Measure, Integral and Probability by Marek Capinski

Measure, Integral and Probability by Marek Capinski

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.

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 anintroduction 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)

SKU	Unavailable
ISBN 13	9781852337810
ISBN 10	1852337818
Title	Measure, Integral and Probability
Author	Marek Capinski
Series	Springer Undergraduate Mathematics Series
Condition	Unavailable
Binding Type	Paperback
Publisher	Springer London Ltd
Year published	2004-08-27
Number of pages	311
Cover note	Book picture is for illustrative purposes only, actual binding, cover or edition may vary.