Real Analysis: Measures, Integrals and Applications
Authors: Makarov, Boris M., Podkorytov, Anatolii N.
Free Preview- A detailed account of measure and integration theory
- Contains over 600 examples
- Covers several topics and applications of integration theory that are rarely studied in literature
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- About this Textbook
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Real Analysis: Measures, Integrals and Applications is devoted to the basics of integration theory and its related topics. The main emphasis is made on the properties of the Lebesgue integral and various applications both classical and those rarely covered in literature.
This book provides a detailed introduction to Lebesgue measure and integration as well as the classical results concerning integrals of multivariable functions. It examines the concept of the Hausdorff measure, the properties of the area on smooth and Lipschitz surfaces, the divergence formula, and Laplace's method for finding the asymptotic behavior of integrals. The general theory is then applied to harmonic analysis, geometry, and topology. Preliminaries are provided on probability theory, including the study of the Rademacher functions as a sequence of independent random variables.
The book contains more than 600 examples and exercises. The reader who has mastered the first third of the book will be able to study other areas of mathematics that use integration, such as probability theory, statistics, functional analysis, partial probability theory, statistics, functional analysis, partial differential equations and others.
Real Analysis: Measures, Integrals and Applications is intended for advanced undergraduate and graduate students in mathematics and physics. It assumes that the reader is familiar with basic linear algebra and differential calculus of functions of several variables.
- About the authors
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The authors are well-known in their respected fields and have several publications on their research. They both have extensive experience in teaching analysis.
- Reviews
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“Written in a didactic style, with clear proofs and intuitive motivations for the abstract notions, the book is a valuable addition to the literature on measure theory and integration and their applications to various areas of analysis and geometry. The numerous nontrivial examples and applications are of great importance for those interested in various domains of modern analysis and geometry, or in teaching.” (S. Cobzaş, Studia Universitatis Babes-Bolyia, Mathematica, Vol. 60 (1), 2015)
“The book contains enough material for a good three-semester graduate course in analysis. Complete proofs are given for all results, and the reader-friendly, exposition style presents lots of details and motivational tips throughout. … Summing Up: Highly recommended. Graduate students.” (D. M. Ha, Choice, Vol. 51 (10), June, 2014)
- Table of contents (13 chapters)
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Measure
Pages 1-39
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The Lebesgue Measure
Pages 41-93
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Measurable Functions
Pages 95-119
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The Integral
Pages 121-203
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The Product Measure
Pages 205-242
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Table of contents (13 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Real Analysis: Measures, Integrals and Applications
- Authors
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- Boris M. Makarov
- Anatolii N. Podkorytov
- Series Title
- Universitext
- Copyright
- 2013
- Publisher
- Springer-Verlag London
- Copyright Holder
- Springer-Verlag London Ltd., part of Springer Nature
- Distribution Rights
- Distribution rights for India: Researchco Book Centre, New Delhi, India
- eBook ISBN
- 978-1-4471-5122-7
- DOI
- 10.1007/978-1-4471-5122-7
- Softcover ISBN
- 978-1-4471-5121-0
- Series ISSN
- 0172-5939
- Edition Number
- 1
- Number of Pages
- XIX, 772
- Number of Illustrations
- 23 b/w illustrations
- Topics
