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From the reviews: The level of explanation is excellent and great care has gone into providing motivation for the study of all aspects of the material…Overall, this is an excellent and interesting text. Times Higher Education Supplement A clear, understandable treatment of a very problematic area…The authors are to be commended for their lucid writing style. Journal of the American Statistical Association From the reviews of the second edition: "This book 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. … Key aspects of financial modelling, including the Black-Scholes formula … help the reader understand the underlying mathematical framework." (L'Enseignement Mathematique, Vol. 50 (3-4), 2004) "The central concepts of this excellent undergraduate text are those of Lebesgue measure and the Lebesgue integral, especially with a view to their applications in probability and, more briefly, finance. … Throughout, the material is presented clearly and rigorously, with an emphasis on accessibility and explicitness. … the book engages the reader actively, and the applications in both probability and finance are clearly developed from a measure-theoretic perspective." (Jennie Golding, The Mathematical Gazette, Vol. 90 (518), 2006) "There exist many books on each of the areas of real analysis and probability, including some which attempt to treat both subjects in the same treatise. … A fundamental strong point of the book under review is that the reader is led through a careful course … . For the second edition, the text has been thoroughly revised and expanded. … The selection and presentation of the material makes this a useful book for an introduction to measure, integration theory and probability." (B. Kirstein, Zeitschrift für Analysis und ihre Anwendungen, Vol. 24 (4), 2005) "This text succeeds in its aim of providing an introduction to measure and integration that is … accessible to undergraduates. Written in a clear engaging style, the text is seasoned with an abundance of concrete examples. … Each chapter concludes with a substantial section on probability and a brief section on finance. … a broad introduction to probability has been presented, extending to martingales, the strong law of large numbers, and the Lindeberg-Feller version of the central limit theorem." (J. W. Hagood, Zentralblatt MATH, Vol. 1103 (5), 2007)
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.
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Most Helpful Customer Reviews
30 of 30 people found the following review helpful
Format:Paperback
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:<y} should read {x<y} (I'm nitpicking)
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!
12 of 12 people found the following review helpful
Format:Paperback
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.
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....
5 of 5 people found the following review helpful
Format:Paperback
I've dredged through quite a few other books and internet material on this subject. But have always been left short of the big picture and motivation behind the basic ideas.
Most other presentations just lay down the theorems, fine if your a maths whizz, not so good if your struggling through your own course of self-study.
This book has useful remarks and comments before/after various definitions and theorems - so you don't feel like they're just being pulled out of the hat. These remarks were of inestimable value and kept providing 'AHA! that now makes sense' moments.
If you've ever struggled in this area of mathematics, I would thoroughly recommend you give this a try.
Most other presentations just lay down the theorems, fine if your a maths whizz, not so good if your struggling through your own course of self-study.
This book has useful remarks and comments before/after various definitions and theorems - so you don't feel like they're just being pulled out of the hat. These remarks were of inestimable value and kept providing 'AHA! that now makes sense' moments.
If you've ever struggled in this area of mathematics, I would thoroughly recommend you give this a try.
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Most Recent Customer Reviews
Bridges a Gap
Many undergraduate mathematics or mathematics and statistics courses cover probability to quite an advanced level but do not cover the required underlying formal mathematics or do... Read more
Published 9 months ago by The Green Flag
Awesome
This book helps your University statistics knowledge, good research book for final year projects and... Also a good book to have in the open book tests XD
Published 16 months ago by Mr. G. Zhou
Elegant and accessible
The Lesbegue measure and Lesbegue integral are developped with many insights. Although probability theory is the primary application that is addressed in the text, I bought this... Read more
Published on 5 April 2010 by Alpha
If only I had this book before!
I wish I had this book when I was enrolled in the course on financial math. As someone with non-math background and being used only to calculus based proba I had loads of trouble... Read more
Published on 14 April 2009 by Geka
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. Read more
Published on 18 Feb 2000
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