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1 - A Panorama of Lebesgue Integration

Published online by Cambridge University Press:  27 May 2021

René L. Schilling  and
Franziska Kühn
René L. Schilling
Affiliation:
Technische Universität, Dresden
Franziska Kühn
Affiliation:
Technische Universität, Dresden
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Summary

This chapter contains a brief non-technical overview on Lebesgue’s integration theory with respect to an abstract measure. Further topics include key theorems from the theory, such as convergence theorems (dominated convergence, monotone convergence, Fatou’s lemma), product measures (Fubini’s and Tonelli’s theorem) and abstract differentiation (Radon--Nikodým theorem).

Keywords

sigma-algebrameasurabilityBorel measuresLebesgue integralconvergence theoremsproduct measuresdifferentiation
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Chapter
Information
Counterexamples in Measure and Integration , pp. 1 - 35
Publisher: Cambridge University Press
Print publication year: 2021

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