The Elements of Integration and Lebesgue Measure [Paperback]

Robert G. Bartle (Author)

Book Description

Publication Date: January 23, 1995 | ISBN-10: 0471042226 | ISBN-13: 978-0471042228 | Edition: 1

The Wiley Classics Library consists of selected books that have become recognized classics in their respective fields. With these new unabridged and inexpensive editions, Wiley hopes to extend the life of these important works by making them available to future generations of mathematicians and scientists. Currently available in the Series: T. W. Anderson The Statistical Analysis of Time Series T. S. Arthanari & Yadolah Dodge Mathematical Programming in Statistics Emil Artin Geometric Algebra Norman T. J. Bailey The Elements of Stochastic Processes with Applications to the Natural Sciences Robert G. Bartle The Elements of Integration and Lebesgue Measure George E. P. Box & George C. Tiao Bayesian Inference in Statistical Analysis R. W. Carter Simple Groups of Lie Type William G. Cochran & Gertrude M. Cox Experimental Designs, Second Edition Richard Courant Differential and Integral Calculus, Volume I Richard Courant Differential and Integral Calculus, Volume II Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume I Richard Courant & D. Hilbert Methods of Mathematical Physics, Volume II D. R. Cox Planning of Experiments Harold M. S. Coxeter Introduction to Modern Geometry, Second Edition Charles W. Curtis & Irving Reiner Representation Theory of Finite Groups and Associative Algebras Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume I Charles W. Curtis & Irving Reiner Methods of Representation Theory with Applications to Finite Groups and Orders, Volume II Bruno de Finetti Theory of Probability, Volume 1 Bruno de Finetti Theory of Probability, Volume 2 W. Edwards Deming Sample Design in Business Research Amos de Shalit & Herman Feshbach Theoretical Nuclear Physics, Volume 1 —Nuclear Structure J. L. Doob Stochastic Processes Nelson Dunford & Jacob T. Schwartz Linear Operators, Part One, General Theory Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Two, Spectral Theory—Self Adjoint Operators in Hilbert Space Nelson Dunford & Jacob T. Schwartz Linear Operators, Part Three, Spectral Operators Herman Feshbach Theoretical Nuclear Physics: Nuclear Reactions Bernard Friedman Lectures on Applications-Oriented Mathematics Phillip Griffiths & Joseph Harris Principles of Algebraic Geometry Gerald J. Hahn & Samuel S. Shapiro Statistical Models in Engineering Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume I—Methods and Applications Morris H. Hansen, William N. Hurwitz & William G. Madow Sample Survey Methods and Theory, Volume II—Theory Peter Henrici Applied and Computational Complex Analysis, Volume 1—Power Series—Integration—Conformal Mapping—Location of Zeros Peter Henrici Applied and Computational Complex Analysis, Volume 2—Special Functions—Integral Transforms—Asymptotics—Continued Fractions Peter Henrici Applied and Computational Complex Analysis, Volume 3—Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions Peter Hilton & Yel-Chiang Wu A Course in Modern Algebra Harry Hochstadt Integral Equations Erwin O. Kreyszig Introductory Functional Analysis with Applications William H. Louisell Quantum Statistical Properties of Radiation Ali Hasan Nayfeh Introduction to Perturbation Techniques Emanuel Parzen Modern Probability Theory and Its Applications P. M. Prenter Splines and Variational Methods Walter Rudin Fourier Analysis on Groups C. L. Siegel Topics in Complex Function Theory, Volume I—Elliptic Functions and Uniformization Theory C. L. Siegel Topics in Complex Function Theory, Volume II—Automorphic and Abelian Integrals C. L. Siegel Topics in Complex Function Theory, Volume III—Abelian Functions & Modular Functions of Several Variables J. J. Stoker Differential Geometry J. J. Stoker Water Waves: The Mathematical Theory with Applications J. J. Stoker Nonlinear Vibrations in Mechanical and Electrical Systems

Editorial Reviews

From the Publisher

Consists of two separate but closely related parts. Originally published in 1966, the first section deals with elements of integration and has been updated and corrected. The latter half details the main concepts of Lebesgue measure and uses the abstract measure space approach of the Lebesgue integral because it strikes directly at the most important results--the convergence theorems.

Product Details

• Paperback: 192 pages
• Publisher: Wiley-Interscience; 1 edition (January 23, 1995)
• Language: English
• ISBN-10: 0471042226
• ISBN-13: 978-0471042228
• Product Dimensions: 9 x 6.1 x 0.5 inches
• Shipping Weight: 9.6 ounces (View shipping rates and policies)
• Average Customer Review: 4.7 out of 5 stars  See all reviews (7 customer reviews)
• Amazon Best Sellers Rank: #863,243 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

30 of 30 people found the following review helpful:

5.0 out of 5 stars Excellent as an itroduction and as a reference, March 31, 2000

By 

Bernardo Vargas - See all my reviews

This review is from: The Elements of Integration and Lebesgue Measure (Paperback)

When I took my first one-semester course on measure and Lebesgue integration my teacher chose Bartle's "The Elements of Integration" as text. After reading many other books on the subject now I'm sure he made a wise decision.

Assuming almost no strong mathematical background, Bartle is able to build up the basic Lebesgue integral theory introducing the fundamental abstract concepts (sigma-algebra, measurable function, measure space, "almost everywhere", step function, etc.) in such an easy way that the student is not only able to handle them but to UNDERSTAND them.

From the first part of the book I appreciate specially chapters 6, 7, and 10, on L_p spaces, modes of convergence, and product measures, respectively. These chapters contain the most used results of the basic theory, and they are stated exactly in the way one needs them, making the book very useful for future reference.

I like the second part very much also, because it stresses the importance of measure theory by itself and not only as a requisite for integration theory. If you are interested in fractal geometry or geometric measure theory you will find chapters 11 to 17 very helpful.

Since I own this book it has never been lazy in my bookshelf.

28 of 28 people found the following review helpful:

5.0 out of 5 stars A great place to begin, February 4, 2000

By 

John M. Morrison (Hillsdale, NJ) - See all my reviews

This review is from: The Elements of Integration and Lebesgue Measure (Paperback)

Measure and Integration is a daunting subject for mathematical neophytes. Bartle's little volume is the right place to start. I first learned measure theory from it 20 years ago and went on to study functional analysis and stochastic approximation.

I was able to master the material on my own with this book. The problems are at the right level and he begins with the correct level of abstraction. I recommend it over anything else because it is straighforward, clear and focused. Master it then go on to Walter Rudin's Real and Complex Analysis.

22 of 25 people found the following review helpful:

5.0 out of 5 stars Excellent textbook!!!, November 18, 1998

By A Customer

This review is from: The Elements of Integration and Lebesgue Measure (Paperback)

This book deals with integration theory in an abstract level (measure theory). It's "straight to point" and should be a reference for senior undergarduates and graduates; well written and wisely structured. I'm a senior undergraduate in statistics and studied this book in a summer course as a preparation for a following measure-theorethic probability course! An excellent pre-requisite for Prof. Bartle's book is his other text 'Elementary Real Analysis', which is also a great textbook. Those interested in speciliasing in measure theory may also check Wheeden and Zygmund: 'Measure and Integration' and Lang: 'Real and Functional Analysis'. For the serious statistician and the mathematician I strongly recommend Bartle's two books, Kolmogorov and Fomim: 'Introductory Real Analysis' (more than an excellent book, Kolmogorov's text is actually an introduction to topology and measure) and Billingsley: 'Probability and Measure'; these books do please the reader and not (only) the authors!!!