The Elements of Integration and Lebesgue Measure (Wiley Classics Library) 1st Edition by Robert G. Bartle (PDF)

Description

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.

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is an excellent introduction to Lebesgue integration and abstract measure theory. It is 1) concise and well-presented enough for a 1-semester course for seniors and 1st year graduate students and 2) covers the subject with enough rigor for an introductory course for graduate students of mathematics. It gets through quite a bit of material, including an elementary presentation of the Riesz representation theorem. The constructions and order of presentation are “vanilla” (i.e., the standard ones), in contrast to Baby and Papa Rudin. The more recent Stein and Shakarchi’s presentation is somewhat unorthodox and arguably more intuitive; unfortunately the book (vol III) is not self-contained. Carother’s presentation is more or less also the standard one, but he spends more verbiage to explain the intuition, and he also covers less ground. Thus, his text is more suited for junior and senior undergrads.On balance, this text is the most suited for a serious course, but also well-written enough for self-study upon completion of a first course in analysis (thus, I was able get through 3/4 of the text in the summer between freshman and sophomore years 🙂 ).

⭐The exposition of integration in this book is the clearest I have read. I also found the chapter on modes of convergence, where it laid out the relationship between things such as L^P-convergence and convergence in measure, to be extremely useful. The second half, where it covers topics like Lebesgue measure, repeats some of the same information from the first part which is a bit iritating if you are reading straight throught, but contains a lot of good information. The book is also quite small making it easy to take with you as a quick reference.Let me warn you though that this is an introduction to integration and measure _not_ an introduction to real analysis. It does not cover important topics like L^P-approximation, differentiation, etc. For a complete treatment of real analysis, I recommend the books “Lebesgue Integration on Euclidean Space” by Frank Jones and the slightly more abstract “Real and Functional Analysis” by Serge Lange.

⭐This is a very accessible intro to measure theory. I’ve been through a few texts on the subject and each had strengths and weaknesses. This book follows the generalized algebra -> sigma algebra -> measure-> measurable function -> integral -> specifically Lebesgue approach, which I prefer to the elementary measure -> Jordan measure -> Lebesgue measure -> Lebesgue integral -> abstract measure space approach. Though the latter is how the theory naturally developed, I prefer the former method, and this is how Bartle presents the material. Moreover, the proofs and definitions are well phrased and easily followed.

⭐I used this book as a reference to my actual text book on measure theory. It is not as clear as my other book in some areas, this is why I gave it a 4, but it has a lot of results my other book didn’t have.

⭐Producto con daño vendido como nuevo pocas opciones de reemplazo, reembolso y recompra no favorable.Useful to understand the relationship among Sets, Linear Algebra, and Calculus

⭐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.

⭐This is a great introduction to integration theory, and probably the only book that is suitable for (1) a one semester course, and (2) a wide audience. The topics presented in this book are the main concepts (“work horse material”) of integration and measure. I highly recommend this book as an introduction or tag along book for mathematicians (analysts), and as a primary book to learn the material for students in economics, electrical engineering, and statistics.

⭐Great book for reference and teaching.

⭐Este livro é de rápido acesso, te levando diretamente aos principais é básicos pontos em teoria essa medida.Ok

⭐Amazing!

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