» » Measure Theory

Download Measure Theory fb2

by Donald L. Cohn

Donald_L._Cohn Mathematics English
  • ISBN: 3764330031
  • Category: Math & Science
  • Author: Donald L. Cohn
  • Subcategory: Mathematics
  • Other formats: lit doc lrf azw
  • Language: English
  • Publisher: Birkhauser (December 1980)
  • Pages: 384 pages
  • FB2 size: 1500 kb
  • EPUB size: 1386 kb
  • Rating: 4.6
  • Votes: 958
Download Measure Theory fb2
Download FB2 Download EPUB

The first five chapters deal with abstract measure and integration. At the end of these chapters, the reader will appreciate the elements of integration

I believe that Cohn's Measure Theory is a fantastic companion for learning Analysis in concert with one of the denser books from Folland or Rudin.

I believe that Cohn's Measure Theory is a fantastic companion for learning Analysis in concert with one of the denser books from Folland or Rudin. While still covering a wide range of subjects, Cohn's exposition is much more conducive to the learning experience than either of the other two, in my opinion. He does an excellent job of explaining his reasoning in proofs, while still leaving enough to the reader to get them involved in the process

I used this book for my graduate measure theory class. We covered the first seven chapters. The first chapter gives an introduction to measure theory

I used this book for my graduate measure theory class. The book is written in a clear fashion and is easy to follow. It is concise and at the same time is almost self contained. The first chapter gives an introduction to measure theory. It deals with sigma algebras, measures, outer measures, completeness and regularity. The lebesgue measure is also introduced in this chapter.

The book can be recommended to anyone having basic knowledge of calculus and point-set topology.

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 book can be recommended to anyone having basic knowledge of calculus and point-set topology. It is very self-contained, and can thus serve as an excellent reference book as well.

Springer Science & Business Media, Jun 29, 2013 - Mathematics - 373 pages

Springer Science & Business Media, Jun 29, 2013 - Mathematics - 373 pages. 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. Measure Theory provides a solid background for study in both harmonic analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics

Measure Theory provides a solid background for study in both harmonic analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics.

Measure Theory provides a solid background for study in both harmonic analysis and probability theory and is an excellent resource for advanced undergraduate and graduate students in mathematics.

and has made this great textbook even better. Those readers unfamiliar with Cohn's style will discover that his writing is lucid.

Measure Theory provides a solid background for study in both functional analysis and probability theory and is an excellent . Birkhäuser Advanced Texts Basler Lehrbücher. Categories: Mathematics\Functional Analysis.

This textbook emphasizes those topics relevant and necessary to the study of analysis and probability theory. The first five chapters deal with abstract measurement and integration. Chapter 6, on differentiation, includes a treatment of changes of variables in Rd.
Reviews about Measure Theory (6):
Whilingudw
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.
Vinainl
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.
Dilkree
One if the best books in the topic. A "must buy" if you are interested in Measure Theory.
Moogugore
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.
Fiarynara
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, Measure Theory (2 Volume Set), 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, Measure Theory and Fine Properties of Functions, Revised Edition (Textbooks in Mathematics).
GYBYXOH
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)

Related to Measure Theory fb2 books: