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Integration Between The Lebesgue Integral And The Henstock-kurzweil Integral: Its Relation To Local Convex Vector Spaces

Author: Jaroslav Kurzweil

Publisher: World Scientific

Published: 2002-06-14

Total Pages: 149

ISBN-13: 9814488267

The main topics of this book are convergence and topologization. Integration on a compact interval on the real line is treated with Riemannian sums for various integration bases. General results are specified to a spectrum of integrations, including Lebesgue integration, the Denjoy integration in the restricted sense, the integrations introduced by Pfeffer and by Bongiorno, and many others. Morever, some relations between integration and differentiation are made clear.The book is self-contained. It is of interest to specialists in the field of real functions, and it can also be read by students, since only the basics of mathematical analysis and vector spaces are required.

The Kurzweil-Henstock Integral and Its Differential

Author: Solomon Leader

Publisher: CRC Press

Published: 2001-06-29

Total Pages: 380

ISBN-13: 9780824705350

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A comprehensive review of the Kurzweil-Henstock integration process on the real line and in higher dimensions. It seeks to provide a unified theory of integration that highlights Riemann-Stieljes and Lebesgue integrals as well as integrals of elementary calculus. The author presents practical applications of the definitions and theorems in each section as well as appended sets of exercises.

Henstock-Kurzweil Integration on Euclidean Spaces

Author: Tuo Yeong Lee

Publisher: World Scientific

Published: 2011

Total Pages: 325

ISBN-13: 9814324582

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The Henstock?Kurzweil integral, which is also known as the generalized Riemann integral, arose from a slight modification of the classical Riemann integral more than 50 years ago. This relatively new integral is known to be equivalent to the classical Perron integral; in particular, it includes the powerful Lebesgue integral. This book presents an introduction of the multiple Henstock?Kurzweil integral. Along with the classical results, this book contains some recent developments connected with measures, multiple integration by parts, and multiple Fourier series. The book can be understood with a prerequisite of advanced calculus.

Integral

Author: Lee Peng Yee

Publisher: Cambridge University Press

Published: 2000-04-20

Total Pages: 328

ISBN-13: 9780521779685

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Textbook on the theory of integration. Suitable for beginning graduate and final year undergraduate students.

Theories of Integration

Author: Douglas S. Kurtz

Publisher: World Scientific

Published: 2004

Total Pages: 286

ISBN-13: 9789812388438

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This book presents a historical development of the integration theories of Riemann, Lebesgue, Henstock-Kurzweil, and McShane, showing how new theories of integration were developed to solve problems that earlier theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and can be used separately in teaching a portion of an introductory course on real analysis. There is a sufficient supply of exercises to make the book useful as a textbook.

The Kurzweil-Henstock Integral for Undergraduates

Author: Alessandro Fonda

Publisher: Springer

Published: 2018-11-11

Total Pages: 216

ISBN-13: 3319953214

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This beginners' course provides students with a general and sufficiently easy to grasp theory of the Kurzweil-Henstock integral. The integral is indeed more general than Lebesgue's in RN, but its construction is rather simple, since it makes use of Riemann sums which, being geometrically viewable, are more easy to be understood. The theory is developed also for functions of several variables, and for differential forms, as well, finally leading to the celebrated Stokes–Cartan formula. In the appendices, differential calculus in RN is reviewed, with the theory of differentiable manifolds. Also, the Banach–Tarski paradox is presented here, with a complete proof, a rather peculiar argument for this type of monographs.

Theories of Integration

Author: Douglas S Kurtz

Publisher: World Scientific Publishing Company

Published: 2011-10-31

Total Pages: 312

ISBN-13: 9813108266

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The book uses classical problems to motivate a historical development of the integration theories of Riemann, Lebesgue, Henstock–Kurzweil and McShane, showing how new theories of integration were developed to solve problems that earlier integration theories could not handle. It develops the basic properties of each integral in detail and provides comparisons of the different integrals. The chapters covering each integral are essentially independent and could be used separately in teaching a portion of an introductory real analysis course. There is a sufficient supply of exercises to make this book useful as a textbook.

Introduction to Gauge Integrals

Author: Charles Swartz

Publisher: World Scientific

Published: 2001

Total Pages: 176

ISBN-13: 9789812810656

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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. Contents: Introduction to the Gauge or Henstock-Kurzweil Integral; Basic Properties of the Gauge Integral; Henstock''s Lemma and Improper Integrals; The Gauge Integral over Unbounded Intervals; Convergence Theorems; Integration over More General Sets: Lebesgue Measure; The Space of Gauge Integrable Functions; Multiple Integrals and Fubini''s Theorem; The McShane Integral; McShane Integrability is Equivalent to Absolute Henstock-Kurzweil Integrability. Readership: Upper level undergraduates and mathematicians interested in gauge integrals.

Henstock-Kurzweil Integration

Author: Jaroslav Kurzweil

Publisher: World Scientific

Published: 2000

Total Pages: 152

ISBN-13: 9789810242077

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"the results of the book are very interesting and profound and can be read successfully without preliminary knowledge. It is written with a great didactical mastery, clearly and precisely It can be recommended not only for specialists on integration theory, but also for a large scale of readers, mainly for postgraduate students".Mathematics Abstracts

The Integrals of Lebesgue, Denjoy, Perron, and Henstock

Author: Russell A. Gordon

Publisher: American Mathematical Soc.

Published: 1994-01-01

Total Pages: 412

ISBN-13: 9780821872222

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This is an elementary, self-contained presentation of the integration processes developed by Lebesgue, Denjoy, Perron, and Henstock. An excellent text for graduate students with a background in real analysis.