A Primer Of Lebesgue Integration
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A Primer Of Lebesgue Integration
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Author : H. S. Bear
language : en
Publisher: Academic Press
Release Date : 2002
A Primer Of Lebesgue Integration written by H. S. Bear and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.
This successful text offers a reader-friendly approach to Lebesgue integration. It is designed for advanced undergraduates, beginning graduate students, or advanced readers who may have forgotten one or two details from their real analysis courses. "The Lebesgue integral has been around for almost a century. Most authors prefer to blast through the preliminaries and get quickly to the more interesting results. This very efficient approach puts a great burden on the reader; all the words are there, but none of the music." Bear's goal is to proceed more slowly so the reader can develop some intuition about the subject. Many readers of the successful first edition would agree that he achieves this goal. The principal change in this edition is the simplified definition of the integral. The integral is defined either with upper and lower sums as in the calculus, or with Riemann sums, but using countable partitions of the domain into measurable sets. This one-shot approach works for bounded or unbounded functions and for sets of finite or infinite measure. The author's style is graceful and pleasant to read. The explanations are exceptionally clear. Someone looking for an introduction to Lebesgue integration could scarcely do better than this text. -John Erdman Portland State University This is an excellent book. Several features make it unique. The author gets through the standard canon in only 150 pages and then arranges the material into easily digestible units (a proof hardly ever exceeds three-fourths of a page). The author writes with concision, clarity, and focus. -Robert Burckel Kansas State University This text achieves its worthy goals. The author tends to the business at hand. The short chapter on Lebesgue integration is refreshing and easily understood. One can use a semester covering the book, and the students will be well-grounded in the basics and ready for any of a dozen possible second semesters. -Joseph Diestel Kent State University
A Primer Of Lebesgue Integration
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Author : Herbert Stanley Bear (Jr.)
language : en
Publisher:
Release Date : 2002
A Primer Of Lebesgue Integration written by Herbert Stanley Bear (Jr.) and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Lebesgue integral categories.
A Primer Of Real Functions
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Author : Ralph P. Boas
language : en
Publisher: Cambridge University Press
Release Date : 1996
A Primer Of Real Functions written by Ralph P. Boas and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This is a revised, updated, and significantly augmented edition of a classic Carus Monograph (a bestseller for over 25 years) on the theory of functions of a real variable. Earlier editions of this classic Carus Monograph covered sets, metric spaces, continuous functions, and differentiable functions. The fourth edition adds sections on measurable sets and functions, the Lebesgue and Stieltjes integrals, and applications. The book retains the informal chatty style of the previous editions, remaining accessible to readers with some mathematical sophistication and a background in calculus. The book is, thus, suitable either for self-study or for supplemental reading in a course on advanced calculus or real analysis. Not intended as a systematic treatise, this book has more the character of a sequence of lectures on a variety of interesting topics connected with real functions. Many of these topics are not commonly encountered in undergraduate textbooks: e.g., the existence of continuous everywhere-oscillating functions (via the Baire category theorem); the universal chord theorem; two functions having equal derivatives, yet not differing by a constant; and application of Stieltjes integration to the speed of convergence of infinite series. This book recaptures the sense of wonder that was associated with the subject in its early days. It is a must for mathematics libraries.
Elementary Introduction To The Lebesgue Integral
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Author : Steven G. Krantz
language : en
Publisher: CRC Press
Release Date : 2018-04-17
Elementary Introduction To The Lebesgue Integral written by Steven G. Krantz and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-17 with Mathematics categories.
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
Measure Integration And A Primer On Probability Theory
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Author : Stefano Gentili
language : en
Publisher: Springer Nature
Release Date : 2020-11-30
Measure Integration And A Primer On Probability Theory written by Stefano Gentili and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-30 with Mathematics categories.
The text contains detailed and complete proofs and includes instructive historical introductions to key chapters. These serve to illustrate the hurdles faced by the scholars that developed the theory, and allow the novice to approach the subject from a wider angle, thus appreciating the human side of major figures in Mathematics. The style in which topics are addressed, albeit informal, always maintains a rigorous character. The attention placed in the careful layout of the logical steps of proofs, the abundant examples and the supplementary remarks disseminated throughout all contribute to render the reading pleasant and facilitate the learning process. The exposition is particularly suitable for students of Mathematics, Physics, Engineering and Statistics, besides providing the foundation essential for the study of Probability Theory and many branches of Applied Mathematics, including the Analysis of Financial Markets and other areas of Financial Engineering.
