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Artikelmerkmale
- Artikelzustand
- Book Title
- Measure, Integral and Probability
- ISBN
- 9781852337810
Über dieses Produkt
Product Identifiers
Publisher
Springer London, The Limited
ISBN-10
1852337818
ISBN-13
9781852337810
eBay Product ID (ePID)
30277361
Product Key Features
Number of Pages
Xv, 311 Pages
Publication Name
Measure, Integral and Probability
Language
English
Publication Year
2004
Subject
Probability & Statistics / General, General, Applied, Mathematical Analysis
Features
Revised
Type
Textbook
Subject Area
Mathematics
Series
Springer Undergraduate Mathematics Ser.
Format
Trade Paperback
Dimensions
Item Weight
44.4 Oz
Item Length
10 in
Item Width
7 in
Additional Product Features
Edition Number
2
Intended Audience
Scholarly & Professional
LCCN
2004-040204
Dewey Edition
22
Reviews
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 AssociationFrom 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), 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), 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), 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), 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 fr 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), 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 materiala? Overall, this is an excellent and interesting text. Times Higher Education Supplement A clear, understandable treatment of a very problematic areaa? 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. a? Key aspects of financial modelling, including the Black-Scholes formula a? help the reader understand the underlying mathematical framework." (L'Enseignement Mathematique, Vol. 50 (3-4), 2004)
Number of Volumes
1 vol.
Illustrated
Yes
Dewey Decimal
515/.42
Table Of Content
Content.- 1. Motivation and preliminaries.- 1.1 Notation and basic set theory.- 1.2 The Riemann integral: scope and limitations.- 1.3 Choosing numbers at random.- 2. Measure.- 2.1 Null sets.- 2.2 Outer measure.- 2.3 Lebesgue-measurable sets and Lebesgue measure.- 2.4 Basic properties of Lebesgue measure.- 2.5 Borel sets.- 2.6 Probability.- 2.7 Proofs of propositions.- 3. Measurable functions.- 3.1 The extended real line.- 3.2 Lebesgue-measurable functions.- 3.3 Examples.- 3.4 Properties.- 3.5 Probability.- 3.6 Proofs of propositions.- 4. Integral.- 4.1 Definition of the integral.- 4.2 Monotone convergence theorems.- 4.3 Integrable functions.- 4.4 The dominated convergence theorem.- 4.5 Relation to the Riemann integral.- 4.6 Approximation of measurable functions.- 4.7 Probability.- 4.8 Proofs of propositions.- 5. Spaces of integrable functions.- 5.1 The space L1.- 5.2 The Hilbert space L2.- 5.3 The LP spaces: completeness.- 5.4 Probability.- 5.5 Proofs of propositions.- 6. Product measures.- 6.1 Multi-dimensional Lebesgue measure.- 6.2 Product ?-fields.- 6.3 Construction of the product measure.- 6.4 Fubini's theorem.- 6.5 Probability.- 6.6 Proofs of propositions.- 7. The Radon--Nikodym theorem.- 7.1 Densities and conditioning.- 7.2 The Radon--Nikodym theorem.- 7.3 Lebesgue--Stieltjes measures.- 7.4 Probability.- 7.5 Proofs of propositions.- 8. LimitL theorems.- 8.1 Modes of convergence.- 8.2 Probability.- 8.3 Proofs of propositions.- Solutions.- References.
Edition Description
Revised edition
Synopsis
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., 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., 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 modeling, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework., 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 modeling, discussed briefly from a measure-theoretical perspective to help the reader understand the underlying mathematical framework.
LC Classification Number
QA273.A1-274.9
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