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Author: Russell A. Gordon
Publisher: American Mathematical Soc.
Published: 1994-01-01
Total Pages: 412
ISBN-13: 9780821872222
DOWNLOAD EBOOK →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.
Author: Krzysztof Ostaszewski
Publisher: American Mathematical Soc.
Published: 1986
Total Pages: 118
ISBN-13: 0821824163
DOWNLOAD EBOOK →This paper deals with the integration of abstract Henstock type. Eleven derivation bases on the plane are investigated, those built with triangles, rectangles, and regular rectangles, and the approximate bases. The relationships between the integration theories generated by them are found.
Author: Ralph Henstock
Publisher:
Published: 1991
Total Pages: 288
ISBN-13:
DOWNLOAD EBOOK →Every good mathematical book stands like a tree with its roots in the past and its branches stretching out towards the future. Whether the fruits of this tree are desirable and whether the branches will be quarried for mathematical wood to build further edifices, I will leave to the judgment of history. The roots of this book take nourishment from the concept of definite integration of continuous functions, where Riemann's method is the high water mark of the simpler theory.
Author: Ralph Henstock
Publisher: World Scientific
Published: 1988
Total Pages: 224
ISBN-13: 9789971504519
DOWNLOAD EBOOK →This book is intended to be self-contained, giving the theory of absolute (equivalent to Lebesgue) and non-absolute (equivalent to Denjoy-Perron) integration by using a simple extension of the Riemann integral. A useful tool for mathematicians and scientists needing advanced integration theory would be a method combining the ideas of the calculus of indefinite integral and Riemann definite integral in such a way that Lebesgue properties can be proved easily.Three important results that have not appeared in any other book distinguish this book from the rest. First a result on limits of sequences under the integral sign, secondly the necessary and sufficient conditions for the various limits under the integral sign and thirdly the application of these results to ordinary differential equations. The present book will give non-absolute integration theory just as easily as the absolute theory, and Stieltjes-type integration too.
Author: Robert G. Bartle
Publisher: American Mathematical Soc.
Published: 2001-03-21
Total Pages: 480
ISBN-13: 9780821883853
DOWNLOAD EBOOK →The theory of integration is one of the twin pillars on which analysis is built. The first version of integration that students see is the Riemann integral. Later, graduate students learn that the Lebesgue integral is ``better'' because it removes some restrictions on the integrands and the domains over which we integrate. However, there are still drawbacks to Lebesgue integration, for instance, dealing with the Fundamental Theorem of Calculus, or with ``improper'' integrals. This book is an introduction to a relatively new theory of the integral (called the ``generalized Riemann integral'' or the ``Henstock-Kurzweil integral'') that corrects the defects in the classical Riemann theory and both simplifies and extends the Lebesgue theory of integration. Although this integral includes that of Lebesgue, its definition is very close to the Riemann integral that is familiar to students from calculus. One virtue of the new approach is that no measure theory and virtually no topology is required. Indeed, the book includes a study of measure theory as an application of the integral. Part 1 fully develops the theory of the integral of functions defined on a compact interval. This restriction on the domain is not necessary, but it is the case of most interest and does not exhibit some of the technical problems that can impede the reader's understanding. Part 2 shows how this theory extends to functions defined on the whole real line. The theory of Lebesgue measure from the integral is then developed, and the author makes a connection with some of the traditional approaches to the Lebesgue integral. Thus, readers are given full exposure to the main classical results. The text is suitable for a first-year graduate course, although much of it can be readily mastered by advanced undergraduate students. Included are many examples and a very rich collection of exercises. There are partial solutions to approximately one-third of the exercises. A complete solutions manual is available separately.
Author: Douglas S. Kurtz
Publisher: World Scientific
Published: 2004
Total Pages: 286
ISBN-13: 9789812388438
DOWNLOAD EBOOK →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.
Author: Peng Yee Lee
Publisher: World Scientific
Published: 1989
Total Pages: 194
ISBN-13: 9789971508920
DOWNLOAD EBOOK →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: Bellow Alexandra
Publisher: World Scientific
Published: 2018-04-24
Total Pages: 252
ISBN-13: 9813237325
DOWNLOAD EBOOK →The book is a collection of original papers, research and surveys, dedicated to the memory of the Romanian mathematician Solomon Marcus (1925-2016). Marcus published many papers and books in mathematical analysis, theoretical computer science, mathematical linguistics, poetics, theory of literature, semiotics, and several other fields less strongly connected to mathematics, like cultural anthropology, biology, history and philosophy of science, education. He exemplified an unimaginable richness of ideas. This volume intends to emphasize the mathematical fields in which Solomon Marcus worked, and demonstrate -- as he also did -- the interconnection between them. The authors who contribute to this volume are well-known experts in their fields. Most of them knew Solomon Marcus well, some even owed him for his decisive impulses for their careers and general development. With articles in so diverse areas, the volume will attract readers who would like to diversify their own knowledge or find unexpected connections with other topics. Contents: Logic, Complexity and Algebra: On Bases of Many-Valued Truth Functions (A Salomaa) Quasiperiods of Infinite Words (L Staiger) Early Romanian Contributions to Algebra and Polynomials (D Ştefănescu) Distributed Compression through the Lens of Algorithmic Information Theory: A Primer (M Zimand) Integrals, Operators, AF Algebras, Proof Mining and Monotone Nonexpansive Mappings: Monotonically Controlled Integrals (T Ball, D Preiss) Fine Properties of Duality Mappings (G Dincă) Primitive Ideal Spaces of Postliminal AF Algebras (A Lazar) An Application of Proof Miningto the Proximal Point Algorithm in CAT(0) Spaces (L Leuştean, A Sipoş) Generic Well-posedness of the Fixed Point Problem for Monotone Nonexpansive Mappings (S Reich, A J Zaslavski) Linguistics, Computer Science and Physics: Analytical Linguistics and Formal Grammars: Contributions of Solomon Marcus and Their Further Developments (M Burgin) A Contagious Creativity (Gh Păun) Entanglement through Path Identification (K Svozil) Solomon Marcus in Context: Memories about Solomon Marcus (A Bruckner) Memories With and About My Uncle (M Marcus) Index Readership: Graduate students and researchers. Keywords: Discrete Mathematics;Mathematical Analysis;Complexity Theory;Proof Mining;Mathematical Biology;Formal Languages;Theoretical Mechanics;Mathematical Linguistics;Theoretical PhysicsReview: Key Features: New results in a variety of mathematical areas including operator theory, measure theory, real and functional analysis, computable algebra, formal languages, proof mining in nonlinear analysis, theoretical mechanics, mathematical logic, and topical surveys in mathematical linguistics, complexity theory and computational biology The authors, coming from various parts of the world, are well-known experts in the areas of their contributions Interconnections between results and domains will make the volume not only informative, but also attractive and unique
Author: Guillermo Curbera
Publisher: Springer Science & Business Media
Published: 2010-02-21
Total Pages: 382
ISBN-13: 3034602111
DOWNLOAD EBOOK →This volume contains a selection of articles on the theme "vector measures, integration and applications" together with some related topics. The articles consist of both survey style and original research papers, are written by experts in thearea and present a succinct account of recent and up-to-date knowledge. The topic is interdisciplinary by nature and involves areas such as measure and integration (scalar, vector and operator-valued), classical and harmonic analysis, operator theory, non-commutative integration, andfunctional analysis. The material is of interest to experts, young researchers and postgraduate students.
Author: DDE NBU
Publisher: Directorate of Distance Education, University of North Bengal
Published: 2019-11-05
Total Pages: 192
ISBN-13:
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