Abstract
We will generalize Riemann integration into a more general notion of integration, namely, Lebesgue integration. We will define Lebesgue integrable functions and measurable functions and prove some of their common properties. In particular, measurable functions include the characteristic functions of intervals and step functions. This extends the scope of functions treated in the previous chapters, which so far are limited to continuous functions. We will follow some ideas in Chap. 6 of Bishop and Bridges [6], but we have to make many changes in order to fit into strict finitism. We will consider only functions of real numbers and will simplify some of the notions.
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References
Bishop, E., and D.S. Bridges. 1985. Constructive analysis. New York: Springer.
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© 2011 Springer Science+Business Media B.V.
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Ye, F. (2011). Integration. In: Strict Finitism and the Logic of Mathematical Applications. Synthese Library, vol 355. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1347-5_6
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DOI: https://doi.org/10.1007/978-94-007-1347-5_6
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Print ISBN: 978-94-007-1346-8
Online ISBN: 978-94-007-1347-5
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