Lebesgue Integration

Author: J.H. Williamson

Publisher: Courier Corporation

ISBN: 0486789772

Category: Mathematics

Page: 128

View: 8098

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
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An Introduction to Lebesgue Integration and Fourier Series

Author: Howard J. Wilcox,David L. Myers

Publisher: Courier Corporation

ISBN: 0486137473

Category: Mathematics

Page: 159

View: 9856

Undergraduate-level introduction to Riemann integral, measurable sets, measurable functions, Lebesgue integral, other topics. Numerous examples and exercises.
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Lebesgue Integration and Measure

Author: Alan J. Weir

Publisher: Cambridge University Press

ISBN: 9780521097512

Category: Mathematics

Page: 281

View: 1128

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.
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Integral, Measure and Derivative

A Unified Approach

Author: G. E. Shilov,B. L. Gurevich

Publisher: Courier Corporation

ISBN: 0486165612

Category: Mathematics

Page: 256

View: 3039

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.
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Theory of Functions of a Real Variable

Author: I.P. Natanson

Publisher: Courier Dover Publications

ISBN: 048680643X

Category: Mathematics

Page: 560

View: 1318

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.
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Lectures on Measure and Integration

Author: Harold Widom

Publisher: Courier Dover Publications

ISBN: 0486810283

Category: Mathematics

Page: 176

View: 6795

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.
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Lectures on Integral Equations

Author: Harold Widom

Publisher: Courier Dover Publications

ISBN: 0486810275

Category: Mathematics

Page: 128

View: 8225

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.
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Elements of the Theory of Functions and Functional Analysis

Author: Andre? Nikolaevich Kolmogorov,Serge? Vasil?evich Fomin,S. V. Fomin

Publisher: Courier Corporation

ISBN: 9780486406831

Category: Mathematics

Page: 288

View: 7022

Advanced-level text, now available in a single volume, discusses metric and normed spaces, continuous curves in metric spaces, measure theory, Lebesque intervals, Hilbert space, more. Exercises. 1957 edition.
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Integration, Measure and Probability

Author: H. R. Pitt,Mathematics

Publisher: Courier Corporation

ISBN: 0486488152

Category: Mathematics

Page: 110

View: 6273

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.
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Partial Differential Equations of Mathematical Physics

Author: S. L. Sobolev

Publisher: Courier Corporation

ISBN: 9780486659640

Category: Science

Page: 427

View: 7935

This volume presents an unusually accessible introduction to equations fundamental to the investigation of waves, heat conduction, hydrodynamics, and other physical problems. Topics include derivation of fundamental equations, Riemann method, equation of heat conduction, theory of integral equations, Green's function, and much more. The only prerequisite is a familiarity with elementary analysis. 1964 edition.
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Functional Analysis

Author: Frigyes Riesz,Béla Sz.-Nagy

Publisher: Courier Corporation

ISBN: 0486162141

Category: Mathematics

Page: 528

View: 7750

DIVClassic exposition of modern theories of differentiation and integration and principal problems and methods of handling integral equations and linear functionals and transformations. 1955 edition. /div
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Lectures on Functional Analysis and the Lebesgue Integral

Author: Vilmos Komornik

Publisher: Springer

ISBN: 1447168119

Category: Mathematics

Page: 403

View: 2310

This textbook, based on three series of lectures held by the author at the University of Strasbourg, presents functional analysis in a non-traditional way by generalizing elementary theorems of plane geometry to spaces of arbitrary dimension. This approach leads naturally to the basic notions and theorems. Most results are illustrated by the small lp spaces. The Lebesgue integral, meanwhile, is treated via the direct approach of Frigyes Riesz, whose constructive definition of measurable functions leads to optimal, clear-cut versions of the classical theorems of Fubini-Tonelli and Radon-Nikodým. Lectures on Functional Analysis and the Lebesgue Integral presents the most important topics for students, with short, elegant proofs. The exposition style follows the Hungarian mathematical tradition of Paul Erdős and others. The order of the first two parts, functional analysis and the Lebesgue integral, may be reversed. In the third and final part they are combined to study various spaces of continuous and integrable functions. Several beautiful, but almost forgotten, classical theorems are also included. Both undergraduate and graduate students in pure and applied mathematics, physics and engineering will find this textbook useful. Only basic topological notions and results are used and various simple but pertinent examples and exercises illustrate the usefulness and optimality of most theorems. Many of these examples are new or difficult to localize in the literature, and the original sources of most notions and results are indicated to help the reader understand the genesis and development of the field.
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Foundations of Mathematical Analysis

Author: Richard Johnsonbaugh,W.E. Pfaffenberger

Publisher: Courier Corporation

ISBN: 0486134776

Category: Mathematics

Page: 448

View: 7103

Definitive look at modern analysis, with views of applications to statistics, numerical analysis, Fourier series, differential equations, mathematical analysis, and functional analysis. More than 750 exercises; some hints and solutions. 1981 edition.
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Real Analysis

Author: Gabriel Klambauer

Publisher: Courier Corporation

ISBN: 0486445240

Category: Mathematics

Page: 448

View: 2326

This text for graduate students introduces contemporary real analysis with a particular emphasis on integration theory. Explores the Lebesgue theory of measure and integration of real functions; abstract measure and integration theory as well as topological and metric spaces. Additional topics include Stone's formulation of Daniell integration and normed linear spaces. Includes exercises. 1973 edition. Index.
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A Concise History of Mathematics

Author: Dirk Jan Struik

Publisher: Courier Corporation

ISBN: 9780486602554

Category: Mathematics

Page: 228

View: 5384

This compact, well-written history covers major mathematical ideas and techniques from the ancient Near East to 20th-century computer theory, surveying the works of Archimedes, Pascal, Gauss, Hilbert, and many others. "The author's ability as a first-class historian as well as an able mathematician has enabled him to produce a work which is unquestionably one of the best." — Nature.
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General Theory of Functions and Integration

Author: Angus Ellis Taylor

Publisher: Courier Corporation

ISBN: 0486649881

Category: Mathematics

Page: 437

View: 401

Uniting a variety of approaches to the study of integration, a well-known professor presents a single-volume "blend of the particular and the general, of the concrete and the abstract." 1966 edition.
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Complex Analysis in Banach Spaces

Author: Jorge Mujica

Publisher: Courier Corporation

ISBN: 0486474666

Category: Mathematics

Page: 440

View: 5277

The development of complex analysis is based on issues related to holomorphic continuation and holomorphic approximation. This volume presents a unified view of these topics in finite and infinite dimensions. A high-level tutorial in pure and applied mathematics, its prerequisites include a familiarity with the basic properties of holomorphic functions, the principles of Banach and Hilbert spaces, and the theory of Lebesgue integration. The four-part treatment begins with an overview of the basic properties of holomorphic mappings and holomorphic domains in Banach spaces. The second section explores differentiable mappings, differentiable forms, and polynomially convex compact sets, in which the results are applied to the study of Banach and Fréchet algebras. Subsequent sections examine plurisubharmonic functions and pseudoconvex domains in Banach spaces, along with Riemann domains and envelopes of holomorphy. In addition to its value as a text for advanced graduate students of mathematics, this volume also functions as a reference for researchers and professionals.
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