The Lebesgue Integral For Undergraduates
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Author : William Johnston
language : en
Publisher: The Mathematical Association of America
Release Date : 2015-09-25
The Lebesgue Integral For Undergraduates written by William Johnston and has been published by The Mathematical Association of America this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-09-25 with Mathematics categories.
In 1902, modern function theory began when Henri Lebesgue described a new "integral calculus." His "Lebesgue integral" handles more functions than the traditional integral-so many more that mathematicians can study collections (spaces) of functions. For example, it defines a distance between any two functions in a space. This book describes these ideas in an elementary accessible way. Anyone who has mastered calculus concepts of limits, derivatives, and series can enjoy the material. Unlike any other text, this book brings analysis research topics within reach of readers even just beginning to think about functions from a theoretical point of view.
The Structure Of Lebesgue Integration Theory
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Author : George Frederick James Temple
language : en
Publisher:
Release Date : 1971
The Structure Of Lebesgue Integration Theory written by George Frederick James Temple and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Introduction To Real Analysis
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Author : William C. Bauldry
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-09
Introduction To Real Analysis written by William C. Bauldry and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-09 with Mathematics categories.
An accessible introduction to real analysis and its connectionto elementary calculus Bridging the gap between the development and history of realanalysis, Introduction to Real Analysis: An EducationalApproach presents a comprehensive introduction to real analysiswhile also offering a survey of the field. With its balance ofhistorical background, key calculus methods, and hands-onapplications, this book provides readers with a solid foundationand fundamental understanding of real analysis. The book begins with an outline of basic calculus, including aclose examination of problems illustrating links and potentialdifficulties. Next, a fluid introduction to real analysis ispresented, guiding readers through the basic topology of realnumbers, limits, integration, and a series of functions in naturalprogression. The book moves on to analysis with more rigorousinvestigations, and the topology of the line is presented alongwith a discussion of limits and continuity that includes unusualexamples in order to direct readers' thinking beyond intuitivereasoning and on to more complex understanding. The dichotomy ofpointwise and uniform convergence is then addressed and is followedby differentiation and integration. Riemann-Stieltjes integrals andthe Lebesgue measure are also introduced to broaden the presentedperspective. The book concludes with a collection of advancedtopics that are connected to elementary calculus, such as modelingwith logistic functions, numerical quadrature, Fourier series, andspecial functions. Detailed appendices outline key definitions and theorems inelementary calculus and also present additional proofs, projects,and sets in real analysis. Each chapter references historicalsources on real analysis while also providing proof-orientedexercises and examples that facilitate the development ofcomputational skills. In addition, an extensive bibliographyprovides additional resources on the topic. Introduction to Real Analysis: An Educational Approach isan ideal book for upper- undergraduate and graduate-level realanalysis courses in the areas of mathematics and education. It isalso a valuable reference for educators in the field of appliedmathematics.
An Introduction To Measure Theory
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-09-03
An Introduction To Measure Theory written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-03 with Education categories.
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.
Real Analysis With Economic Applications
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Author : Efe A. Ok
language : en
Publisher: Princeton University Press
Release Date : 2011-09-05
Real Analysis With Economic Applications written by Efe A. Ok and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-05 with Business & Economics categories.
There are many mathematics textbooks on real analysis, but they focus on topics not readily helpful for studying economic theory or they are inaccessible to most graduate students of economics. Real Analysis with Economic Applications aims to fill this gap by providing an ideal textbook and reference on real analysis tailored specifically to the concerns of such students. The emphasis throughout is on topics directly relevant to economic theory. In addition to addressing the usual topics of real analysis, this book discusses the elements of order theory, convex analysis, optimization, correspondences, linear and nonlinear functional analysis, fixed-point theory, dynamic programming, and calculus of variations. Efe Ok complements the mathematical development with applications that provide concise introductions to various topics from economic theory, including individual decision theory and games, welfare economics, information theory, general equilibrium and finance, and intertemporal economics. Moreover, apart from direct applications to economic theory, his book includes numerous fixed point theorems and applications to functional equations and optimization theory. The book is rigorous, but accessible to those who are relatively new to the ways of real analysis. The formal exposition is accompanied by discussions that describe the basic ideas in relatively heuristic terms, and by more than 1,000 exercises of varying difficulty. This book will be an indispensable resource in courses on mathematics for economists and as a reference for graduate students working on economic theory.