Differentiability through change of variables
HTML articles powered by AMS MathViewer
- by A. M. Bruckner and C. Goffman PDF
- Proc. Amer. Math. Soc. 61 (1976), 235-241 Request permission
Abstract:
A real function $f$ on $[0,\;1]$ can be transformed by a homeomorphism into a differentiable function with bounded derivative if and only if $f$ is continuous and of bounded variation. This condition does not suffice for $f$ to be transformed into a continuously differentiable function. The additional condition for this to hold is found and the theorem is proved.References
- A. M. Bruckner and John L. Leonard, On differentiable functions having an everywhere dense set of intervals of constancy, Canad. Math. Bull. 8 (1965), 73–76. MR 174670, DOI 10.4153/CMB-1965-009-1 S. Saks, Theory of the integral, Monografie Mat., Warsaw, 1933; rev. ed., English transl., Stechert, New York, 1937.
- Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69 (1950), 1–54 (French). MR 37338, DOI 10.1090/S0002-9947-1950-0037338-9
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 235-241
- MSC: Primary 26A24
- DOI: https://doi.org/10.1090/S0002-9939-1976-0432831-2
- MathSciNet review: 0432831