Henstock Kurzweil Integration On Euclidean Spaces
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Henstock Kurzweil Integration On Euclidean Spaces
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Author : Tuo Yeong Lee
language : en
Publisher: World Scientific
Release Date : 2011
Henstock Kurzweil Integration On Euclidean Spaces written by Tuo Yeong Lee and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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.
Henstock Kurzweil Integration On Euclidean Spaces
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Author : Tuo Yeong Lee
language : en
Publisher: World Scientific
Release Date : 2011-03-16
Henstock Kurzweil Integration On Euclidean Spaces written by Tuo Yeong Lee and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-16 with Mathematics categories.
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.
Henstock Kurzweil Integration
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Author : Jaroslav Kurzweil
language : en
Publisher: World Scientific
Release Date : 2000
Henstock Kurzweil Integration written by Jaroslav Kurzweil and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
"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
Theories Of Integration The Integrals Of Riemann Lebesgue Henstock Kurzweil And Mcshane 2nd Edition
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Author : Charles W Swartz
language : en
Publisher: World Scientific Publishing Company
Release Date : 2011-10-31
Theories Of Integration The Integrals Of Riemann Lebesgue Henstock Kurzweil And Mcshane 2nd Edition written by Charles W Swartz and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-31 with Mathematics categories.
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
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Author : Charles Swartz
language : en
Publisher: World Scientific
Release Date : 2001
Introduction To Gauge Integrals written by Charles Swartz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
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.
The Kurzweil Henstock Integral For Undergraduates
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Author : Alessandro Fonda
language : en
Publisher: Springer
Release Date : 2018-11-11
The Kurzweil Henstock Integral For Undergraduates written by Alessandro Fonda and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-11 with Mathematics categories.
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.
Kurzweil Henstock Integral In Riesz Spaces
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Author : Antonio Boccuto
language : en
Publisher: Bentham Science Publishers
Release Date : 2010-04-02
Kurzweil Henstock Integral In Riesz Spaces written by Antonio Boccuto and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-02 with Mathematics categories.
"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. "
Nonabsolute Integration On Measure Spaces
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Author : Wee Leng Ng
language : en
Publisher: World Scientific
Release Date : 2017-10-20
Nonabsolute Integration On Measure Spaces written by Wee Leng Ng and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-20 with Mathematics categories.
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.
Theories Of Integration
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Author : Douglas S. Kurtz
language : en
Publisher: World Scientific
Release Date : 2004
Theories Of Integration written by Douglas S. Kurtz and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Mathematics categories.
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.
Kurzweil Stieltjes Integral Theory And Applications
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Author : Giselle Antunes Monteiro
language : en
Publisher: World Scientific
Release Date : 2018-09-26
Kurzweil Stieltjes Integral Theory And Applications written by Giselle Antunes Monteiro and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-09-26 with Mathematics categories.
The book is primarily devoted to the Kurzweil-Stieltjes integral and its applications in functional analysis, theory of distributions, generalized elementary functions, as well as various kinds of generalized differential equations, including dynamic equations on time scales. It continues the research that was paved out by some of the previous volumes in the Series in Real Analysis. Moreover, it presents results in a thoroughly updated form and, simultaneously, it is written in a widely understandable way, so that it can be used as a textbook for advanced university or PhD courses covering the theory of integration or differential equations.