Measure Theory: Second Edition (Birkhäuser Advanced Texts Basler Lehrbücher) 2nd Edition by Donald L. Cohn (PDF)

Description

Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, and the existence of liftings. Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics. The prerequisites for this book are basic courses in point-set topology and in analysis, and the appendices present a thorough review of essential background material.

User’s Reviews

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

⭐I see customer reviews from students, saying it’s a great book for learning basic measure theory. Someone should point out that it’s also great for professional mathematicians and others who already know the basics of the subject. Full of fascinating stuff about Polish spaces, analytic sets, the dual of L^1 in general, etc.Note: If like me you already know basic measure theory and you’re skimming through the book looking ffor the good stuff you may notice that any space with a singleton of infinite measure is a counterexample to Prop 3.3.5. The resolution is that Cohn’s L-infinity norm is not what you think it is; see page 92.

⭐Measure Theory is a difficult subject and every student will acknowledge this fact. So at least we need a text that makes things appear to be simple and tries to take the fear out of us. This text is helping me get over my fears. The proofs in this book are simple and easy to understand. A student can use this book to study the course. So this book is not just for reference.I bought this book as a supplementary text because the recommended text for the course is the book by A. N. Kolmogorov.I have not regretted my decision to buy this book in my effort to understand the course.I strongly recommend this text book.

⭐So far, the content of the book is fine.However, the pages in this textbook began falling out of the binding within days of its arrival. This is a book that does not even leave my office. This being the case, I cannot imagine this book was never meant to actually be opened and read.Somehow, this book will have to make it through two semesters of graduate school. I suppose I will have to pay to get it rebound myself.Needless to say, this is inexcusable for a $60 pile of paper.

⭐Unfortunately this popular measure theory book (in the form sold by Amazon) has clearly been the product of a low-quality, low-budget, pulpy printing process resulting in faded, dot-matrix like fonts which is becoming the norm with Amazon and academic science titles.HOW AND WHY IS AMAZON USING A CHEAP MEANS OF PRODUCING ACADEMIC TITLES?Why do I say the norm?Because I had made precisely the same, very descriptive complaint about another book (Interest Rate Models – Theory and Practice: With Smile, Inflation and Credit)which I ordered in in July 2014.

⭐This 2nd edition is superior to the first. It’s meticulously done and the book print and binding are top notch. If you want a solid measure theory book, try this one.

⭐One if the best books in the topic. A “must buy” if you are interested in Measure Theory.

⭐Often a student learns measure theory as part of a larger analysis course that includes Hilbert spaces and harmonic analysis. Such a course focuses on constructing of Lebesgue measure and characterizing integrable functions. Cohn’s book will be useful to people who have taken a course like this and want to learn measure theory more deeply. The book is quite good for Lp spaces. Commonly these are defined as equivalence classes and are then a Banach space, yet in many arguments authors slide between using functions and equivalence classes of functions. It is clarifying to define a seminormed space Borel measurable functions the pth powerful of whose absolute value is integrable, then the Banach space of equivalence classes of these functions. Indeed, if we have good notation it is usually not misleading to confound equivalence classes and elements of equivalence classes, but it is sometimes useful to keep these apart as different objects.This book proves conditions for when an Lp space is separable, and this is nearly the only well known measure theory book that proves this (Proposition 3.4.5): For a measure space X with a sigma-finite measure and countably generated sigma-algebra, Lp(X) is a separable Banach space. It is reassuring to have conditions for when an Lp space is separable because it is common to tacitly take Hilbert spaces to be separable.Aside from the topics that must be in any measure theory book, there are chapters on Borel measures on locally compact spaces and the Riesz representation theorem, Polish spaces, Haar measure on topological groups, and probability. The chapter on probability is more weighty than the chapter on probability in Folland. It has things like tight collections of measures and the portmanteau theorem (Proposition 10.3.2), martingales and the upcrossing inequality (Proposition 10.4.11), a detailed freestanding construction of Brownian motion, and the Kolmogorov consistency theorem (Theorem 10.6.2).Cohn is less comprehensive than Bogachev,

⭐, but almost everything in Cohn would be worth learning by almost any analyst, whereas Bogachev has topics that would be a long diversion. Cohn does not do geometric measure theory: the co-area formula and Hausdorff measure do not appear, for which see Evans and Gariepy,

⭐.

⭐Solid book for measure theory , but if Amazon can host a discussion forum for this book (or Others), that would benefit more the reader like me who teaches himself/herself.I really can’t understand the proof of equation (2) of the theorem 1.3.6 (page 17)

⭐En mi caso soy ingeniero y estudio por mi cuenta matemáticas. Creo que se complementa muy bien con el libro de Terence Tao que está muy orientado a ejercicios mientras que éste es más abstracto pero más elegante en la exposición. En cualquier caso es lo de siempre y requiere muchísimo esfuerzo hasta que se asimila.It’s a pretty good book but the paucity of problems and the lack of solutions are inexcusable.

⭐Un buen libro para estudiar esta materia. Esta en inglés pero se entiende perfectamente y va al grano pero sin perder solidez.

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