On characterizing derivatives
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- by D. Preiss and M. Tartaglia PDF
- Proc. Amer. Math. Soc. 123 (1995), 2417-2420 Request permission
Abstract:
We show that the set of derivatives of real functions of a real variable can be characterized by prescribing, for each subset of the real line, the set of its possible inverse images.References
- Andrew M. Bruckner, Differentiation of real functions, Lecture Notes in Mathematics, vol. 659, Springer, Berlin, 1978. MR 507448, DOI 10.1007/BFb0069821
- A. M. Bruckner and J. L. Leonard, Derivatives, Amer. Math. Monthly 73 (1966), no. 4, 24–56. MR 197632, DOI 10.2307/2313749
- Alexander S. Kechris and Alain Louveau, Descriptive set theory and the structure of sets of uniqueness, London Mathematical Society Lecture Note Series, vol. 128, Cambridge University Press, Cambridge, 1987. MR 953784, DOI 10.1017/CBO9780511758850 C. Kuratowski, Topology. I, Academic Press, New York and London, 1968. S. Mazurkiewicz, Über die Menge der differenzierbaren Funktionen, Fund. Math. 27 (1936), 244-249.
- David Preiss, Level sets of derivatives, Trans. Amer. Math. Soc. 272 (1982), no. 1, 161–184. MR 656484, DOI 10.1090/S0002-9947-1982-0656484-0 M. Tartaglia, Sulla caratterizzazione delle derivate, Pubbl. Dip. Mat. Stat., Napoli, 1988.
- 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 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 123 (1995), 2417-2420
- MSC: Primary 26A24
- DOI: https://doi.org/10.1090/S0002-9939-1995-1246535-1
- MathSciNet review: 1246535