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Author : Thomas William Hawkins
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (959 download)
Download or read book The Origins and Early Development of Lebesgue's Theory of Integration written by Thomas William Hawkins and published by . This book was released on 1977 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Thomas Hawkins
Publisher : American Mathematical Soc.
ISBN 13 : 9780828402828
Total Pages : 256 pages
Book Rating : 4.4/5 (28 download)
Download or read book Lebesgue's Theory of Integration written by Thomas Hawkins and published by American Mathematical Soc.. This book was released on 1975 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, Hawkins places Lebesgue's early work on integration theory within in proper historical context by relating it to the developments during the nineteenth century that motivated it and gave it significance and also to the contributions made inthis field by Lebesgue's contemporaries.
Author : Thomas William Hawkins
Publisher :
ISBN 13 :
Total Pages : 756 pages
Book Rating : 4.:/5 (89 download)
Download or read book The Origins and Early Development of Lebesgue's Theory of Integration written by Thomas William Hawkins and published by . This book was released on 1968 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : David M. Bressoud
Publisher : Cambridge University Press
ISBN 13 : 0521884748
Total Pages : 15 pages
Book Rating : 4.5/5 (218 download)
Download or read book A Radical Approach to Lebesgue's Theory of Integration written by David M. Bressoud and published by Cambridge University Press. This book was released on 2008-01-21 with total page 15 pages. Available in PDF, EPUB and Kindle. Book excerpt: Meant for advanced undergraduate and graduate students in mathematics, this introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author tells the story of the mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work of Jordan, Borel, and Lebesgue.
Author : Frank Jones
Publisher : Jones & Bartlett Learning
ISBN 13 : 9780763717087
Total Pages : 626 pages
Book Rating : 4.7/5 (17 download)
Download or read book Lebesgue Integration on Euclidean Space written by Frank Jones and published by Jones & Bartlett Learning. This book was released on 2001 with total page 626 pages. Available in PDF, EPUB and Kindle. Book excerpt: "'Lebesgue Integration on Euclidean Space' contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. It contains many exercises that are incorporated throughout the text, enabling the reader to apply immediately the new ideas that have been presented" --
Author : Howard J. Wilcox
Publisher : Courier Corporation
ISBN 13 : 0486137473
Total Pages : 194 pages
Book Rating : 4.4/5 (861 download)
Download or read book An Introduction to Lebesgue Integration and Fourier Series written by Howard J. Wilcox and published by Courier Corporation. This book was released on 2012-04-30 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.
Author : Douglas S. Kurtz
Publisher : World Scientific
ISBN 13 : 9789812388438
Total Pages : 286 pages
Book Rating : 4.3/5 (884 download)
Download or read book Theories of Integration written by Douglas S. Kurtz and published by World Scientific. This book was released on 2004 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Georgeana Bobos-Kristof
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (11 download)
Download or read book The Development of the Modern Integration Theory from Cauchy to Lebesgue written by Georgeana Bobos-Kristof and published by . This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this thesis, we describe the historical development of the modern integration theory by presenting the key ideas and insights that led to its shaping, from the first rigorous definition of the definite integral given by Cauchy in 1823, to Lebesgue's theory as it first appeared in his doctoral thesis of 1902. In the final part we also present recent approaches in integration theory. We show that various problems motivated the enrichment of the notion of integral, while one in particular constituted the most important trigger of this development from the beginnings well into the 20th century: the search for a better understanding of Fourier series. For our study, we principally look at original sources, and we provide detailed proofs for important results, often by elaborating on the authors' sketchy or heuristic arguments, malting thus the original results accessible to the modern reader. We then use this historical and epistemological analysis to raise some issues related to the teaching of integration at various levels at university, i.e., in calculus, analysis and measure theory courses. For this, we look at some typical textbooks and, inspired by the historical analysis, we give some suggestions for teaching. Our findings show that there might be some conceptual gaps between subsequent levels that are not necessarily insuperable, but require careful didactical analysis.
