Format:
Online Ressource (x, 315 pages)
Edition:
Online-Ausg. [S.l.] HathiTrust Digital Library Online-Ausg. [S.l.] : HathiTrust Digital Library
ISBN:
9780080874289
,
0080874282
,
9780120957804
Series Statement:
Pure and applied mathematics 109
Content:
Front Cover; Theory of Charges: A Study of Finitely Additive Measures; Copyright Page; Contents; Foreword; Preface; CHAPTER 1 PRELIMINARIES; 1.1 Classes of sets; 1.2 Set theoretical concepts; 1.3 Topological concepts; 1.4 Boolean algebras; 1.5 Functional analytic concepts; CHAPTER 2 CHARGES; 2.1 Basic concepts; 2.2 The space of all bounded charges, ba(Ω, F); 2.3 Measures; 2.4 The space of all bounded measures, ca(Ω, F); 2.5 Jordan Decomposition theorem; 2.6 Hahn Decomposition theorem; CHAPTER 3 EXTENSIONS OF CHARGES; 3.1 Real valued set functions and induced functionals.
Content:
6.1 Absolute continuity and singularity6.2 Lebesgue Decomposition theorem; 6.3 Radon-Nikodym theorem; CHAPTER 7 Vp-SPACES; 7.1 Lp- spaces-An overview; 7.2 Vp- spaces; 7.3 Duals of Vp- spaces; 7.4 Strong Convergence; 7.5 Weak Convergence; CHAPTER 8 NIKODYM THEOREM, WEAK CONVERGENCE AND VITALI-HAHN-SAKS THEOREM; 8.1 Nikodym and Vitali-Hahn-Saks theorems in the classical case; 8.2 Examples; 8.3 Phillips' lemma; 8.4 Nikodym theorem; 8.5 Norm bounded sets in the presence of uniform absolute continuity; 8.6 A decomposition theorem; 8.7 Weak convergence; 8.8 Vitali-Hahn-Saks theorem.
Content:
3.2 Real partial charges and their extensions3.3 Extension procedure of Los and Marczewski; 3.4 Extension of partial charges in the general case; 3.5 Miscellaneous extensions; 3.6 Common extensions; CHAPTER 4 INTEGRATION; 4.1 Total variation and outer charges; 4.2 Null sets and null functions; 4.3 Hazy convergence; 4.4 D-integral; 4.5 S-integral; 4.6 Lp- spaces; 4.7 ba(Ω, F) as a dual space; CHAPTER 5 NONATOMIC CHARGES; 5.1 Basic concepts; 5.2 Sobczyk-Hammer Decomposition theorem; 5.3 Existence of nonatomic charges; 5.4 Denseness; CHAPTER 6 ABSOLUTE CONTINUITY.
Content:
Appendix 1 Notes and CommentsAppendix 2 Selected Annotated Bibliography; Appendix 3 Some Set Theoretic Nomenclature; Index of Symbols and Function Spaces; Subject Index.
Content:
CHAPTER 9 THE DUAL OF ba (Ω, F) AND THE REFINEMENT INTEGRAL9.1 Refinement integral; 9.2 The dual of ba(Ω, F); CHAPTER 10 PURE CHARGES; 10.1 Definitions and properties; 10.2 A decomposition theorem; 10.3 Pure charges on σ-fields; 10.4 Examples; 10.5 Pure charges on Boolean algebras; CHAPTER 11 RANGES OF CHARGES; 11.1 Ranges of bounded charges on fields; 11.2 Ranges of charges on σ-fields; 11.3 Cardinalities of ranges of charges; 11.4 Charges with closed range; 11.5 Charges whose ranges are neither Lebesgue measurable nor have the property of Baire; CHAPTER 12 ON LIFTING.
