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Hancock, Don L.

Derivatives and Lebesgue points via homeomorphic changes of scale. (English) Zbl 0488.26004

Trans. Am. Math. Soc. 267, 197-218 (1981).
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MSC:

26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable

Keywords:

homeomorphic transformation of the real line; Lebesgue points; approximately continuous functions; non-invariance of differentiation
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References:

[1] Nina Bary, Mémoire sur la représentation finie des fonctions continues, Math. Ann. 103 (1930), no. 1, 185 – 248 (French). · JFM 56.0919.03 · doi:10.1007/BF01455694
[2] A. M. Bruckner, Creating differentiability and destroying derivatives, Amer. Math. Monthly 85 (1978), no. 7, 554 – 562. · Zbl 0403.26002 · doi:10.2307/2320863
[3] A. M. Bruckner, Differentiability a.e. and approximate differentiability a.e, Proc. Amer. Math. Soc. 66 (1977), no. 2, 294 – 298. · Zbl 0375.26007
[4] Andrew M. Bruckner, Differentiation of real functions, Lecture Notes in Mathematics, vol. 659, Springer, Berlin, 1978. · Zbl 0382.26002
[5] A. M. Bruckner, Inflexible derivatives, Quart. J. Math. Oxford Ser. (2) 29 (1978), no. 113, 1 – 10. · Zbl 0398.26006 · doi:10.1093/qmath/29.1.1
[6] A. M. Bruckner and C. Goffman, Differentiability through change of variables, Proc. Amer. Math. Soc. 61 (1976), no. 2, 235 – 241 (1977). · Zbl 0358.26006
[7] Richard J. Fleissner and James Foran, Transformations of differentiable functions, Colloq. Math. 39 (1978), no. 2, 277 – 284. · Zbl 0398.26007
[8] D. Hancock, Homeomorphic transformations of approximately continuous functions into derivatives, Doctoral Dissertation, University of California, Santa Barbara, 1979.
[9] Marius Iosifesku, Conditions that the product of two derivatives be a derivative, Rev. Math. Pures Appl. 4 (1959), 641 – 649 (Russian).
[10] Isaiah Maximoff, On continuous transformation of some functions into an ordinary derivative, Ann. Scuola Norm. Super. Pisa (2) 12 (1943), 147 – 160 (1947). · Zbl 0061.09402
[11] Isaie Maximoff, Sur la transformation continue de fonctions, Bull. Soc. Phys.-Math. Kazan (3) 12 (1940), 9 – 41 (Russian, with French summary). · Zbl 0063.03848
[12] Isaie Maximoff, Sur la transformation continue de quelques fonctions en dérivées exactes, Bull. Soc. Phys.-Math. Kazan (3) 12 (1940), 57 – 81 (Russian, with French summary). · Zbl 0063.03850
[13] I. P. Natanson, Theory of functions of a real variable. Vol. II, Translated from the Russian by Leo F. Boron, Frederick Ungar Publishing Co., New York, 1961.
[14] David Preiss, Maximoff’s theorem, Real Anal. Exchange 5 (1979/80), no. 1, 92 – 104. · Zbl 0442.26004
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