A Course on Integration Theory

including more than 150 exercises with detailed answers

Authors: Lerner, Nicolas

  • Includes over 150 exercises with detailed solutions
  • Requires no prior knowledge of advanced mathematics although the results proven in the book are not elementary
  • Is self-contained, providing detailed arguments for each statement
  • Includes a helpful appendix to recall basic notions
see more benefits

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0348-0694-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-0348-0693-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
About this Textbook

This textbook provides a detailed treatment of abstract integration theory, construction of the Lebesgue measure via the Riesz-Markov Theorem and also via the Carathéodory Theorem. It also includes some elementary properties of Hausdorff measures as well as the basic properties of spaces of integrable functions and standard theorems on integrals depending on a parameter. Integration on a product space, change of variables formulas as well as the construction and study of classical Cantor sets are treated in detail. Classical convolution inequalities, such as Young's inequality and Hardy-Littlewood-Sobolev inequality are proven. The Radon-Nikodym theorem, notions of harmonic analysis, classical inequalities and interpolation theorems, including Marcinkiewicz's theorem, the definition of Lebesgue points and Lebesgue differentiation theorem are further topics included.   A detailed appendix provides the reader with various elements of elementary mathematics, such as a discussion around the calculation of antiderivatives or the Gamma function. The appendix also provides more advanced material such as some basic properties of cardinals and ordinals which are useful in the study of measurability.​  

About the authors

Nicolas Lerner is Professor at Université Pierre and Marie Curie in Paris, France. He held professorial positions in the United States (Purdue University), and in France. His research work is concerned with microlocal analysis and partial differential equations. His recent book Metrics on the Phase Space and Non-Selfadjoint Pseudodifferential Operators was published by Birkhäuser. He was an invited section speaker at the Beijing International Congress of Mathematicians in 2002.

Reviews

“It is well written and the proofs are given in great detail, so that it can serve as a textbook for students as well as a reference for more advanced readers. It consists of nine chapters and an appendix devoted to making the book as self-contained as possible.” (José Rodríguez, Mathematical Reviews, October, 2016)


Table of contents (10 chapters)

  • General Theory of Integration

    Lerner, Nicolas

    Pages 1-66

  • Actual Construction of Measure Spaces

    Lerner, Nicolas

    Pages 67-123

  • Spaces of Integrable Functions

    Lerner, Nicolas

    Pages 125-187

  • Integration on a Product Space

    Lerner, Nicolas

    Pages 189-217

  • Diffeomorphisms of Open Subsets of ℝ n and Integration

    Lerner, Nicolas

    Pages 219-281

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-3-0348-0694-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $89.99
price for USA
  • ISBN 978-3-0348-0693-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
A Course on Integration Theory
Book Subtitle
including more than 150 exercises with detailed answers
Authors
Copyright
2014
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-3-0348-0694-7
DOI
10.1007/978-3-0348-0694-7
Softcover ISBN
978-3-0348-0693-0
Edition Number
1
Number of Pages
XVIII, 492
Number of Illustrations and Tables
12 b/w illustrations, 3 illustrations in colour
Topics