Abstract
This brief closing chapter is devoted to two twentieth century developments that have in very different ways served to complete the historical development of the calculus. The comprehensive theory of integration that stems from the work of Henri Lebesgue (1875–1941) is (in a certain technical sense) the ultimate generalization of the concept of the integral for real-valued functions of a real variable. The non-standard analysis of Abraham Robinson (1918–1974) provides at long last a logical foundation for infinitesimals as they were frequently used in the seventeenth and eighteenth centuries.
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References
T. Hawkins, Lebesgue’s Theory of Integration: Its Origins and Development. New York: Chelsea, 1975, 2nd. ed.
H. J. Keisler, Elementary Calculus. Boston: Prindle, Weber & Schmidt, 1976.
H. J. Keisler, Foundations of Infinitesimal Calculus. Boston: Prindle, Weber & Schmidt, 1976.
H. Lebesgue, Integrale, longueur, aire. Ann Mat 7 (3) 231–359, 1902.
H. Lebesgue, Leçons sur l’integration et la recherche des fonctions primitives. Paris: Gauthier-Villars, 1904.
A. Robinson, Non-standard Analysis. Amsterdam, London: North-Holland, 1966.
H. L. Royden, Real Analysis. New York: Macmillan, 1964.
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© 1979 Springer-Verlag New York, Inc.
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Edwards, C.H. (1979). Postscript: The Twentieth Century. In: The Historical Development of the Calculus. Springer Study Edition. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-6230-5_12
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DOI: https://doi.org/10.1007/978-1-4612-6230-5_12
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94313-8
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