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Agronsky, S. J.; Biskner, R.; Bruckner, A. M.; Marik, J.

Representations of functions by derivatives. (English) Zbl 0455.26002

Trans. Am. Math. Soc. 263, 493-500 (1981).
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Cited in 2 Reviews
Cited in 7 Documents

MSC:

26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems
26A21 Classification of real functions; Baire classification of sets and functions
26A27 Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives

Keywords:

derivatives; approximate derivatives; approximately continuous functions; functions of Baire class 1; Darboux property; Zahorski’s class M3
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References:

[1] S. Agronsky, Characterizations of certain subclasses of the Baire class \( 1\), Doctoral Dissertation, Univ. of California, Santa Barbara, 1974.
[2] 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
[3] A. M. Bruckner and J. G. Ceder, Darboux continuity, Jber. Deutsch. Math.-Verein. 67 (1964/1965), no. Abt. 1, 93 – 117. · Zbl 0144.30003
[4] Richard J. Fleissner, Multiplication and the fundamental theorem of calculus — a survey, Real Anal. Exchange 2 (1976/77), no. 1, 7 – 34.
[5] Casper Goffman and C. J. Neugebauer, On approximate derivatives, Proc. amer. Math. Soc. 11 (1960), 962 – 966. · Zbl 0097.26901
[6] Richard J. O’Malley, Baire* 1, Darboux functions, Proc. Amer. Math. Soc. 60 (1976), 187 – 192. · Zbl 0339.26010
[7] R. J. O’Malley, Selective derivates, Acta Math. Acad. Sci. Hungar. 29 (1977), no. 1 – 2, 77 – 97. · Zbl 0345.26003 · doi:10.1007/BF01896470
[8] Richard J. O’Malley, Decomposition of approximate derivatives, Proc.#Amer. Math. Soc. 69 (1978), no. 2, 243 – 247. · Zbl 0393.26003
[9] G. Petruska and M. Laczkovich, Baire 1 functions, approximately continuous functions and derivatives, Acta Math. Acad. Sci. Hungar. 25 (1974), 189 – 212. · Zbl 0279.26003 · doi:10.1007/BF01901760
[10] David Preiss, Level sets of derivatives, Trans. Amer. Math. Soc. 272 (1982), no. 1, 161 – 184. · Zbl 0508.26001
[11] Clifford E. Weil, On properties of derivatives, Trans. Amer. Math. Soc. 114 (1965), 363 – 376. · Zbl 0163.29604
[12] Clifford E. Weil, A property for certain derivatives, Indiana Univ. Math. J. 23 (1973/74), 527 – 536. · Zbl 0273.26003 · doi:10.1512/iumj.1973.23.23044
[13] Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69 (1950), 1 – 54 (French). · Zbl 0038.20602
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