Author : Ivor Grattan-Guiness
Publisher : Routledge
ISBN 13 : 1134887558
Total Pages : 578 pages
Book Rating : 4.1/5 (348 download)
Download or read book Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences written by Ivor Grattan-Guiness and published by Routledge. This book was released on 2004-11-11 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: First published in 2004. Routledge is an imprint of Taylor & Francis, an informa company.
Author : Ivor Grattan-Guinness
Publisher : Routledge
ISBN 13 : 1134957491
Total Pages : 1788 pages
Book Rating : 4.1/5 (349 download)
Download or read book Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences written by Ivor Grattan-Guinness and published by Routledge. This book was released on 2002-09-11 with total page 1788 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Examines the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times up to the twentieth century * 176 articles contributed by authors of 18 nationalities * Chronological table of main events in the development of mathematics * Fully integrated index of people, events and topics * Annotated bibliographies of both classic and contemporary sources * Unique coverage of Ancient and non-Western traditions of mathematics
Author : Terence Tao
Publisher : American Mathematical Soc.
ISBN 13 : 1470466406
Total Pages : 206 pages
Book Rating : 4.4/5 (74 download)
Download or read book An Introduction to Measure Theory written by Terence Tao and published by American Mathematical Soc.. This book was released on 2021-09-03 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text introducing the fundamentals of measure theory and integration theory, which is the foundation of modern real analysis. The text focuses first on the concrete setting of Lebesgue measure and the Lebesgue integral (which in turn is motivated by the more classical concepts of Jordan measure and the Riemann integral), before moving on to abstract measure and integration theory, including the standard convergence theorems, Fubini's theorem, and the Carathéodory extension theorem. Classical differentiation theorems, such as the Lebesgue and Rademacher differentiation theorems, are also covered, as are connections with probability theory. The material is intended to cover a quarter or semester's worth of material for a first graduate course in real analysis. There is an emphasis in the text on tying together the abstract and the concrete sides of the subject, using the latter to illustrate and motivate the former. The central role of key principles (such as Littlewood's three principles) as providing guiding intuition to the subject is also emphasized. There are a large number of exercises throughout that develop key aspects of the theory, and are thus an integral component of the text. As a supplementary section, a discussion of general problem-solving strategies in analysis is also given. The last three sections discuss optional topics related to the main matter of the book.
Author : Frank Burk
Publisher : John Wiley & Sons
ISBN 13 : 1118030982
Total Pages : 314 pages
Book Rating : 4.1/5 (18 download)
Download or read book Lebesgue Measure and Integration written by Frank Burk and published by John Wiley & Sons. This book was released on 2011-10-14 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: A superb text on the fundamentals of Lebesgue measure and integration. This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R. Starting with a thorough presentation of the preliminary concepts of undergraduate analysis, this book covers all the important topics, including measure theory, measurable functions, and integration. It offers an abundance of support materials, including helpful illustrations, examples, and problems. To further enhance the learning experience, the author provides a historical context that traces the struggle to define "area" and "area under a curve" that led eventually to Lebesgue measure and integration. Lebesgue Measure and Integration is the ideal text for an advanced undergraduate analysis course or for a first-year graduate course in mathematics, statistics, probability, and other applied areas. It will also serve well as a supplement to courses in advanced measure theory and integration and as an invaluable reference long after course work has been completed.
Author : H. S. Bear
Publisher : Academic Press
ISBN 13 : 9780120839711
Total Pages : 184 pages
Book Rating : 4.8/5 (397 download)
Download or read book A Primer of Lebesgue Integration written by H. S. Bear and published by Academic Press. This book was released on 2002 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Lebesgue integral is now standard for both applications and advanced mathematics. This books starts with a review of the familiar calculus integral and then constructs the Lebesgue integral from the ground up using the same ideas. A Primer of Lebesgue Integration has been used successfully both in the classroom and for individual study. Bear presents a clear and simple introduction for those intent on further study in higher mathematics. Additionally, this book serves as a refresher providing new insight for those in the field. The author writes with an engaging, commonsense style that appeals to readers at all levels.
