Henstock Kurzweil Integration On Euclidean Spaces

Author : Tuo Yeong Lee
Publisher : World Scientific
Page : 325 pages
File Size : 48,6 Mb
Release : 2011
Category : Mathematics
ISBN : 9789814324588

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Henstock-Kurzweil Integration on Euclidean Spaces by Tuo Yeong Lee Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 40,7 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9789814462877

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Henstockƒ€“Kurzweil Integration on Euclidean Spaces by Anonim Pdf

Author : Wee Leng Ng
Publisher : Series in Real Analysis
Page : 160 pages
File Size : 49,5 Mb
Release : 2017
Category : Mathematics
ISBN : 9813221968

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Nonabsolute Integration on Measure Spaces by Wee Leng Ng Pdf

The book provides a comprehensive coverage of the widely accepted desiderata of component-based software development, as well as the foundations that these desiderata necessitate. Its unique focus is on component models, the cornerstone of component-based

Author : Charles Swartz
Publisher : World Scientific
Page : 176 pages
File Size : 44,9 Mb
Release : 2001
Category : Mathematics
ISBN : 981281065X

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Introduction to Gauge Integrals by Charles Swartz Pdf

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.

Author : Jaroslav Kurzweil
Publisher : World Scientific
Page : 149 pages
File Size : 44,5 Mb
Release : 2002
Category : Mathematics
ISBN : 9789812777195

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Integration Between the Lebesgue Integral and the Henstock-Kurzweil Integral by Jaroslav Kurzweil Pdf

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.

Author : Antonio Boccuto,Beloslav Riečan,Marta Vrábelová
Publisher : Bentham Science Publishers
Page : 235 pages
File Size : 43,6 Mb
Release : 2010-04-02
Category : Mathematics
ISBN : 9781608050031

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Kurzweil-Henstock Integral in Riesz spaces by Antonio Boccuto,Beloslav Riečan,Marta Vrábelová Pdf

"This Ebook is concerned with both the theory of the Kurzweil-Henstock integral and the basic facts on Riesz spaces. Moreover, even the so-called Sipos integral, which has several applications in economy, is illustrated. The aim of this Ebook is two-fold. "

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 51,5 Mb
Release : 2024-07-01
Category : Electronic
ISBN : 9789814493697

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Henstock-Kurzweil Integration: Its Relation to Topological Vector Spaces by Anonim Pdf

Author : Douglas S Kurtz,Charles W Swartz
Publisher : World Scientific Publishing Company
Page : 312 pages
File Size : 53,9 Mb
Release : 2011-10-31
Category : Mathematics
ISBN : 9789813108264

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Theories of Integration by Douglas S Kurtz,Charles W Swartz Pdf

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.

Author : Jaroslav Kurzweil
Publisher : World Scientific
Page : 152 pages
File Size : 51,8 Mb
Release : 2000
Category : Mathematics
ISBN : 9810242077

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Henstock-Kurzweil Integration by Jaroslav Kurzweil Pdf

"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

Author : Lee Peng Yee,Rudolf Vyborny
Publisher : Cambridge University Press
Page : 328 pages
File Size : 40,5 Mb
Release : 2000-04-20
Category : Mathematics
ISBN : 0521779685

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Integral by Lee Peng Yee,Rudolf Vyborny Pdf

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

Author : Ng Wee Leng
Publisher : World Scientific
Page : 248 pages
File Size : 45,6 Mb
Release : 2017-10-20
Category : Mathematics
ISBN : 9789813221987

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Nonabsolute Integration On Measure Spaces by Ng Wee Leng Pdf

