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Level sets of derivatives. (English) Zbl 0508.26001


MSC:

26A24 Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems

Citations:

Zbl 0142.307
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References:

[1] B. Bojarski, Sur la dérivée d’une fonction discontinue, Annales de la Société Polonaise de Mathématique 24 (1953), 190-191.
[2] 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. · Zbl 0144.05103
[3] A. M. Bruckner and J. L. Leonard, Derivatives, Amer. Math. Monthly 73 (1966), no. 4, 24 – 56. · Zbl 0138.27805
[4] V. Jarník, O derivaci funkcí jedné proměnné, Rozpravy Československé Akad. Věd Řada Mat. Přírod. Věd 32 (1923), 1-8.
[5] -, Über die Menge der Punkte, in welchen die Ableitung unendlich ist, Tôhoku Math. J. 37 (1933), 248-253. · Zbl 0007.40101
[6] K. Kuratowski, Topology. Vol. I, New edition, revised and augmented. Translated from the French by J. Jaworowski, Academic Press, New York-London; Państwowe Wydawnictwo Naukowe, Warsaw, 1966. · Zbl 0158.40901
[7] J. S. Lipiński, Une propriété des ensembles {\?’(\?)>\?}, Fund. Math. 42 (1955), 339 – 342 (French). · Zbl 0065.28803
[8] J. S. Lipiński, Sur certains problèmes de Choquet et de Zahorski concernant les fonctions dérivées, Fund. Math. 44 (1957), 94 – 102 (French). · Zbl 0081.27903
[9] J. S. Lipiński, Sur les ensembles {\?’(\?)>\?}, Fund. Math. 45 (1958), 254 – 260 (French). · Zbl 0085.04503
[10] Solomon Marcus, Sur un problème de Z. Zahorski concernant les points où la dérivée est infinie, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. (8) 29 (1960), 176 – 180 (French). · Zbl 0100.28105
[11] Solomon Markus, Points of discontinuity and points at which the derivative is infinite., Rev. Math. Pures Appl. 7 (1962), 309 – 318 (Russian).
[12] Isaiah Maximoff, On density points and approximately continuous functions, Tôhoku Math. J. 47 (1940), 237 – 250. · Zbl 0024.30401
[13] L. Mišík, Über die Klasse \( {M_2}\), Časopis Pěst. Mat. 91 (1966), 389-393.
[14] Ladislav Mišík, Bemerkungen über approximative Ableitung, Mat. Časopis Sloven. Akad. Vied 19 (1969), 283 – 291 (German, with Loose English summary). · Zbl 0191.34503
[15] I. P. Natanson, Teorija funkcij veščestvenuoj peremennoj, ”Nauka”, Moscow, 1950.
[16] 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
[17] G. Piranian, The derivative of a monotonic discontinuous function, Proc. Amer. Math. Soc. 16 (1965), 243 – 244. · Zbl 0128.27902
[18] David Preiss, Approximate derivatives and Baire classes, Czechoslovak Math. J. 21 (96) (1971), 373 – 382. · Zbl 0221.26007
[19] S. Saks, Theory of the integral, Monografie Matematyczne \( 7\), Warszawa-Lwow, 1937. · Zbl 0017.30004
[20] Z. Zahorski, Über die Konstruktion einer differenzierbaren monotonen, nicht konstanten Funktion mit überall dichter Menge von Konstanzintervalen, C. R. Société de Sciences et Lettres de Varsovie III 30 (1937), 202-206. · Zbl 0019.05601
[21] Zygmunt Zahorski, Über die Menge der Punkte in welchen die Ableitung unendlich ist, Tôhoku Math. J. 48 (1941), 321 – 330 (German). · Zbl 0061.11301
[22] -, Sur la première dérivé, Trans. Amer. Math. Soc. 69 (1950), 1-54.
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