Customer Reviews

Measure, Integral and Probability

5 star:		(7)
4 star:		(5)
3 star:		(2)
2 star:		(0)
1 star:		(1)

 

 

This book is, as it were, manna from heaven for the aspiring financial mathematician, especially someone without a first degree in mathematics or a mathematically-based subject. The only prerequisites are a very good understanding of set-theory and some knowledge of the theory of continuous functions (at the level of a first course in real analysis, e.g. Apostol's Mathematical Analysis). The development is patient and there is sufficient help for the beginner (full solutions at the back, and, for practice, unproved propositions in the text with proofs at chapter-ends). The coverage is not overwhelming and anyone with the requisite preparation can digest the book in a term's work. Measure theory on its own is an incredibly dry subject. The authors do a great job of covering the essentials in about 300 pages, while making the subject interesting and applicable at the same time. A very attractive feature of the book is its brief focus on mathematical-finance applications. Most chapters end with a small section on such applications which is very useful for someone simultaneously studying mathematical finance. Particularly, it shows how to conceptualize financial models measure-theoretically. A very useful little volume indeed!

Highly accessible and clear intro to measure and Lebesgue integration. Can relax with this book while waiting for the train after work. Only minor negatives are: (1) not enough exercises and (2) there are typos but Springer Verlag doesn't provide any errata list whatsoever.

(Update 2008) There are now other similar books on the market and the paucity of exercises in this book is just not acceptable. For an inexpensive alternative, I recommend Klambauer's "Real Analysis" published by Dover. He uses Carathéodory's definition of a measurable set which (to me) is a faster path to results. Also his exercises are insightful.

A correction to one of the previous comments. There is now an 'errata' on Springer's website. A 2nd edition of the book should be coming sometime, so you might want to check on that before buying.

This text is a leisurely development of the major concepts in measure of probability theory. There are many useful examples that are sprinkled throughout the text that motivate the discussion. The solutions to the problems are also provided. This book is suitable for advanced undergraduate. Although I don't have any major complaints about the book, there already exists a much better book with many more exercises, diagrams, and much more thorough development and extension of the principal concepts. That book is Jones' "Lebesgue integration on Euclidean space", which I cannot recommend highly enough.

A very good introduction for further grduate work in this field. I used it to review the basics for mathematical economics and probability. It's very concise, there are a lot of examples, exercises with detailed answers. Everything is proved.

Very good intro for first encounters with measure theory. Throughout the application in probability theory is emphasized. The necessity of each concept introduced is motivated with clear examples. Interesting problem sets are provided after each section; their solutions are given in the appendix.

To other customers of Amazon bookstore- First of all, I apologize for writing more about the service of Amazon than about the book itself. If I knew any other place to complain about their service, I would've done so. Still, I suspect that what I write below may be useful to anyone who is considering to pay for the so-called Amazon upgrade.

I think the book itself to be very nice (although I could not study the later half of the book). For a starter, the authors point out several problems of Riemann integration; so, the reader can understand why we need a more complex, but also more general, method for integration. Next, they explain important concepts: outer measure function m*, measurable sets, Borel sets, and so on. Then, they introduce the reader to Lebesgue integration. Their construction of Lebesgue integral is similar to that of Kolmogorov, but it is more elegant and conceptually lucid. As a self-studying beginner, I found their approach to be pedagogically efficient, because I could see where they were (or I was) going.

Unfortunately, I had to stop in the middle of Chapter 4. It was because I paid for the so-called Amazon upgrade, and sold my paper copy, but all of sudden, they blocked my access to the digital copy. I emailed twice to ask why, but each time they sent a very short reply, which only explains where I can find the digital copy of my book. Since I already knew that information, I had to dig into the deep part of FAQ about Amazon upgrade. As it turned out, they blocked my access because I read the book on more than seven different computers within one month. It is a restriction imposed by the publisher.

Fair enough, but my complaint is "Why didn't they inform me of this restriction when I was paying?" Also, I emailed them to unlock my library, which contains two other books, but they have sent the same email about "Where you can find the digital copy..." So I am stuck in this situation.

Again, I am sorry for writing about a problem of Amazon upgrade rather than the book itself. However, this problem can be yours too, if you pay for Amazon upgrade. So before you pay, be aware that your access to your own book may be arbitrarily limited by the publisher or Amazon.

This a good book but will be a bit difficult for engineering graduates like me.. Should know real analysis and set theory to venture into this one.

A good introduction to measure theory. Highly recomended if you are an undergraduate student in Mathematics or a graduate student in subjects such as Mathematical Statistics or Econometrics. Unfortunately, chapter 6 (on product measures) lacks of the clarity of exposition of precedent ones (what may be problem for anyone interested in probability theory).
In any case, this is a book worth having.

The text is written at a level which is suitable for the classroom or self-teaching by an advanced student. The authors spare few details. I am very satisfied with my purchase.