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Lebesgue’s Road to Antiderivatives
Vol. 86, No. 4 (October 2013), pp. 255-260
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/math.mag.86.4.255
Page Count: 6
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Summary The traditional way of proving the existence of antiderivatives of continuous functions is through the concept of definite integrals. In the years 1904–1905, H. Lebesgue provided an alternative proof of this result not relying on the theory of integrals. His method is based on piecewise linear approximations of continuous functions, which also yields the mean value inequality as a by-product. In this note we recall Lebesgue’s ideas.
Copyright the Mathematical Association of America 2013