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The Lebesgue Integral

In: An Introduction to Multivariable Analysis from Vector to Manifold

Author

Listed:
  • Piotr Mikusiński

    (University of Central Florida, Department of Mathematics)

  • Michael D. Taylor

    (University of Central Florida, Department of Mathematics)

Abstract

The standard approach to the Lebesgue integral is based on measure theory. One first develops a substantial amount of measure theory and then defines the Lebesgue integral in terms of measure. This makes the theory of the integral more complicated and unnecessarily increases the level of abstraction. In this book we are going to follow the approach used in An Introduction to Analysis: From Number to Integral by Jan Mikusiński and Piotr Mikusiński. In that book the Lebesgue integral in ℝ is defined directly without mentioning measure theory.

Suggested Citation

  • Piotr Mikusiński & Michael D. Taylor, 2002. "The Lebesgue Integral," Springer Books, in: An Introduction to Multivariable Analysis from Vector to Manifold, chapter 4, pages 113-151, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-0073-4_4
    DOI: 10.1007/978-1-4612-0073-4_4
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