Chapter 5 The Integral

  1. Leonard F. Richardson

Published Online: 29 JUN 2009

DOI: 10.1002/9780470501153.ch5

Measure and Integration: A Concise Introduction to Real Ananysis

Measure and Integration: A Concise Introduction to Real Ananysis

How to Cite

Richardson, L. F. (2009) Chapter 5 The Integral, in Measure and Integration: A Concise Introduction to Real Ananysis, John Wiley & Sons, Inc., Hoboken, NJ, USA. doi: 10.1002/9780470501153.ch5

Publication History

  1. Published Online: 29 JUN 2009
  2. Published Print: 17 JUN 2009

ISBN Information

Print ISBN: 9780470259542

Online ISBN: 9780470501153

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Keywords:

  • special simple functions;
  • domain of the integral;
  • convex functions;
  • Jensen's inequality;
  • Lebesgue Dominated Convergence theorem (LDC);
  • monotone convergence;
  • Fatou's theorem;
  • pointwise convergence;
  • Banach space;
  • class L+

Summary

This chapter contains sections titled:

  • Special Simple Functions

  • Extending the Domain of the Integral

  • Lebesgue Dominated Convergence Theorem

  • Monotone Convergence and Fatou's Theorem

  • Completeness of L1 (X, ��, μ) and the Pointwise Convergence Lemma

  • Complex-Valued Functions