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Product Description
A superb text on the fundamentals of Lebesgue measure and integration.
This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R. Starting with a thorough presentation of the preliminary concepts of undergraduate analysis, this book covers all the important topics, including measure theory, measurable functions, and integration. It offers an abundance of support materials, including helpful illustrations, examples, and problems. To further enhance the learning experience, the author provides a historical context that traces the struggle to define "area" and "area under a curve" that led eventually to Lebesgue measure and integration.
Lebesgue Measure and Integration is the ideal text for an advanced undergraduate analysis course or for a first-year graduate course in mathematics, statistics, probability, and other applied areas. It will also serve well as a supplement to courses in advanced measure theory and integration and as an invaluable reference long after course work has been completed.
This book is designed to give the reader a solid understanding of Lebesgue measure and integration. It focuses on only the most fundamental concepts, namely Lebesgue measure for R and Lebesgue integration for extended real-valued functions on R. Starting with a thorough presentation of the preliminary concepts of undergraduate analysis, this book covers all the important topics, including measure theory, measurable functions, and integration. It offers an abundance of support materials, including helpful illustrations, examples, and problems. To further enhance the learning experience, the author provides a historical context that traces the struggle to define "area" and "area under a curve" that led eventually to Lebesgue measure and integration.
Lebesgue Measure and Integration is the ideal text for an advanced undergraduate analysis course or for a first-year graduate course in mathematics, statistics, probability, and other applied areas. It will also serve well as a supplement to courses in advanced measure theory and integration and as an invaluable reference long after course work has been completed.
From the Publisher
Filled with illustrations, problems and five appendices of examples, this lively, clearly written text informs and motivate students about Lebesgue measure and integration through its rich use of detail and historical perspectives. Ideal as an undergraduate text for advanced students in an analysis course and for students considering graduate school in mathematics and statistics. As a graduate text, it provides an excellent foundation upon which to develop an abstract measure and integration theory course.
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Inside This Book
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First Sentence:
The figures below demonstrate the general idea of "rearranging"; in the first example, a circle rearranged into a parallelogram. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonnegative simple function, disjoint measurable subsets, nonnegative measurable functions, outer measure, countable additivity, disjoint open intervals, finite additivity, measure zero, finite subcover, measurable sets Key Phrases - Capitalized Phrases (CAPs): (learn more)
Approximation Theorem, Problem Let, Problem Calculate, Definition Let, Definitions Let, Lebesgue Dominated Convergence Theorem New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The figures below demonstrate the general idea of "rearranging"; in the first example, a circle rearranged into a parallelogram. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
nonnegative simple function, disjoint measurable subsets, nonnegative measurable functions, outer measure, countable additivity, disjoint open intervals, finite additivity, measure zero, finite subcover, measurable sets Key Phrases - Capitalized Phrases (CAPs): (learn more)
Approximation Theorem, Problem Let, Problem Calculate, Definition Let, Definitions Let, Lebesgue Dominated Convergence Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 45
books:
See all 45 books this book cites
2
books
cite this book:
- Real Variables (Essentials) by Tefera Worku in Back Matter (1), and Back Matter (2)
- Foundations of Analysis (AMS Chelsea Publishing) by Edmund Landau in Front Matter, and Back Matter
- Differential Equations, 3rd Edition by Shepley L. Ross in Back Matter
- Principles of Mathematical Analysis (International Series in Pure & Applied Mathematics) by Walter Rudin in Back Matter
- Conformal Differential Geometry and Its Generalizations by Maks A. Akivis in Back Matter
See all 45 books this book cites
- Principles of Random Signal Analysis and Low Noise Design: The Power Spectral Density and its Applications by Roy M. Howard in Back Matter
- Convexity and Optimization in Rn by Leonard D. Berkovitz in Back Matter
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