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Real Analysis: Measures, Integrals and Applications

  • Boris Makarov
  • Anatolii Podkorytov

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages I-XIX
  2. Boris Makarov, Anatolii Podkorytov
    Pages 1-39
  3. Boris Makarov, Anatolii Podkorytov
    Pages 41-93
  4. Boris Makarov, Anatolii Podkorytov
    Pages 95-119
  5. Boris Makarov, Anatolii Podkorytov
    Pages 121-203
  6. Boris Makarov, Anatolii Podkorytov
    Pages 205-242
  7. Boris Makarov, Anatolii Podkorytov
    Pages 243-305
  8. Boris Makarov, Anatolii Podkorytov
    Pages 307-393
  9. Boris Makarov, Anatolii Podkorytov
    Pages 395-506
  10. Boris Makarov, Anatolii Podkorytov
    Pages 507-534
  11. Boris Makarov, Anatolii Podkorytov
    Pages 535-638
  12. Boris Makarov, Anatolii Podkorytov
    Pages 639-669
  13. Boris Makarov, Anatolii Podkorytov
    Pages 671-695
  14. Boris Makarov, Anatolii Podkorytov
    Pages 697-760
  15. Back Matter
    Pages 761-772

About this book

Introduction

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.

Keywords

Fourier Analysis Geometry Measure and Integration Real Functions

Authors and affiliations

  • Boris Makarov
    • 1
  • Anatolii Podkorytov
    • 2
  1. 1.Mathematics and Mechanics FacultySt Petersburg State UniversitySt PetersburgRussia
  2. 2.Mathematics and Mechanics FacultySt Petersburg State UniversitySt PetersburgRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4471-5122-7
  • Copyright Information Springer-Verlag London 2013
  • Publisher Name Springer, London
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4471-5121-0
  • Online ISBN 978-1-4471-5122-7
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site