Nonabsolute Integration On Measure Spaces
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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.
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.
Measure Theory And Integration
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Author : M.M. Rao
language : en
Publisher: CRC Press
Release Date : 2018-10-03
Measure Theory And Integration written by M.M. Rao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-10-03 with Mathematics categories.
Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications. With more than 170 references for further investigation of the subject, this Second Edition provides more than 60 pages of new information, as well as a new chapter on nonabsolute integrals contains extended discussions on the four basic results of Banach spaces presents an in-depth analysis of the classical integrations with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties details the basic properties and extensions of the Lebesgue-Carathéodory measure theory, as well as the structure and convergence of real measurable functions covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theory Measure Theory and Integration, Second Edition is a valuable reference for all pure and applied mathematicians, statisticians, and mathematical analysts, and an outstanding text for all graduate students in these disciplines.
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.
Summability Fixed Point Theory And Generalized Integrals With Applications
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Author : Hemanta Kalita
language : en
Publisher: CRC Press
Release Date : 2025-06-19
Summability Fixed Point Theory And Generalized Integrals With Applications written by Hemanta Kalita and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-06-19 with Mathematics categories.
This book presents contemporary mathematical concepts and techniques including theories of summability, fixed point and non-absolute integration and applications, providing an overview of recent developments in the foundations of the field as well as its applications. It discusses the recent results of double sequence spaces as the four-dimensional forward difference matrix in double sequence spaces, several new fixed point on Hadamard type fractional integral and differential operator related to the qualitative properties of solutions like, existence and uniqueness, stability, continuous dependence, controllability, oscillations, etc. It also includes several new areas of nonabsolute integration theory are introduced and their applications to other fields. This reference text is for researchers, academics, and professionals in the field of pure and applied mathematics. • Covers recent research breakthroughs in this field offering new approaches and methods for both theoretical exploration and practical application • Presents insights into functional analytic methods in summability, absolute and strong summability, direct theorems on summability, special and general summability methods, and their applications • Highlights fixed-point theory’s application to real-world problems and offers solutions to various complex challenges • Introduces new areas of non-absolute integration theory, such as the Henstock-Kurzweil integral and generalized Riemann integral • Discusses sequence spaces and functional analysis, including the exploration of double sequence spaces and the four-dimensional forward difference matrix, offering valuable contributions to ongoing research.
Topics In Banach Space Integration
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Author : ?tefan Schwabik
language : en
Publisher: World Scientific
Release Date : 2005
Topics In Banach Space Integration written by ?tefan Schwabik and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
The relatively new concepts of the Henstock-Kurzweil and McShane integrals based on Riemann type sums are an interesting challenge in the study of integration of Banach space-valued functions. This timely book presents an overview of the concepts developed and results achieved during the past 15 years. The Henstock-Kurzweil and McShane integrals play the central role in the book. Various forms of the integration are introduced and compared from the viewpoint of their generality. Functional analysis is the main tool for presenting the theory of summation gauge integrals.
Measure Theory And Integration Second Edition
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Author : M.M. Rao
language : en
Publisher: CRC Press
Release Date : 2004-01-30
Measure Theory And Integration Second Edition written by M.M. Rao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-30 with Mathematics categories.
Significantly revised and expanded, this authoritative reference/text comprehensively describes concepts in measure theory, classical integration, and generalized Riemann integration of both scalar and vector types-providing a complete and detailed review of every aspect of measure and integration theory using valuable examples, exercises, and applications. With more than 170 references for further investigation of the subject, this Second Edition provides more than 60 pages of new information, as well as a new chapter on nonabsolute integrals contains extended discussions on the four basic results of Banach spaces presents an in-depth analysis of the classical integrations with many applications, including integration of nonmeasurable functions, Lebesgue spaces, and their properties details the basic properties and extensions of the Lebesgue-Carathéodory measure theory, as well as the structure and convergence of real measurable functions covers the Stone isomorphism theorem, the lifting theorem, the Daniell method of integration, and capacity theory Measure Theory and Integration, Second Edition is a valuable reference for all pure and applied mathematicians, statisticians, and mathematical analysts, and an outstanding text for all graduate students in these disciplines.
Real Analysis
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Author : J. Yeh
language : en
Publisher: World Scientific
Release Date : 2006
Real Analysis written by J. Yeh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
This book presents a unified treatise of the theory of measure and integration. In the setting of a general measure space, every concept is defined precisely and every theorem is presented with a clear and complete proof with all the relevant details. Counter-examples are provided to show that certain conditions in the hypothesis of a theorem cannot be simply dropped.The dependence of a theorem on earlier theorems is explicitly indicated in the proof, not only to facilitate reading but also to delineate the structure of the theory. The precision and clarity of presentation make the book an ideal textbook for a graduate course in real analysis while the wealth of topics treated also make the book a valuable reference work for mathematicians.
Selected Topics On Generalized Integration
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Author : Tin Lam Toh
language : en
Publisher: World Scientific
Release Date : 2025-05-20
Selected Topics On Generalized Integration written by Tin Lam Toh and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-20 with Mathematics categories.
This comprehensive volume offers an in-depth exploration of advanced integration theories, extending beyond classical methods to unify and expand the field. Building on the foundational work of Jaroslav Kurzweil and Ralph Henstock, the book delves into the Henstock-Kurzweil and McShane gauge integrals, presenting a more intuitive and versatile alternative to the traditional Lebesgue integral. By bridging gaps in existing literature, the authors provide a rigorous treatment of integration on metric measure spaces, exploring critical concepts such as completeness, compactness, and Cousin's lemma.The book systematically introduces advanced topics, including the variational Henstock integral in locally convex spaces, the Riemann-Lebesgue integral for vector-valued functions, and generalizations of the Sugeno integral. Further chapters explore convergence in Banach spaces on time scales, set-valued integrals, and applications to harmonic analysis and partial differential equations, including solutions to the heat equation in distribution spaces.Notably, the text presents innovative approaches like the symmetric Laplace integral and the q-Homotopy Analysis Method for solving nonlinear integral equations, offering practical tools for modern analysis. Unified integral representations for generalized Mittag-Leffler functions further highlight the book's engagement with special functions.Ideal for researchers and advanced students in mathematical analysis, this book seamlessly integrates classical theories with modern advancements, offering both theoretical insights and practical applications across mathematics, physics, and engineering.
Real Analysis
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Author : Brian S. Thomson
language : en
Publisher: ClassicalRealAnalysis.com
Release Date : 2008
Real Analysis written by Brian S. Thomson and has been published by ClassicalRealAnalysis.com this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This is the second edition of a graduate level real analysis textbook formerly published by Prentice Hall (Pearson) in 1997. This edition contains both volumes. Volumes one and two can also be purchased separately in smaller, more convenient sizes.