Note:
Includes bibliographical references (pages 282-304) and index. - Print version record
,
Print version record
,
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002
,
Front Cover; Theory of Charges: A Study of Finitely Additive Measures; Copyright Page; Contents; Foreword; Preface; CHAPTER 1 PRELIMINARIES; 1.1 Classes of sets; 1.2 Set theoretical concepts; 1.3 Topological concepts; 1.4 Boolean algebras; 1.5 Functional analytic concepts; CHAPTER 2 CHARGES; 2.1 Basic concepts; 2.2 The space of all bounded charges, ba(O,F); 2.3 Measures; 2.4 The space of all bounded measures, ca(O,F); 2.5 Jordan Decomposition theorem; 2.6 Hahn Decomposition theorem; CHAPTER 3 EXTENSIONS OF CHARGES; 3.1 Real valued set functions and induced functionals
,
3.2 Real partial charges and their extensions3.3 Extension procedure of Los and Marczewski; 3.4 Extension of partial charges in the general case; 3.5 Miscellaneous extensions; 3.6 Common extensions; CHAPTER 4 INTEGRATION; 4.1 Total variation and outer charges; 4.2 Null sets and null functions; 4.3 Hazy convergence; 4.4 D-integral; 4.5 S-integral; 4.6 Lp- spaces; 4.7 ba(O,F) as a dual space; CHAPTER 5 NONATOMIC CHARGES; 5.1 Basic concepts; 5.2 Sobczyk-Hammer Decomposition theorem; 5.3 Existence of nonatomic charges; 5.4 Denseness; CHAPTER 6 ABSOLUTE CONTINUITY
,
6.1 Absolute continuity and singularity6.2 Lebesgue Decomposition theorem; 6.3 Radon-Nikodym theorem; CHAPTER 7 Vp-SPACES; 7.1 Lp- spaces-An overview; 7.2 Vp- spaces; 7.3 Duals of Vp- spaces; 7.4 Strong Convergence; 7.5 Weak Convergence; CHAPTER 8 NIKODYM THEOREM, WEAK CONVERGENCE AND VITALI-HAHN-SAKS THEOREM; 8.1 Nikodym and Vitali-Hahn-Saks theorems in the classical case; 8.2 Examples; 8.3 Phillips' lemma; 8.4 Nikodym theorem; 8.5 Norm bounded sets in the presence of uniform absolute continuity; 8.6 A decomposition theorem; 8.7 Weak convergence; 8.8 Vitali-Hahn-Saks theorem
,
CHAPTER 9 THE DUAL OF ba (O, F) AND THE REFINEMENT INTEGRAL9.1 Refinement integral; 9.2 The dual of ba(O,F); CHAPTER 10 PURE CHARGES; 10.1 Definitions and properties; 10.2 A decomposition theorem; 10.3 Pure charges on s-fields; 10.4 Examples; 10.5 Pure charges on Boolean algebras; CHAPTER 11 RANGES OF CHARGES; 11.1 Ranges of bounded charges on fields; 11.2 Ranges of charges on s-fields; 11.3 Cardinalities of ranges of charges; 11.4 Charges with closed range; 11.5 Charges whose ranges are neither Lebesgue measurable nor have the property of Baire; CHAPTER 12 ON LIFTING
,
Appendix 1 Notes and CommentsAppendix 2 Selected Annotated Bibliography; Appendix 3 Some Set Theoretic Nomenclature; Index of Symbols and Function Spaces; Subject Index
,
Online-Ausg. [S.l.] : HathiTrust Digital Library
,
Master and use copy. Digital master created according to Benchmark for Faithful Digital Reproductions of Monographs and Serials, Version 1. Digital Library Federation, December 2002.
Additional Edition:
ISBN 0120957809
Additional Edition:
Erscheint auch als Druck-Ausgabe Bhaskara Rao, K.P.S Theory of charges London ; New York : Academic Press, 1983
Language:
English
Keywords:
Electronic books
;
Electronic books
URL:
Volltext
(lizenzpflichtig)
URL:
Volltext
(lizenzpflichtig)
Bookmarklink
