The Theory of Lebesgue Measure and Integration
eBook - PDF

The Theory of Lebesgue Measure and Integration

  1. 177 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

The Theory of Lebesgue Measure and Integration

About this book

The Theory of Lebesgue Measure and Integration deals with the theory of Lebesgue measure and integration and introduces the reader to the theory of real functions. The subject matter comprises concepts and theorems that are now considered classical, including the Yegorov, Vitali, and Fubini theorems. The Lebesgue measure of linear sets is discussed, along with measurable functions and the definite Lebesgue integral. Comprised of 13 chapters, this volume begins with an overview of basic concepts such as set theory, the denumerability and non-denumerability of sets, and open sets and closed sets on the real line. The discussion then turns to the theory of Lebesgue measure of linear sets based on the method of M. Riesz, together with the fundamental properties of measurable functions. The Lebesgue integral is considered for both bounded functions — upper and lower integrals — and unbounded functions. Later chapters cover such topics as the Yegorov, Vitali, and Fubini theorems; convergence in measure and equi-integrability; integration and differentiation; and absolutely continuous functions. Multiple integrals and the Stieltjes integral are also examined. This book will be of interest to mathematicians and students taking pure and applied mathematics.

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Information

Publisher
Pergamon
Year
2014
Print ISBN
9780080095257
eBook ISBN
9781483280332
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Front Cover
  2. The Theory of Lebesgue Measure and Integration
  3. Copyright Page
  4. Table of Contents
  5. Foreword to the English Edition
  6. CHAPTER I. INTRODUCTORY CONCEPTS
  7. CHAPTER II. LEBESGUE MEASURE OF LINEAR SETS
  8. CHAPTER III. MEASURABLE FUNCTIONS
  9. CHAPTER IV. THE DEFINITE LEBESGUE INTEGRAL
  10. CHAPTER V. CONVERGENCE IN MEASURE AND EQUI-INTEGRABILITY
  11. CHAPTER VI. INTEGRATION AND DIFFERENTIATION FUNCTIONS OF FINITE VARIATION
  12. CHAPTER VII. ABSOLUTELY CONTINUOUS FUNCTIONS
  13. CHAPTER VIII. SPACES OF p-th POWER INTEGRABLE FUNCTIONS
  14. CHAPTER IX. ORTHOGONAL EXPANSIONS
  15. CHAPTER X. COMPLEX-VALUED FUNCTIONS OF A REAL VARIABLE
  16. CHAPTER XI. MEASURE IN THE PLANE AND IN SPACE
  17. CHAPTER XII. MULTIPLE INTEGRALS
  18. CHAPTER XIII. THE STIELTJES INTEGRAL
  19. Literature
  20. Index

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Yes, you can access The Theory of Lebesgue Measure and Integration by S. Hartman,J. Mikusinski, I. N. Sneddon,M. Stark,S. Ulam in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.