Abstract
This chapter looks briefly at the Lebesgue integral, to see what questions it answered and what it is good for. The first half takes up two problems in analysis before 1900, the second half looks at how they, and the problem of the fundamental theorem of the calculus, were resolved using Lebesgue ’s theory.
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Notes
- 1.
For a thorough account of the contributions of Peano and Lebesgue, see Gandon and Perrin (2009).
- 2.
See Corry (2006, 148).
- 3.
Hausdorff (1915).
- 4.
See the second edition of his Leçons sur la théorie des functions (1914).
- 5.
Borel (1914, 256), quoted in Moore (1982, 188), who also notes that a number of Italian mathematicians had already explicitly rejected the idea that one can make infinitely many arbitrary choices, Peano among them, see Moore (1982, 76–82).
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Gray, J. (2015). Towards Lebesgue’s Theory of Integration. In: The Real and the Complex: A History of Analysis in the 19th Century. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-23715-2_27
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DOI: https://doi.org/10.1007/978-3-319-23715-2_27
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