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
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Halmos, P.: Measure Theory. Van Nostrand, Princeton (1950) [reprinted as Graduate Texts in Mathematics, Springer-Verlag, NY 1975]
Tao, T.: An introduction to measure theory. http://terrytao.files.wordpress.com/2011/01/measure-book1.pdf
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Sohrab, H.H. (2014). Lebesgue Measure and Integral in \(\mathbb{R}\) . In: Basic Real Analysis. Birkhäuser, New York, NY. https://doi.org/10.1007/978-1-4939-1841-6_10
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DOI: https://doi.org/10.1007/978-1-4939-1841-6_10
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