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Lebesgue Measure and Integral in \(\mathbb{R}\)

Chapter
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Abstract

In Chap. 7 we saw that the Riemann integral of a (bounded) function \(f: [a,b] \rightarrow \mathbb{R}\) can be obtained as a “limit” of integrals of step functions that approximate f. In fact, we have (cf. Exercise 7.4.8)

Keywords

Riemann Integral Lebesgue Integral Pairwise Disjoint Measurable Subsets Measurable Set Fundamental Convergence Results 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Bibliography

  1. [Hal50]
    Halmos, P.: Measure Theory. Van Nostrand, Princeton (1950) [reprinted as Graduate Texts in Mathematics, Springer-Verlag, NY 1975]Google Scholar
  2. [Tao11]
    Tao, T.: An introduction to measure theory. http://terrytao.files.wordpress.com/2011/01/measure-book1.pdf

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.MathematicsTowson UniversityTowsonUSA

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