Measure and Integral
eBook - PDF

Measure and Integral

  1. 592 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Measure and Integral

About this book

Probability and Mathematical Statistics: Measure and Integral provides information pertinent to the general mathematical notions and notations. This book discusses how the machinery of?-extension works and how?-content is derived from?-measure. Organized into 16 chapters, this book begins with an overview of the classical Hahnā€“Banach theorem and introduces the Banach limits in the form of a major exercise. This text then presents the Daniell extension theory for positive?-measures. Other chapters consider the transform of?-contents and?-measures by measurable mappings and kernels. This text is also devoted to a thorough study of the vector lattice of signed contents. This book discusses as well an abstract regularity theory and applied to the standard cases of compact, locally compact, and Polish spaces. The final chapter deals with the rudiments of the Kreinā€“Milman theorem, along with some of their applications. This book is a valuable resource for graduate students.

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Yes, you can access Measure and Integral by Konrad Jacobs, Z. W. Birnbaum,E. Lukacs in PDF and/or ePUB format, as well as other popular books in Mathematics & Calculus. We have over one million books available in our catalogue for you to explore.

Information

Publisher
Academic Press
Year
2014
Print ISBN
9780123785503
eBook ISBN
9781483263045
Topic
Mathematics
Subtopic
Calculus
Index
Mathematics

Table of contents

  1. Front Cover
  2. Measure and Integral
  3. Copyright Page
  4. Table of Contents
  5. PREFACE
  6. CHAPTER 0. BASIC NOTIONS AND NOTATION
  7. CHAPTER I. POSITIVE CONTENTS AND MEASURES
  8. CHAPTER II. EXTENSION OF Ļƒ-CONTENTS AFTER CARATHƉODORY
  9. CHAPTER III. EXTENSION OF POSITIVE Ļƒ- AND Ļ„-MEASURES, AFTER DANIELL
  10. CHAPTER IV. TRANSFORM OF Ļƒ-CONTENTS
  11. CHAPTER V. CONTENTS AND MEASURES IN TOPOLOGICAL SPACES. PART I: REGULARITY
  12. CHAPTER VI. CONTENTS AND MEASURES IN PRODUCT SPACES
  13. CHAPTER VII. SET FUNCTIONS IN GENERAL
  14. CHAPTER VIII. THE VECTOR LATTICE OF SIGNED CONTENTS
  15. CHAPTER IX. THE VECTOR LATTICE OF SIGNED MEASURES
  16. CHAPTER X. THE SPACES Lp
  17. CHAPTER XI. CONTENTS AND MEASURES IN TOPOLOGICAL SPACES. PART II: THE WEAK TOPOLOGY
  18. CHAPTER XII. THE HAAR MEASURE ON LOCALLY COMPACT GROUPS
  19. CHAPTER XIII. SOUSLIN SETS, ANALYTIC SETS, AND CAPACITIES
  20. CHAPTER XIV. ATOMS, CONDITIONAL ATOMS, AND ENTROPY
  21. CHAPTER XV. CONVEX COMPACT SETS AND THEIR EXTREMAL POINTS
  22. CHAPTER XVI. LIFTING
  23. APPENDIX A: THE PERRON-WARD INTEGRAL AND RELATED CONCEPTS
  24. APPENDIX B: CONTENTS WITH GIVEN MARGINALS
  25. SELECTED BIBLIOGRAPHY
  26. INDEX
  27. Probability and Mathematical Statistics