Lebesgue Integration

Author: J.H. Williamson

Publisher: Courier Corporation

ISBN: 0486789772

Category: Mathematics

Page: 128

View: 6163

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: 9361

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: 4877

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: 8430

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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Lectures on Measure and Integration

Author: Harold Widom

Publisher: Courier Dover Publications

ISBN: 0486810283

Category: Mathematics

Page: 176

View: 8947

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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Galoissche Theorie

Author: Emil Artin

Publisher: N.A

ISBN: N.A

Category: Galois theory

Page: 86

View: 3395

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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: 8666

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 Integral Equations

Author: Harold Widom

Publisher: Courier Dover Publications

ISBN: 0486810275

Category: Mathematics

Page: 128

View: 3944

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: 9329

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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Complex Analysis in Banach Spaces

Author: Jorge Mujica

Publisher: Courier Corporation

ISBN: 0486474666

Category: Mathematics

Page: 440

View: 1841

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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Differentialgeometrie von Kurven und Flächen

Author: Manfredo P. do Carmo

Publisher: Springer-Verlag

ISBN: 3322850722

Category: Technology & Engineering

Page: 263

View: 6020

Inhalt: Kurven - Reguläre Flächen - Die Geometrie der Gauß-Abbildung - Die innere Geometrie von Flächen - Anhang
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Real Analysis

Author: Gabriel Klambauer

Publisher: Courier Corporation

ISBN: 0486445240

Category: Mathematics

Page: 448

View: 6240

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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Foundations of Mathematical Analysis

Author: Richard Johnsonbaugh,W.E. Pfaffenberger

Publisher: Courier Corporation

ISBN: 0486134776

Category: Mathematics

Page: 448

View: 6121

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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Partial Differential Equations of Mathematical Physics

Author: S. L. Sobolev

Publisher: Courier Corporation

ISBN: 9780486659640

Category: Science

Page: 427

View: 2276

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: 5421

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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General Theory of Functions and Integration

Author: Angus Ellis Taylor

Publisher: Courier Corporation

ISBN: 0486649881

Category: Mathematics

Page: 437

View: 7347

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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Foundations of Modern Analysis

Author: Avner Friedman

Publisher: Courier Corporation

ISBN: 9780486640624

Category: Mathematics

Page: 250

View: 9395

Measure and integration, metric spaces, the elements of functional analysis in Banach spaces, and spectral theory in Hilbert spaces — all in a single study. Only book of its kind. Unusual topics, detailed analyses. Problems. Excellent for first-year graduate students, almost any course on modern analysis. Preface. Bibliography. Index.
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