| Description |
1 online resource (x, 157 pages) |
| Contents |
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. 9.1. Definition and basic properties. 9.2. Convergence theorems. 9.3. Integrability of products and integration by parts. 9.4. More general convergence theorems. 9.5. The space of McShane integrable functions. 9.6. Multiple integrals and Fubini's theorem -- 10. McShane integrability is equivalent to absolute Henstock-Kurzweil integrability |
| Summary |
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 |
| Bibliography |
Includes bibliographical references (pages 149-153) and index |
| Notes |
Print version record |
| Subject |
Henstock-Kurzweil integral.
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McShane integral.
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Henstock-Kurzweil integral
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McShane integral
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| Form |
Electronic book
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| ISBN |
9789812810656 |
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981281065X |
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1281956317 |
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9781281956316 |
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