Author : Alan J. Weir
Publisher : CUP Archive
ISBN 13 : 9780521204071
Total Pages : 316 pages
Book Rating : 4.2/5 (4 download)
Download or read book General Integration and Measure written by Alan J. Weir and published by CUP Archive. This book was released on 1974-11-14 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a sequel to Dr Weir's undergraduate textbook on Lebesgue Integration and Measure (CUP. 1973) in which he provided a concrete approach to the Lebesgue integral in terms of step functions and went on from there to deduce the abstract concept of Lebesgue measure. In this second volume, the treatment of the Lebesgue integral is generalised to give the Daniell integral and the related general theory of measure. This approach via integration of elementary functions is particularly well adapted to the proof of Riesz's famous theorems about linear functionals on the classical spaces C (X) and LP and also to the study of topological notions such as Borel measure. This book will be used for final year honours courses in pure mathematics and for graduate courses in functional analysis and measure theory.
Author : Gail S. Nelson
Publisher : American Mathematical Soc.
ISBN 13 : 1470421992
Total Pages : 233 pages
Book Rating : 4.4/5 (74 download)
Download or read book A User-Friendly Introduction to Lebesgue Measure and Integration written by Gail S. Nelson and published by American Mathematical Soc.. This book was released on 2015-11-09 with total page 233 pages. Available in PDF, EPUB and Kindle. Book excerpt: A User-Friendly Introduction to Lebesgue Measure and Integration provides a bridge between an undergraduate course in Real Analysis and a first graduate-level course in Measure Theory and Integration. The main goal of this book is to prepare students for what they may encounter in graduate school, but will be useful for many beginning graduate students as well. The book starts with the fundamentals of measure theory that are gently approached through the very concrete example of Lebesgue measure. With this approach, Lebesgue integration becomes a natural extension of Riemann integration. Next, -spaces are defined. Then the book turns to a discussion of limits, the basic idea covered in a first analysis course. The book also discusses in detail such questions as: When does a sequence of Lebesgue integrable functions converge to a Lebesgue integrable function? What does that say about the sequence of integrals? Another core idea from a first analysis course is completeness. Are these -spaces complete? What exactly does that mean in this setting? This book concludes with a brief overview of General Measures. An appendix contains suggested projects suitable for end-of-course papers or presentations. The book is written in a very reader-friendly manner, which makes it appropriate for students of varying degrees of preparation, and the only prerequisite is an undergraduate course in Real Analysis.
Author : Marek Capinski
Publisher : Springer Science & Business Media
ISBN 13 : 1447136314
Total Pages : 229 pages
Book Rating : 4.4/5 (471 download)
Download or read book Measure, Integral and Probability written by Marek Capinski and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This very well written and accessible book emphasizes the reasons for studying measure theory, which is the foundation of much of probability. By focusing on measure, many illustrative examples and applications, including a thorough discussion of standard probability distributions and densities, are opened. The book also includes many problems and their fully worked solutions.
Author : Samopriya Basu
Publisher : SIAM
ISBN 13 : 1611977827
Total Pages : 620 pages
Book Rating : 4.6/5 (119 download)
Download or read book A Ramble Through Probability written by Samopriya Basu and published by SIAM. This book was released on 2024-03-06 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: Measure theory and measure-theoretic probability are fascinating subjects. Proofs describing profound ways to reason lead to results that are frequently startling, beautiful, and useful. Measure theory and probability also play roles in the development of pure and applied mathematics, statistics, engineering, physics, and finance. Indeed, it is difficult to overstate their importance in the quantitative disciplines. This book traces an eclectic path through the fundamentals of the topic to make the material accessible to a broad range of students. A Ramble through Probability: How I Learned to Stop Worrying and Love Measure Theory brings together the key elements and applications in a unified presentation aimed at developing intuition; contains an extensive collection of examples that illustrate, explain, and apply the theories; and is supplemented with videos containing commentary and explanations of select proofs on an ancillary website. This book is intended for graduate students in engineering, mathematics, science, and statistics. Researchers who need to use probability theory will also find it useful. It is appropriate for graduate-level courses on measure theory and/or probability theory.
