Abstract
This chapter presents a geometric theory of Lebesgue measure and integration. In calculus you certainly learned that the integral is the area under the curve. With a good definition of area that is the point of view I advance here. Deriving the basic theory of Lebesgue integration then becomes a matter of inspecting the right picture. See Appendix E for the geometric relation between Riemann integration and Lebesgue integration.
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© 2015 Springer International Publishing Switzerland
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Pugh, C.C. (2015). Lebesgue Theory. In: Real Mathematical Analysis. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-17771-7_6
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DOI: https://doi.org/10.1007/978-3-319-17771-7_6
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-17770-0
Online ISBN: 978-3-319-17771-7
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