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- 168 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Introduction To Gauge Integrals
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About This Book
This book presents the Henstock/Kurzweil integral and the McShane integral. These two integrals are obtained by changing slightly the definition of the Riemann integral. These variations lead to integrals which are much more powerful than the Riemann integral. The Henstock/Kurzweil integral is an unconditional integral for which the fundamental theorem of calculus holds in full generality, while the McShane integral is equivalent to the Lebesgue integral in Euclidean spaces.A basic knowledge of introductory real analysis is required of the reader, who should be familiar with the fundamental properties of the real numbers, convergence, series, differentiation, continuity, etc.
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Yes, you can access Introduction To Gauge Integrals by Charles W Swartz in PDF and/or ePUB format, as well as other popular books in Mathematics & Differential Equations. We have over one million books available in our catalogue for you to explore.
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Table of contents
- Contents
- Preface
- 1 Introduction to the Gauge or Henstock-Kurzweil Integral
- 2 Basic Properties of the Gauge Integral
- 3 Henstock's Lemma and Improper Integrals
- 4 The Gauge Integral over Unbounded Intervals
- 5 Convergence Theorems
- 6 Integration over More General Sets: Lebesgue Measure
- 7 The Space of Gauge Integrable Functions
- 8 Multiple Integrals and Fubini's Theorem
- 9 The McShane Integral
- 10 McShane Integrability is Equivalent to Absolute Henstock-Kurzweil Integrability
- Appendix 1: The Riemann Integral
- Appendix 2: Functions of Bounded Variations
- Appendix 3: Differentiating Indefinite Integrals
- Appendix 4: Equivalence of Lebesgue and McShane Integrals
- Appendix 5: Change of Variable in Multiple Integrals
- Bibliography
- Index