This book is intended to be self-contained, giving the theory of absolute (equivalent to Lebesgue) and non-absolute (equivalent to Denjoy-Perron) integration by using a simple extension of the Riemann integral. A useful tool for mathematicians and scientists needing advanced integration theory would be a method combining the ideas of the calculus of indefinite integral and Riemann definite integral in such a way that Lebesgue properties can be proved easily.Three important results that have not appeared in any other book distinguish this book from the rest. First a result on limits of sequences under the integral sign, secondly the necessary and sufficient conditions for the various limits under the integral sign and thirdly the application of these results to ordinary differential equations. The present book will give non-absolute integration theory just as easily as the absolute theory, and Stieltjes-type integration too.
- 223 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Lectures On The Theory Of Integration
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Topic
MathématiquesSubtopic
Mathématiques généralesTable of contents
- CONTENTS
- PREFACE
- 0 Prerequisites
- CHAPTER 1 - INTRODUCTION
- CHAPTER 2 SIMPLE PROPERTIES OF THE GENERALIZED RIEMANN INTEGRAL IN FINITE DIMENSIONAL EUCLIDEAN SPACE
- CHAPTER 3 LIMIT THEOREMS FOR SEQUENCES OF FUNCTIONS
- CHAPTER 4 LIMIT THEOREMS FOR MORE GENERAL CONVERGENCE, WITH CONTINUITY
- CHAPTER 5 DIFFERENTIATION, INSURABILITY AND INNER VARIATION
- CHAPTER 6 CARTESIAN PRODUCTS AND THE FUBINI AND TONELLI THEOREMS
- CHAPTER 7 APPLICATIONS
- CHAPTER 8 HISTORY AND FURTHER DISCUSSION
- REFERENCES
- INDEX
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Yes, you can access Lectures On The Theory Of Integration by Ralph Henstock in PDF and/or ePUB format, as well as other popular books in Mathématiques & Mathématiques générales. We have over 1.5 million books available in our catalogue for you to explore.