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Author : J. C. Burkill
Publisher :
ISBN 13 :
Total Pages : 87 pages
Book Rating : 4.:/5 (97 download)
Download or read book The Lebesgue Integral written by J. C. Burkill and published by . This book was released on 1958 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 : John M. Franks
Publisher : American Mathematical Soc.
ISBN 13 : 0821848623
Total Pages : 219 pages
Book Rating : 4.8/5 (218 download)
Download or read book A (Terse) Introduction to Lebesgue Integration written by John M. Franks and published by American Mathematical Soc.. This book was released on 2009 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides a student's first encounter with the concepts of measure theory and functional analysis. This book reflects the belief that difficult concepts should be introduced in their simplest and most concrete forms. It is suitable for an advanced undergraduate course or for the start of a graduate course.
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 : Open University. M431 Course Team
Publisher :
ISBN 13 : 9780749220723
Total Pages : 20 pages
Book Rating : 4.2/5 (27 download)
Download or read book The Lebesgue Integral written by Open University. M431 Course Team and published by . This book was released on 1992 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : S. Hartman
Publisher : Elsevier
ISBN 13 : 1483280330
Total Pages : 177 pages
Book Rating : 4.4/5 (832 download)
Download or read book The Theory of Lebesgue Measure and Integration written by S. Hartman and published by Elsevier. This book was released on 2014-07-14 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Theory of Lebesgue Measure and Integration deals with the theory of Lebesgue measure and integration and introduces the reader to the theory of real functions. The subject matter comprises concepts and theorems that are now considered classical, including the Yegorov, Vitali, and Fubini theorems. The Lebesgue measure of linear sets is discussed, along with measurable functions and the definite Lebesgue integral. Comprised of 13 chapters, this volume begins with an overview of basic concepts such as set theory, the denumerability and non-denumerability of sets, and open sets and closed sets on the real line. The discussion then turns to the theory of Lebesgue measure of linear sets based on the method of M. Riesz, together with the fundamental properties of measurable functions. The Lebesgue integral is considered for both bounded functions — upper and lower integrals — and unbounded functions. Later chapters cover such topics as the Yegorov, Vitali, and Fubini theorems; convergence in measure and equi-integrability; integration and differentiation; and absolutely continuous functions. Multiple integrals and the Stieltjes integral are also examined. This book will be of interest to mathematicians and students taking pure and applied mathematics.
Author : Edward James McShane
Publisher : American Mathematical Soc.
ISBN 13 : 0821812882
Total Pages : 57 pages
Book Rating : 4.8/5 (218 download)
Download or read book A Riemann-Type Integral that Includes Lebesgue-Stieltjes, Bochner and Stochastic Integrals written by Edward James McShane and published by American Mathematical Soc.. This book was released on 1969 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the difficulties with integration theory is that there are so many different detailed definitions that the non-expert is confused about their relative strengths and usefulness. A surprising recent development in the theory of integration has been the discovery that suitable modifications to the Riemann definition using approximating sums can produce a wide variety of different integrals including integrals of great power.
Author : Bruce Desmond Craven
Publisher : Pitman Publishing
ISBN 13 :
Total Pages : 240 pages
Book Rating : 4.3/5 (91 download)
Download or read book Lebesgue Measure & Integral written by Bruce Desmond Craven and published by Pitman Publishing. This book was released on 1982 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alan J. Weir
Publisher : Cambridge University Press
ISBN 13 : 9780521097512
Total Pages : 300 pages
Book Rating : 4.0/5 (975 download)
Download or read book Lebesgue Integration and Measure written by Alan J. Weir and published by Cambridge University Press. This book was released on 1973-05-10 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: A textbook for the undergraduate who is meeting the Lebesgue integral for the first time, relating it to the calculus and exploring its properties before deducing the consequent notions of measurable functions and measure.
