
  • Probabilities
  • Measure theory
  • Measure theory
  • Probabilities
Label
An introduction to measure-theoretic probability, by George G. Roussas, Department of Statistics, University of California, Davis
Instantiates
Publication
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
Bibliography note
Includes bibliographical references (pages 391-392) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Certain classes of sets, measurability, and pointwise approximation -- Definition and construction of a measure and its basic properties -- Some modes of convergence of sequences of random variables and their relationships -- The integral of a random variable and its basic properties -- Standard convergence theorems, the Fubini theorem -- Standard moment and probability inequalities, convergence in the rth mean and its implications -- The Hahn-Jordan decomposition theorem, the Lebesgue decomposition theorem, and the Radon-Nikodym theorem -- Distribution functions and their basic properties, Helly-Bray type results -- Conditional expectation and conditional probability, and related properties and results -- Independence -- Topics from the theory of characteristic functions -- The central limit problem: the centered case -- The central limit problem: the noncentered case -- Topics from sequences of independent random variables -- Topics from Ergodic theory -- Two cases of statistical inference: estimation of a real-valued parameter, nonparametric estimation of a probability density function -- Appendixes: A. Brief review of chapters 1-16 -- B. Brief review of Riemann-Stieltjes integral -- C. Notation and abbreviations
Dimensions
25 cm
Edition
Second edition.
Extent
xxiv, 401 pages
Isbn
9780128002902
Isbn Type
(electronic bk.)
Lccn
2014007243
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
System control number
  • (OCoLC)868642456
  • (OCoLC)ocn868642456
Label
An introduction to measure-theoretic probability, by George G. Roussas, Department of Statistics, University of California, Davis
Publication
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
Bibliography note
Includes bibliographical references (pages 391-392) and index
Carrier category
volume
Carrier category code
nc
Carrier MARC source
rdacarrier
Content category
text
Content type code
txt
Content type MARC source
rdacontent
Contents
Certain classes of sets, measurability, and pointwise approximation -- Definition and construction of a measure and its basic properties -- Some modes of convergence of sequences of random variables and their relationships -- The integral of a random variable and its basic properties -- Standard convergence theorems, the Fubini theorem -- Standard moment and probability inequalities, convergence in the rth mean and its implications -- The Hahn-Jordan decomposition theorem, the Lebesgue decomposition theorem, and the Radon-Nikodym theorem -- Distribution functions and their basic properties, Helly-Bray type results -- Conditional expectation and conditional probability, and related properties and results -- Independence -- Topics from the theory of characteristic functions -- The central limit problem: the centered case -- The central limit problem: the noncentered case -- Topics from sequences of independent random variables -- Topics from Ergodic theory -- Two cases of statistical inference: estimation of a real-valued parameter, nonparametric estimation of a probability density function -- Appendixes: A. Brief review of chapters 1-16 -- B. Brief review of Riemann-Stieltjes integral -- C. Notation and abbreviations
Dimensions
25 cm
Edition
Second edition.
Extent
xxiv, 401 pages
Isbn
9780128002902
Isbn Type
(electronic bk.)
Lccn
2014007243
Media category
unmediated
Media MARC source
rdamedia
Media type code
n
System control number
  • (OCoLC)868642456
  • (OCoLC)ocn868642456

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