Lebesgue integration and measure

Alan J. Weir

Lebesgue integration is a technique of great power and elegance which can be applied in situations where other methods of integration fail. It is now one of the standard tools of modern mathematics, and forms part of many undergraduate courses in pure mathematics. Dr Weir's book is aimed at the student who is meeting the Lebesgue integral for the first time. Defining the integral in terms of step functions provides an immediate link to elementary integration theory as taught in calculus courses. The more abstract concept of Lebesgue measure, which generalises the primitive notions of length, area and volume, is deduced later. The explanations are simple and detailed with particular stress on motivation. Over 250 exercises accompany the text and are grouped at the ends of the sections to which they relate; notes on the solutions are given.

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[目次]

  • Preface
  • 1. The completeness of the reals
  • 2. Null sets
  • 3. The Lebesgue integral on R
  • 4. The Lebesgue integral on Rk
  • 5. The convergence theorems
  • 6. Measurable functions and Lebesgue measure
  • 7. The spaces Lp
  • Appendix: the elements of topology
  • Solutions
  • References
  • Index.

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この本の情報

書名 Lebesgue integration and measure
著作者等 Weir, Alan J.
書名別名 General integration and measure
シリーズ名 Integration and measure
出版元 Cambridge University Press
刊行年月 1973
ページ数 xii, 281 p.
大きさ 24 cm
ISBN 0521097517
0521087287
NCID BA06846183
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言語 英語
出版国 イギリス
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