Author : Steven G. Krantz
Publisher : CRC Press
ISBN 13 : 1351056816
Total Pages : 184 pages
Book Rating : 4.3/5 (51 download)
Download or read book Elementary Introduction to the Lebesgue Integral written by Steven G. Krantz and published by CRC Press. This book was released on 2018-04-17 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elementary Introduction to the Lebesgue Integral is not just an excellent primer of the Lebesgue integral for undergraduate students but a valuable tool for tomorrow’s mathematicians. Since the early twentieth century, the Lebesgue integral has been a mainstay of mathematical analysis because of its important properties with respect to limits. For this reason, it is vital that mathematical students properly understand the complexities of the Lebesgue integral. However, most texts about the subject are geared towards graduate students, which makes it a challenge for instructors to properly teach and for less advanced students to learn. Ensuring that the subject is accessible for all readers, the author presents the text in a clear and concrete manner which allows readers to focus on the real line. This is important because Lebesgue integral can be challenging to understand when compared to more widely used integrals like the Riemann integral. The author also includes in the textbook abundant examples and exercises to help explain the topic. Other topics explored in greater detail are abstract measure spaces and product measures, which are treated concretely. Features: Comprehensibly written introduction to the Lebesgue integral for undergraduate students Includes many examples, figures and exercises Features a Table of Notation and Glossary to aid readers Solutions to selected exercises
Author : Zoltán Magyar
Publisher : Akademiai Kiads
ISBN 13 :
Total Pages : 120 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Lebesgue Integral written by Zoltán Magyar and published by Akademiai Kiads. This book was released on 1997 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is recommended to those who are familiar with calculus and are interested in the field of Lebesgue integral and the related theory of measures. It may be useful both for those first meeting the topic and for those deepening its understanding. So we propose it to students and researchers in mathematics, physics, engineering, etc.
Author : Ronald B. Guenther
Publisher : CRC Press
ISBN 13 : 1000925935
Total Pages : 159 pages
Book Rating : 4.0/5 (9 download)
Download or read book Aspects of Integration written by Ronald B. Guenther and published by CRC Press. This book was released on 2023-08-24 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aspects of Integration: Novel Approaches to the Riemann and Lebesgue Integrals is comprised of two parts. The first part is devoted to the Riemann integral, and provides not only a novel approach, but also includes several neat examples that are rarely found in other treatments of Riemann integration. Historical remarks trace the development of integration from the method of exhaustion of Eudoxus and Archimedes, used to evaluate areas related to circles and parabolas, to Riemann’s careful definition of the definite integral, which is a powerful expansion of the method of exhaustion and makes it clear what a definite integral really is. The second part follows the approach of Riesz and Nagy in which the Lebesgue integral is developed without the need for any measure theory. Our approach is novel in part because it uses integrals of continuous functions rather than integrals of step functions as its starting point. This is natural because Riemann integrals of continuous functions occur much more frequently than do integrals of step functions as a precursor to Lebesgue integration. In addition, the approach used here is natural because step functions play no role in the novel development of the Riemann integral in the first part of the book. Our presentation of the Riesz-Nagy approach is significantly more accessible, especially in its discussion of the two key lemmas upon which the approach critically depends, and is more concise than other treatments. Features Presents novel approaches designed to be more accessible than classical presentations A welcome alternative approach to the Riemann integral in undergraduate analysis courses Makes the Lebesgue integral accessible to upper division undergraduate students How completion of the Riemann integral leads to the Lebesgue integral Contains a number of historical insights Gives added perspective to researchers and postgraduates interested in the Riemann and Lebesgue integrals
Author : John Charles Burkill
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (133 download)
Download or read book The Lebesgue Integral written by John Charles Burkill and published by . This book was released on 1971 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Russell A. Gordon
Publisher : American Mathematical Soc.
ISBN 13 : 9780821872222
Total Pages : 412 pages
Book Rating : 4.8/5 (722 download)
Download or read book The Integrals of Lebesgue, Denjoy, Perron, and Henstock written by Russell A. Gordon and published by American Mathematical Soc.. This book was released on 1994-01-01 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : 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 : 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 : Soo B. Chae
Publisher : Springer Science & Business Media
ISBN 13 : 1461207819
Total Pages : 275 pages
Book Rating : 4.4/5 (612 download)
Download or read book Lebesgue Integration written by Soo B. Chae and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 275 pages. Available in PDF, EPUB and Kindle. Book excerpt: Responses from colleagues and students concerning the first edition indicate that the text still answers a pedagogical need which is not addressed by other texts. There are no major changes in this edition. Several proofs have been tightened, and the exposition has been modified in minor ways for improved clarity. As before, the strength of the text lies in presenting the student with the difficulties which led to the development of the theory and, whenever possi ble, giving the student the tools to overcome those difficulties for himself or herself. Another proverb: Give me a fish, I eat for a day. Teach me to fish, I eat for a lifetime. Soo Bong Chae March 1994 Preface to the First Edition This book was developed from lectures in a course at New College and should be accessible to advanced undergraduate and beginning graduate students. The prerequisites are an understanding of introductory calculus and the ability to comprehend "e-I) arguments. " The study of abstract measure and integration theory has been in vogue for more than two decades in American universities since the publication of Measure Theory by P. R. Halmos (1950). There are, however, very few ele mentary texts from which the interested reader with a calculus background can learn the underlying theory in a form that immediately lends itself to an understanding of the subject. This book is meant to be on a level between calculus and abstract integration theory for students of mathematics and physics.
