An elementary proof of the one-dimensional Rademacher theorem

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Article

An elementary proof of the one-dimensional Rademacher theorem. (English). Mathematica Bohemica, vol. 117 (1992), issue 2, pp. 133-136

Keywords:
differentiability almost everywhere; Dini derivatives; Rademacher theorem; Lipschitz function; derivative

Summary:
An elementary short proof of the one-dimensional Rademacher theorem on differentiability of Lipschitz functions is given.

References:

[1] V. Jarník: Differential Calculus II. Prague, 1956. (In Czech.)

[2] A. Nekvinda L. Zajíček: A simple proof of the Rademacher theorem. Časopis pěst. mat. 113 (1988), 337-341. MR 0981874

[3] H. Rademacher: Über partielle und totale Differenzierbarkeit I. Math. Ann. 89 (1919), 340-359. MR 1511935

[4] S. Saks: Theory of the Integral. New York, 1937. Zbl 0017.30004

[5] L. Zajíček: An elementary proof of the one-dimensional density theorem. Amer. Math. Monthly 86 (1979), 297-298. DOI 10.1080/00029890.1979.11994796 | MR 0525764

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