This book offers to the reader a self-contained treatment and systematic exposition of the real-valued theory of a nonabsolute integral on measure spaces. It is an introductory textbook to Henstock–Kurzweil type integrals defined on abstract spaces. It contains both classical and original results that are accessible to a large class of readers. It is widely acknowledged that the biggest difficulty in defining a Henstock–Kurzweil integral beyond Euclidean spaces is the definition of a set of measurable sets which will play the role of "intervals" in the abstract setting. In this book the author shows a creative and innovative way of defining "intervals" in measure spaces, and prove many interesting and important results including the well-known Radon–Nikodým theorem. Contents: A Nonabsolute Integral on Measure Spaces: PreliminariesExistence of a Division and the H-IntegralSimple Properties of the H-IntegralThe Absolute H-Integral and the McShane-Type Integrals: The Absolute H-Integral and the M-IntegralThe H-Integral and the Lebesgue IntegralThe Davies Inetgral and the Davies-McShane IntegralFurther Results of the H-Integral: A Necessary and Sufficient Condition for H-IntegrabilityGeneralised Absolute Continuity and EquiintegrabilityThe Controlled Convergence TheoremThe Radon–Nikodým Theorem for the H-integral: The Main TheoremDescriptive Definition of H-integralHenstock Integration in the Euclidean SpaceHarnack Extension and Convergence Theorems for the H-Integral: The H-Integral on Metric SpacesHarnack Extension for the H-IntegralThe Category ArgumentAn Improved Version of the Controlled Convergence Theorem Readership: Graduate students and researchers interested in analysis. Keywords: Henstock-Kurzweil Type Integral;Generalized Intervals;Nonabsolute Integration;Measure Spaces;Locally Compact Hausdorff Space;Radon-Nikodym Theorem;Controlled Convergence Theorem;Harnack ExtensionReview: Key Features: To our knowledge there is no book on integration theory whose setting is measure spaces with a topological structureThe theory is developed in a progressive and elementary manner in that the fundamental properties are first established before further results are proved. That way, even though the setting is abstract, this book is accessible to any undergraduate who has done an advanced calculus courseThe key idea behind each original concept is always explained in an intuitive manner before the formal definitions and results are presented in detail

Author : Peng Yee Lee
Publisher : World Scientific
Page : 194 pages
File Size : 42,6 Mb
Release : 1989
Category : Mathematics
ISBN : 9971508923

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Lanzhou Lectures on Henstock Integration by Peng Yee Lee Pdf

This is an introductory book on Henstock integration, otherwise known as generalized Riemann integral. It is self-contained and introductory. The author has included a series of convergence theorems for the integral, previously not available. In this book, he has also developed a technique of proof required to present the new as well as the classical results.

Author : Jaroslav Kurzweil
Publisher : World Scientific
Page : 208 pages
File Size : 51,7 Mb
Release : 2012
Category : Mathematics
ISBN : 9789814324021

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Generalized Ordinary Differential Equations by Jaroslav Kurzweil Pdf

Explores the basics of social policy and program analysis, such as designing new programs or evaluating and improving existing ones. Social Policy and Social Programs is distinctive in providing specific criteria for judging the effectiveness of social policies and programs. These criteria can be applied to the analysis of widely different social services such as counseling and therapeutic services, supportive assistance, and "hard" benefits like food stamps, cash, and housing vouchers. By focusing especially on social problems, policies, and programs in major practice areas like child welfare, health, poverty, and mental illness, the author provides students with the tools they need to understand and evaluate the programs in which they are doing their field placements. Upon completing this book readers will be able to: Analyze the effectiveness of current social programs Create new programs based on the criteria provided Apply what they have learned to evaluate their field placement programs Note: MySearchLab does not come automatically packaged with this text. To purchase MySearchLab, please visit: www.mysearchlab.com or you can purchase a ValuePack of the text + MySearchLab (at no additional cost): ValuePack ISBN-10: 0205222943 / ValuePack ISBN-13: 9780205222940.

Author : Alessandro Fonda
Publisher : Springer Nature
Page : 442 pages
File Size : 50,7 Mb
Release : 2023-03-21
Category : Mathematics
ISBN : 9783031237133

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A Modern Introduction to Mathematical Analysis by Alessandro Fonda Pdf

This textbook presents all the basics for the first two years of a course in mathematical analysis, from the natural numbers to Stokes-Cartan Theorem. The main novelty which distinguishes this book is the choice of introducing the Kurzweil-Henstock integral from the very beginning. Although this approach requires a small additional effort by the student, it will be compensated by a substantial advantage in the development of the theory, and later on when learning about more advanced topics. The text guides the reader with clarity in the discovery of the many different subjects, providing all necessary tools – no preliminaries are needed. Both students and their instructors will benefit from this book and its novel approach, turning their course in mathematical analysis into a gratifying and successful experience.

Author : Douglas S. Kurtz,Jaroslav Kurzweil,Charles W. Swartz
Publisher : World Scientific
Page : 286 pages
File Size : 45,7 Mb
Release : 2004
Category : Mathematics
ISBN : 9812388435

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Theories of Integration by Douglas S. Kurtz,Jaroslav Kurzweil,Charles W. Swartz Pdf

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.