Lebesgue Integration


Author: J.H. Williamson
Publisher: Courier Corporation
ISBN: 0486789772
Category: Mathematics
Page: 128
View: 6556

Continue Reading →

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

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: 2883

Continue Reading →

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

Integral, Measure and Derivative

A Unified Approach
Author: G. E. Shilov,B. L. Gurevich
Publisher: Courier Corporation
ISBN: 0486165612
Category: Mathematics
Page: 256
View: 6378

Continue Reading →

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.

Lebesgue Integration and Measure


Author: Alan J. Weir
Publisher: Cambridge University Press
ISBN: 9780521097512
Category: Mathematics
Page: 281
View: 8708

Continue Reading →

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.

Lectures on Measure and Integration


Author: Harold Widom
Publisher: Courier Dover Publications
ISBN: 0486810283
Category: Mathematics
Page: 176
View: 7565

Continue Reading →

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.

Theory of Functions of a Real Variable


Author: I.P. Natanson
Publisher: Courier Dover Publications
ISBN: 048680643X
Category: Mathematics
Page: 560
View: 3574

Continue Reading →

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.

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: 3528

Continue Reading →

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.

Lectures on Integral Equations


Author: Harold Widom
Publisher: Courier Dover Publications
ISBN: 0486817822
Category: Mathematics
Page: 144
View: 668

Continue Reading →

Concise classic presents main results of integral equation theory as consequences of theory of operators on Banach and Hilbert spaces. Also, applications to second order linear differential equations and Fourier integral techniques. 1969 edition.

Functional Analysis


Author: Frigyes Riesz,Béla Sz.-Nagy
Publisher: Courier Corporation
ISBN: 0486162141
Category: Mathematics
Page: 528
View: 4266

Continue Reading →

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

Complex Analysis in Banach Spaces


Author: Jorge Mujica
Publisher: Courier Corporation
ISBN: 0486474666
Category: Mathematics
Page: 440
View: 5312

Continue Reading →

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.

Foundations of Mathematical Analysis


Author: Richard Johnsonbaugh,W.E. Pfaffenberger
Publisher: Courier Corporation
ISBN: 0486134776
Category: Mathematics
Page: 448
View: 1021

Continue Reading →

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.

Real Analysis


Author: Gabriel Klambauer
Publisher: Courier Corporation
ISBN: 0486445240
Category: Mathematics
Page: 448
View: 3083

Continue Reading →

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.

Differentialgeometrie von Kurven und Flächen


Author: Manfredo P. do Carmo
Publisher: Springer-Verlag
ISBN: 3322850722
Category: Technology & Engineering
Page: 263
View: 9776

Continue Reading →

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

Integration, Measure and Probability


Author: H. R. Pitt,Mathematics
Publisher: Courier Corporation
ISBN: 0486488152
Category: Mathematics
Page: 110
View: 7916

Continue Reading →

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.

Partial Differential Equations of Mathematical Physics


Author: S. L. Sobolev
Publisher: Courier Corporation
ISBN: 9780486659640
Category: Science
Page: 427
View: 3348

Continue Reading →

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.

Foundations of Modern Analysis


Author: Avner Friedman
Publisher: Courier Corporation
ISBN: 9780486640624
Category: Mathematics
Page: 250
View: 3646

Continue Reading →

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.