Abstract
In chapter 5 we define the Lebesgue measure and the concept of Lebesgue measurable set. We show that the set of Lebesgue measurable sets is a σ-algebra so that the earlier results, proven for more general measure spaces, remain valid in the present context (such as the Lebesgue monotone and dominated convergence theorems).
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References
E.M. Stein, R. Shakarchi, Real Analysis, Princeton Lectures in Analysis III, (Princeton University Press, 2005)
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© 2014 Springer International Publishing Switzerland
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Botelho, F. (2014). The Lebesgue Measure in \(\mathbb{R}^{n}\) . In: Functional Analysis and Applied Optimization in Banach Spaces. Springer, Cham. https://doi.org/10.1007/978-3-319-06074-3_5
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DOI: https://doi.org/10.1007/978-3-319-06074-3_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-06073-6
Online ISBN: 978-3-319-06074-3
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