Measure, Integral and Probability | 
 enlarge | Authors: Marek Capinski, Peter E. Kopp
Publisher: Springer
Category: Book
List Price: $39.95
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Rating:  13 reviews
Sales Rank: 389538
Media: Paperback
Edition: 2nd
Pages: 312
Number Of Items: 1
Shipping Weight (lbs): 1.2
Dimensions (in): 9.1 x 6.9 x 0.8
ISBN: 1852337818
Dewey Decimal Number: 515.42
EAN: 9781852337810
Publication Date: September 18, 2007
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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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| Customer Reviews: Read 8 more reviews...
 Highly accessible June 11, 2001
esseyo (Jersey City, NJ United States)
16 out of 16 found this review helpful
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 Caratheodory's definition of a measurable set which (to me) is a faster path to results. Also his exercises are insightful.
Best Introduction for the Financial Mathematician October 13, 2005
Gaurav Saroliya
15 out of 15 found this review helpful
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!
A thorough study of measure theory. Very clear August 4, 1999
17 out of 21 found this review helpful
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 introduction to measure theory April 13, 2007
R. P. P. Grasman (Amsterdam, the Netherlands)
1 out of 1 found this review helpful
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.
Excellent Book June 27, 2007
J. Nisen (Corvallis, OR)
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.
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