Measure and Integration Theory
eBook - PDF

Measure and Integration Theory

  1. 246 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Measure and Integration Theory

About this book

This book gives a straightforward introduction to the field as it is nowadays required in many branches of analysis and especially in probability theory. The first three chapters (Measure Theory, Integration Theory, Product Measures) basically follow the clear and approved exposition given in the author's earlier book on "Probability Theory and Measure Theory". Special emphasis is laid on a complete discussion of the transformation of measures and integration with respect to the product measure, convergence theorems, parameter depending integrals, as well as the Radon-Nikodym theorem.

The final chapter, essentially new and written in a clear and concise style, deals with the theory of Radon measures on Polish or locally compact spaces. With the main results being Luzin's theorem, the Riesz representation theorem, the Portmanteau theorem, and a characterization of locally compact spaces which are Polish, this chapter is a true invitation to study topological measure theory.

The text addresses graduate students, who wish to learn the fundamentals in measure and integration theory as needed in modern analysis and probability theory. It will also be an important source for anyone teaching such a course.

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Yes, you can access Measure and Integration Theory by Heinz Bauer, Robert B. Burckel in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Information

Publisher
De Gruyter
Year
2011
Print ISBN
9783110167191
eBook ISBN
9783110866209
Edition
1
Topic
Mathematics
Subtopic
Mathematical Analysis
Index
Mathematics

Table of contents

  1. Preface
  2. Introduction
  3. Notations
  4. Chapter I Measure Theory
  5. § 1. σ-algebras and their generators
  6. § 2. Dynkin systems
  7. § 3. Contents, premeasures, measures
  8. § 4. Lebesgue premeasure
  9. § 5. Extension of a premeasure to a measure
  10. § 6. Lebesgue-Borel measure and measures on the number line
  11. § 7. Measurable mappings and image measures
  12. § 8. Mapping properties of the Lebesgue-Borel measure
  13. Chapter II Integration Theory
  14. § 9. Measurable numerical functions
  15. § 10. Elementary functions and their integral
  16. §11. The integral of non-negative measurable functions
  17. § 12. Integrability
  18. § 13. Almost everywhere prevailing properties
  19. § 14. The spaces ℒp(μ)
  20. § 15. Convergence theorems
  21. § 16. Applications of the convergence theorems
  22. § 17. Measures with densities: the Radon-Nikodym theorem
  23. § 18.* Signed measures
  24. § 19. Integration with respect to an image measure
  25. § 20. Stochastic convergence
  26. § 21. Equi-integrability
  27. Chapter III Product Measures
  28. § 22. Products of σ-algebras and measures
  29. § 23. Product measures and Fubini’s theorem
  30. § 24. Convolution of finite Borel measures
  31. Chapter IV Measures on Topological Spaces
  32. § 25. Borel sets, Borel and Radon measures
  33. § 26. Radon measures on Polish spaces
  34. § 27. Properties of locally compact spaces
  35. § 28. Construction of Radon measures on locally compact spaces
  36. § 29. Riesz representation theorem
  37. § 30. Convergence of Radon measures
  38. § 31. Vague compactness and metrizability questions
  39. Bibliography
  40. Symbol Index
  41. Name Index
  42. Subject Index