Measure, Integral and Probability (Springer Undergraduate Mathematics Series) (Paperback)

by Marek Capinski (Author), Ekkehard Kopp (Author) "Life is an uncertain business..." (more)
Key Phrases: Proof Suppose, Proof First, Proof Let (more...)

Editorial Reviews

Review
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 SupplementA 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) --This text refers to the Paperback edition.

Product Description
Measure Integral and Probability serves as a gentle introduction to subject matter which is central to the foundations of analysis and probability. With an emphasis on clear explanations, and a step-by-step development of basic ideas, the level and style are ideal for advanced undergraduate students.

The development of the Lebesgue integral provides the essential ideas; the role of basic convergence theorems, a discussion of modes of convergence for measurable functions, and relations to the Riemann Integral lead to the definition of Lebesgue spaces, the Fubini theorem and their roles in describing the properties of random variables and their distributions. With significant applications to probability, including laws of large numbers and the central limit theorem, this book will also be of interest to postgraduates needing to refresh or enhance their knowledge. Numerous exercises are provided, each with solutions.

Product Details

• Paperback: 227 pages
• Publisher: Springer-Verlag (January 1999)
• Language: English
• ISBN-10: 3540762604
• ISBN-13: 978-3540762607
• Product Dimensions: 9.3 x 6.7 x 0.6 inches
• Shipping Weight: 14.1 ounces
• Average Customer Review: 4.3 out of 5 stars See all reviews (13 customer reviews)
• Amazon.com Sales Rank: #1,713,882 in Books (See Bestsellers in Books)

Customer Reviews

Most Helpful Customer Reviews

18 of 18 people found the following review helpful:

5.0 out of 5 stars Highly accessible, June 11, 2001

By	esseyo (Jersey City, NJ United States) - See all my reviews

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.

17 of 17 people found the following review helpful:

5.0 out of 5 stars Best Introduction for the Financial Mathematician, October 13, 2005

By	Gaurav Saroliya - See all my reviews (REAL NAME)

This review is from: Measure, Integral and Probability (Paperback)

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!

25 of 27 people found the following review helpful:

4.0 out of 5 stars A solid introductory text, October 8, 2001

By	UNPINGCO (Los Angeles, CA) - See all my reviews

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.