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Book Cover
Author Swartz, Charles, 1938-

Title Introduction to gauge integrals / Charles Swartz.

Publication Info. Singapore ; River Edge, NJ : World Scientific, [2001]


Location Call No. Status
 Rocky Hill - Downloadable Materials  EBSCO Ebook    Downloadable
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Description 1 online resource (x, 157 pages)
Bibliography Includes bibliographical references (pages 149-153) and index.
Note Print version record.
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, et cetera.
Subject Henstock-Kurzweil integral.
McShane integral.
MATHEMATICS -- Calculus.
MATHEMATICS -- Mathematical Analysis.
Henstock-Kurzweil integral. (OCoLC)fst00955178
McShane integral. (OCoLC)fst01013095
Genre/Form Electronic books.
Added Title Gauge integrals
Other Form: Print version: Swartz, Charles, 1938- Introduction to gauge integrals. Singapore ; River Edge, NJ : World Scientific, ©2001 9810242395 9789810242398 (DLC) 00068521 (OCoLC)45506028
ISBN 9789812810656 (electronic bk.)
981281065X (electronic bk.)
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