Abstract
We discuss the fundamental convergence theorems of Fatou, B. Levi, and Lebesgue, saying that under certain assumptions, the integral of a limit of a sequence of functions equals the limit of the integrals. Instructive examples show the necessity of those assumptions. As an application, results that justify the derivation under the integral sign w.r.t. a parameter are given.
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© 2003 Springer-Verlag Berlin Heidelberg
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Jost, J. (2003). The Convergence Theorems of Lebesgue Integration Theory. In: Postmodern Analysis. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05306-5_17
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DOI: https://doi.org/10.1007/978-3-662-05306-5_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-43873-1
Online ISBN: 978-3-662-05306-5
eBook Packages: Springer Book Archive