The Lebesgue Integral

Piotr Mikusiński and Michael D. Taylor
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Piotr Mikusiński: University of Central Florida, Department of Mathematics
Michael D. Taylor: University of Central Florida, Department of Mathematics

Chapter 4 in An Introduction to Multivariable Analysis from Vector to Manifold, 2002, pp 113-151 from Springer

Abstract: 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.

Keywords: Characteristic Function; Integrable Function; Convergence Theorem; Step Function; Measure Zero (search for similar items in EconPapers)
Date: 2002
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-0073-4_4

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DOI: 10.1007/978-1-4612-0073-4_4

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