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.
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© 2002 Springer Science+Business Media New York
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Mikusiński, P., Taylor, M.D. (2002). The Lebesgue Integral. In: An Introduction to Multivariable Analysis from Vector to Manifold. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-0073-4_4
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DOI: https://doi.org/10.1007/978-1-4612-0073-4_4
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6600-6
Online ISBN: 978-1-4612-0073-4
eBook Packages: Springer Book Archive