An Introduction to Lebesgue Integration and Fourier Series


Author: Howard J. Wilcox,David L. Myers
Publisher: Courier Corporation
ISBN: 0486137473
Category: Mathematics
Page: 159
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Undergraduate-level introduction to Riemann integral, measurable sets, measurable functions, Lebesgue integral, other topics. Numerous examples and exercises.

Lebesgue Integration


Author: J.H. Williamson
Publisher: Courier Corporation
ISBN: 0486789772
Category: Mathematics
Page: 128
View: 3640

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This concise introduction to Lebesgue integration is geared toward advanced undergraduate math majors and may be read by any student possessing some familiarity with real variable theory and elementary calculus. The self-contained treatment features exercises at the end of each chapter that range from simple to difficult. The approach begins with sets and functions and advances to Lebesgue measure, including considerations of measurable sets, sets of measure zero, and Borel sets and nonmeasurable sets. A two-part exploration of the integral covers measurable functions, convergence theorems, convergence in mean, Fourier theory, and other topics. A chapter on calculus examines change of variables, differentiation of integrals, and integration of derivatives and by parts. The text concludes with a consideration of more general measures, including absolute continuity and convolution products. Dover (2014) republication of the edition originally published by Holt, Rinehart & Winston, New York, 1962. See every Dover book in print at www.doverpublications.com

Integration, Measure and Probability


Author: H. R. Pitt,Mathematics
Publisher: Courier Corporation
ISBN: 0486488152
Category: Mathematics
Page: 110
View: 9745

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Introductory treatment develops the theory of integration in a general context, making it applicable to other branches of analysis. More specialized topics include convergence theorems and random sequences and functions. 1963 edition.

Integral, Measure and Derivative

A Unified Approach
Author: G. E. Shilov,B. L. Gurevich
Publisher: Courier Corporation
ISBN: 0486165612
Category: Mathematics
Page: 256
View: 3967

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This treatment examines the general theory of the integral, Lebesque integral in n-space, the Riemann-Stieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." — Sci-Tech Book News. 1966 edition.

Elementary Introduction to the Lebesgue Integral


Author: Steven G. Krantz
Publisher: CRC Press
ISBN: 1351056808
Category: Mathematics
Page: 184
View: 5644

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It is important and useful to have a text on the Lebesgue theory that is accessible to bright undergraduates. This is such a text. Going back to the days of Isaac Newton and Gottfried Wilhelm von Leibniz, and even to Newton's teacher Isaac Barrow, the integral has been a mainstay of mathematical analysis. The integral is a device for amalgamating information. It is a powerful and irreplaceable tool. The text concentrates on the real line. The student will be familiar with the real numbers and will be comfortable internalizing the new ideas of measure theory in that context. In addition to having copious examples and numerous figures, this book includes a Table of Notation and a Glossary.

Lebesgue Integration on Euclidean Space


Author: Frank Jones
Publisher: Jones & Bartlett Learning
ISBN: 9780763717087
Category: Computers
Page: 588
View: 2310

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Lebesgue Integration on Euclidean Space contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. Throughout the text, many exercises are incorporated, enabling students to apply new ideas immediately. Jones strives to present a slow introduction to Lebesgue integration by dealing with n-dimensional spaces from the outset. In addition, the text provides students a thorough treatment of Fourier analysis, while holistically preparing students to become workers in real analysis.

Measure, Integral, Derivative

A Course on Lebesgue's Theory
Author: Sergei Ovchinnikov
Publisher: Springer Science & Business Media
ISBN: 1461471966
Category: Mathematics
Page: 146
View: 933

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This classroom-tested text is intended for a one-semester course in Lebesgue’s theory. With over 180 exercises, the text takes an elementary approach, making it easily accessible to both upper-undergraduate- and lower-graduate-level students. The three main topics presented are measure, integration, and differentiation, and the only prerequisite is a course in elementary real analysis. In order to keep the book self-contained, an introductory chapter is included with the intent to fill the gap between what the student may have learned before and what is required to fully understand the consequent text. Proofs of difficult results, such as the differentiability property of functions of bounded variations, are dissected into small steps in order to be accessible to students. With the exception of a few simple statements, all results are proven in the text. The presentation is elementary, where σ-algebras are not used in the text on measure theory and Dini’s derivatives are not used in the chapter on differentiation. However, all the main results of Lebesgue’s theory are found in the book. http://online.sfsu.edu/sergei/MID.htm

Lectures on Measure and Integration


Author: Harold Widom
Publisher: Courier Dover Publications
ISBN: 0486810283
Category: Mathematics
Page: 176
View: 4847

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These well-known and concise lecture notes present the fundamentals of the Lebesgue theory of integration and an introduction to some of the theory's applications. Suitable for advanced undergraduates and graduate students of mathematics, the treatment also covers topics of interest to practicing analysts. Author Harold Widom emphasizes the construction and properties of measures in general and Lebesgue measure in particular as well as the definition of the integral and its main properties. The notes contain chapters on the Lebesgue spaces and their duals, differentiation of measures in Euclidean space, and the application of integration theory to Fourier series.

