Modern Theory of Integration

Häftad, Engelska, 2001

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Presents a relative new theory. Included are many examples and a very rich collection of exercises. There are partial solutions to approximately one-third of the exercises. A complete solutions manual is available separately. From the top series published by the AMS.

Produktinformation

Utgivningsdatum2001-11-30
FormatHäftad
SpråkEngelska
SerieGraduate Studies in Mathematics
Antal sidor458
FörlagAmerican Mathematical Society
ISBN9781470479015

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Part 1. Integration on compact intervalsChapter 1. Gauges and integralsChapter 2. Some examplesChapter 3. Basic properties of the integralChapter 4. The fundamental theorems of calculusChapter 5. The Saks-Henstock lemmaChapter 6. Measurable functionsChapter 7. Absolute integrabilityChapter 8. Convergence theoremsChapter 9. Integrability and mean convergenceChapter 10. Measure, measurability, and multipliersChapter 11. Modes of convergenceChapter 12. Applications to calculusChapter 13. Substitution theoremsChapter 14. Absolute continuityPart 2. Integration on infinite intervalsChapter 15. Introduction to Part 2Chapter 16. Infinite intervalsChapter 17. Further re-examinationChapter 18. Measurable setsChapter 19. Measurable functionsChapter 20. Sequences of functionsAppendixesAppendix A. Limits superior and inferiorAppendix B. Unbounded sets and sequencesAppendix C. The arctangent lemmaAppendix D. Outer measureAppendix E. Lebesgue's differentiation theoremAppendix F. Vector spacesAppendix G. Semimetric spacesAppendix H. Riemann-Stieltjes integralAppendix I. Normed linear spacesSome partial solutionsSolutions Manual

The book presents its subject in a pleasing, didactically surprising, and well worth reading exposition. The proofs are, as a rule, easily understandable and the significance of the theorems that are worked through is illustrated by means of numerous examples. It can be recommended as a self-study book to every student with a basic foundation in analysis. It is also very suitable as a supplementary text for a course on integration on $\mathbf{R}$. -- Translated fromJahresbericht der Deutschen Mathematiker-Vereinigung A comprehensive, beautifully written exposition of the Henstock-Kurzweil (gauge, Riemann complete) integral ... There is an abundant supply of exercises which serve to make this book an excellent choice for a text for a course which would contain an elementary introduction to modern integration theory. -- Zentralblatt MATH