Overview
Lebesgue Integration on Euclidean Space contains a concrete, intuitive, and patient derivation of Lebesgue measure and integration on Rn. Throughout the text, many exercises are incorporated, enabling students to apply new ideas immediately. Jones strives to present a slow introduction to Lebesgue integration by dealing with n-dimensional spaces from the outset. In addition, the text provides students a thorough treatment of Fourier analysis, while holistically preparing students to become "workers" in real analysis.
ShowKey Features
- Present a slow introduction to Lebesgue integration.
- Deals with n-dimensional spaces from the outset.
- Provides a thorough treatment of Fourier analysis.
- The text provides students the ability to transpose the material they have learned into other areas that they are interested in. Jones calls this preparation to become "workers" in real analysis.
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ShowTable of Contents
Preface
Bibliography
Acknowledgements
1. Introduction to Rn
2. Lebesgue Measure on Rn
3. Invariance of Lebesgue Measure
4. Some Interesting Sets
5. Algebra of Sets and Measurable Functions
6. Integration
7. Lebesgue Integral on Rn
8. Fubini's Theorem for Rn
9. The Gamma Function
10. Lp Spaces
11. Products of Abstract Measures
12. Convolutions
13. Fourier Transform on Rn
14. Fourier Series in One Variable
15. Differentiation
16. Differentiation for Function on R
Index
Symbol Index
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ShowAbout the Author(s)
Frank Jones, PhD-Rice University, Texas
Frank Jones, Rice University
Frank Jones received his bachelor's and Ph.D. degrees from Rice University. His major research interest include real analysis and partial differential equations. In addition, he has been awarded several distinguished teaching awards throughout his career at Rice. Frank's current intereest are partial differential equations and real analysis.
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ShowReviews
The treatment of integration developed by Henri Lebesgue almost a century ago rendered previous theories obsolete and has yet to be replaced by a better one. The author presents an extended introduction to Lebesgue integration, deals with n-dimensional space from the outset, and provides a thorough treatment of Fourier analysis. Other topics include Lebesgue measure, invariance, Cantor sets, algebras of sets and measurable functions, the gamma function, convolutions, and products of abstract measures.
Book News, Inc. , August 1, 1993
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ShowAppropriate Courses
This book was designed as a higher level undergraduate and graduate mathematical text.
- Introduction to Lebesgue Integration
- Real Analysis
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