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The Resource An introduction to measuretheoretic probability, by George G. Roussas, Department of Statistics, University of California, Davis
An introduction to measuretheoretic probability, by George G. Roussas, Department of Statistics, University of California, Davis
Resource Information
The item An introduction to measuretheoretic probability, by George G. Roussas, Department of Statistics, University of California, Davis represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.This item is available to borrow from all library branches.
Resource Information
The item An introduction to measuretheoretic probability, by George G. Roussas, Department of Statistics, University of California, Davis represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in Boston University Libraries.
This item is available to borrow from all library branches.
 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"
 Language
 eng
 Edition
 Second edition.
 Extent
 xxiv, 401 pages
 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 rth Mean and Its Implications 7. The HahnJordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and The RadonNikcodym Theorem 8. Distribution Functions and Their Basic Properties, HellyBray 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
 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 HahnJordan decomposition theorem, the Lebesgue decomposition theorem, and the RadonNikodym theorem
 Distribution functions and their basic properties, HellyBray 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 realvalued parameter, nonparametric estimation of a probability density function
 Appendixes: A. Brief review of chapters 116
 B. Brief review of RiemannStieltjes integral
 C. Notation and abbreviations
 Isbn
 9780128002902
 Label
 An introduction to measuretheoretic probability
 Title
 An introduction to measuretheoretic probability
 Statement of responsibility
 by George G. Roussas, Department of Statistics, University of California, Davis
 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 measuretheoretic probability, by George G. Roussas, Department of Statistics, University of California, Davis
 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 rth Mean and Its Implications 7. The HahnJordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and The RadonNikcodym Theorem 8. Distribution Functions and Their Basic Properties, HellyBray 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 391392) 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 HahnJordan decomposition theorem, the Lebesgue decomposition theorem, and the RadonNikodym theorem  Distribution functions and their basic properties, HellyBray 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 realvalued parameter, nonparametric estimation of a probability density function  Appendixes: A. Brief review of chapters 116  B. Brief review of RiemannStieltjes 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 measuretheoretic probability, by George G. Roussas, Department of Statistics, University of California, Davis
 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 rth Mean and Its Implications 7. The HahnJordan Decomposition Theorem, The Lebesgue Decomposition Theorem, and The RadonNikcodym Theorem 8. Distribution Functions and Their Basic Properties, HellyBray 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 391392) 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 HahnJordan decomposition theorem, the Lebesgue decomposition theorem, and the RadonNikodym theorem  Distribution functions and their basic properties, HellyBray 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 realvalued parameter, nonparametric estimation of a probability density function  Appendixes: A. Brief review of chapters 116  B. Brief review of RiemannStieltjes 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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