A (terse) Introduction to Lebesgue Integration


Author: John M. Franks
Publisher: American Mathematical Soc.
ISBN: 0821848623
Category: Mathematics
Page: 202
View: 1969

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This book provides a student's first encounter with the concepts of measure theory and functional analysis. Its structure and content reflect the belief that difficult concepts should be introduced in their simplest and most concrete forms. Despite the use of the word ``terse'' in the title, this text might also have been called A (Gentle) Introduction to Lebesgue Integration. It is terse in the sense that it treats only a subset of those concepts typically found in a substantial graduate-level analysis course. The book emphasizes the motivation of these concepts and attempts to treat them simply and concretely. In particular, little mention is made of general measures other than Lebesgue until the final chapter and attention is limited to $R$ as opposed to $R^n$. After establishing the primary ideas and results, the text moves on to some applications. Chapter 6 discusses classical real and complex Fourier series for $L^2$ functions on the interval and shows that the Fourier series of an $L^2$ function converges in $L^2$ to that function. Chapter 7 introduces some concepts from measurable dynamics. The Birkhoff ergodic theorem is stated without proof and results on Fourier series from Chapter 6 are used to prove that an irrational rotation of the circle is ergodic and that the squaring map on the complex numbers of modulus 1 is ergodic. This book is suitable for an advanced undergraduate course or for the start of a graduate course. The text presupposes that the student has had a standard undergraduate course in real analysis.

General Integration and Measure


Author: Alan J. Weir
Publisher: CUP Archive
ISBN: 9780521204071
Category: Mathematics
Page: 298
View: 1897

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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.

A Radical Approach to Lebesgue's Theory of Integration


Author: David M. Bressoud
Publisher: Cambridge University Press
ISBN: 0521884748
Category: Mathematics
Page: 329
View: 2329

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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.

Theory of Functions of a Real Variable


Author: I.P. Natanson
Publisher: Courier Dover Publications
ISBN: 048680643X
Category: Mathematics
Page: 560
View: 9430

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Long out-of-print volume by a prominent Soviet mathematician presents a thorough examination of the theory of functions of a real variable. Intended for advanced undergraduates and graduate students of mathematics. 1955 and 1960 editions.

Geometric Integration Theory


Author: Hassler Whitney
Publisher: Courier Corporation
ISBN: 048615470X
Category: Mathematics
Page: 400
View: 6861

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Geared toward upper-level undergraduates and graduate students, this treatment of geometric integration theory consists of an introduction to classical theory, a postulational approach to general theory, and a section on Lebesgue theory. 1957 edition.

The Integrals of Lebesgue, Denjoy, Perron, and Henstock


Author: Russell A. Gordon
Publisher: American Mathematical Soc.
ISBN: 9780821872222
Category: Mathematics
Page: 395
View: 1034

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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.

Lectures on Integral Equations


Author: Harold Widom
Publisher: Courier Dover Publications
ISBN: 0486810275
Category: Mathematics
Page: 128
View: 5871

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This concise and classic volume presents the main results of integral equation theory as consequences of the theory of operators on Banach and Hilbert spaces. In addition, it offers a brief account of Fredholm's original approach. The self-contained treatment requires only some familiarity with elementary real variable theory, including the elements of Lebesgue integration, and is suitable for advanced undergraduates and graduate students of mathematics. Other material discusses applications to second order linear differential equations, and a final chapter uses Fourier integral techniques to investigate certain singular integral equations of interest for physical applications as well as for their own sake. A helpful index concludes the text.

A Primer of Lebesgue Integration


Author: Herbert Stanley Bear
Publisher: Academic Press
ISBN: 9780120839711
Category: Mathematics
Page: 164
View: 4635

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"This succcssful 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."--BOOK JACKET.

Advanced Calculus


Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 0486137864
Category: Mathematics
Page: 432
View: 9663

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Intended for students who have already completed a one-year course in elementary calculus, this two-part treatment advances from functions of one variable to those of several variables. Solutions. 1971 edition.

An Introduction to Fourier Series and Integrals


Author: Robert T. Seeley
Publisher: Courier Corporation
ISBN: 0486151794
Category: Mathematics
Page: 112
View: 2354

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DIVThis compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition. /div