Product Description

Measure, Integral and Probability is a gentle introduction that makes measure and integration theory accessible to the average third-year undergraduate student. The ideas are developed at an easy pace in a form that is suitable for self-study, with an emphasis on clear explanations and concrete examples rather than abstract theory. For this second edition, the text has been thoroughly revised and expanded. New features include: · a substantial new chapter, featuring a constructive proof of the Radon-Nikodym theorem, an analysis of the structure of Lebesgue-Stieltjes measures, the Hahn-Jordan decomposition, and a brief introduction to martingales · key aspects of financial modelling, including the Black-Scholes formula, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework. In addition, further exercises and examples are provided to encourage the reader to become directly involved with the material.

Product Details

• Amazon Sales Rank: #92827 in Books
• Published on: 2004-04-01
• Original language: English
• Number of items: 1
• Binding: Paperback
• 312 pages

Customer Reviews

An excellent book for undergrads, with one caveat
I bought this book because I was enrolled in a Stochastic Processes class and was looking for a good, easy self-study book to understand Lebesgue integration and probability. I am extremely pleased I bought the book and actually spent three weeks of my life working out every single problem. The good news is that I came out with a solid understanding of real analysis, and integration in particular. The bad news is that probability is given short shrift, a very small proportion of the worked examples and an even smaller proportion of correct answers to the worked problems. With that said, the treatment of real analysis is so accessible and so thorough that I am still very happy with the book. It brought back memories of my freshman year in college.

The book is made up of seven chapters: 1. Intro 2. Measure 3. Measurable functions 4. Integral 5. Elements of (relevant) functional analysis 6. Product measures 7. Modes of Convergence, Strong and Weak laws and CLT. The seventh chapter is 100% probability. The first six are not. They first do a fantastic job of explaining the real-analysis concepts and then, almost as an afterthought, have a few tacked-on paragraphs that explain how it all translates in probability terms. For example, in the Measure chapter we are told what a probability measure is and in the Integration chapter the authors introduce expectation, but their heart really isn't in it. Either that or it's a case of good author and bad author.

Regardless, this is a book I can wholeheartedly recommend, because the 75% of the book that does not regard probability is a true five-star job.

A few final comments:

1. It is a true, honest-to-God self-study guide that a semi-awake undergrad can follow. Have no fear.

2. Contrary to the description, I did not learn Radon-Nikodym from here.

3. Comfortably the worst appendix of any book I have ever bought.

4. Loads of errata, as it's a first edition. Here's a few I think I got:

p.39 "i" should range from zero to n, not infinity in the last summation
p.106 {x:p.113 the proof of proposition 4.5 is incomplete
p.126 need to mention (a,zb) = conjugate of z(a,b) for the brave readers who will attempt to prove the polarization identity
p.149 Aù2 is not in F2
p. 150 and 152 integration over omega 1 and omega 2 is consistently backwards, undermining the entire discussion. In other words, when he is integrating over omega 1 he ought to be integrating over omega 2 and vice versa.
p. 151 (THIS COST ME AN HOUR OF MY LIFE) in the last three lines A1, A2, Ai should read B1, B2, Bi and all Bs should be As.
p. 208 "This implies convergence to zero of {funky expression} almost surely." I disagree.

5. Even more errata in the solutions to the exercises. Definitely done by grad students. I disagree with the answers to 4.1.b. 5.3, 5.4. a, b and c, 6.5, 6.6 (only half the answer), 6.8 and 7.4

With all that said, this is a superb book, unless you are buying it to learn probability theory!

Review of the Second Edition - excellent improvements
Having studied extensively through the first edition of this book, I was very aware of its qualities and defects. It was one of the first of its kind (the only other Introductory Measure&Integration monograph I know of providing answers to exercises for the lonely climber is Ash and DoleansDade - a very very fine book indeed), it was set in readable print (although some people cringe when looking at latex..) and most importantly it was very very well written. Unfortunately it was peppered with a number of typos, some quite irritating. But time passed, the typos were corrected, and we are now provided with a new edition which (FINALLY!) contains material on the Radon-Nikodym theorem and Lebesgue Stieltjes measures. Most importantly the links between existence of density, absolute continuity, RN derivative are all clearly established (the irritating - please forgive me - Skorohod argument has left its place to the intuitive construction of the Lebesgue Stieltjes measure - thus simplifying the transition from measure probability theory, but also risk-neutral pricing (pricing kernels and all that)).
The inclusion of material on the Hahn-Jordan, Riesz and Doob-Meyer decompositions (forgive the order) only makes this book more desirable and interesting.

Many, Many thanks to Professors Capinski and Kopp for pushing these changes through.

One last issue: Dear Prof Kopp, please have your book on Martingales and Stochastic Calculus reprinted....

The perfect intro to the formal study of real analysis.
Many years ago I took a course in Real Analysis using the standard text by Royden. Though I labored mightily, much of the material did not make sense to me. Subsequent self-tuition finally enabled me to master the material, but with an enormous investment of time.

If only "Measure, Integral and Probability" had been available to me at that time! This book very clearly and simply introduces the basic concepts of measure and integral, in a way that will greatly benefit the person intending to make a formal study Real Analysis. The exercises are very carefully chosen, and the solutions in the back of the book are accessible.

This book will also be useful to the person who just wants some idea of what measure theory is all about, and has no intention of pursuing Real Analysis. Though why any person would not want to learn Real Analysis is beyond me. :)

At the time I studied Real Analysis, I searched long and hard for just such a book as this, and found none. I doubt that any other has been published. Capinski and Kopp are to be commended for their ability to bring measure theory to the mere mortal.

- an anonymous person who is embarrassed to admit that he had difficulty mastering Royden's text