Symmetric and ordinary differentiation
HTML articles powered by AMS MathViewer
- by C. L. Belna, M. J. Evans and P. D. Humke PDF
- Proc. Amer. Math. Soc. 72 (1978), 261-267 Request permission
Abstract:
In 1927, A. Khintchine proved that a measurable symmetrically differentiable function f mapping the real line R into itself is differentiable in the ordinary sense at each point of R except possibly for a set of Lebesgue measure zero. Here it is shown that this exceptional set is also of the first Baire category; even more, it is shown to be a $\sigma$-porous set of E. P. Dolženko.References
-
E. P. Dolženko, Boundary properties of arbitrary functions, Math. USSR-Izv. 1 (1967), 1-12.
J. Foran, The symmetric and ordinary derivative, Real Analysis Exchange 2 (1977), 105-108.
- Casper Goffman, On Lebesgue’s density theorem, Proc. Amer. Math. Soc. 1 (1950), 384–388. MR 36816, DOI 10.1090/S0002-9939-1950-0036816-1 A. Khintchine, Recherches sur la structure des fonctions mesurables, Fund. Math. 9 (1927), 212-279.
- Luděk Zajíček, Sets of $\sigma$-porosity and sets of $\sigma$-porosity $(q)$, Časopis Pěst. Mat. 101 (1976), no. 4, 350–359 (English, with Loose Russian summary). MR 0457731
Additional Information
- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 72 (1978), 261-267
- MSC: Primary 26A24
- DOI: https://doi.org/10.1090/S0002-9939-1978-0507319-2
- MathSciNet review: 507319