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On the differentiability structure of real functions. (English) Zbl 0182.38301


Keywords:

real functions
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[1] F. Bagemihl, Curvilinear cluster sets of arbitrary functions, Proc. Nat. Acad. Sci. U. S. A. 41 (1955), 379 – 382. · Zbl 0065.06604
[2] A. Besicovitch, Diskussion der stetigen Funktionen im Zusammenhang mit der Frage über ihre Differenzierbarkeit, Bull. Acad. Sci. Russie 19 (1925), 527-540.
[3] Henry Blumberg, New properties of all real functions, Trans. Amer. Math. Soc. 24 (1922), no. 2, 113 – 128. · JFM 49.0176.04
[4] F. M. Filipczak, Sur les fonctions continues relativement monotones, Fund. Math. 58 (1966), 75 – 87 (French). · Zbl 0185.12204
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[6] O. Hájek, Note sur la mesurabilité B de la dérivée supérieure, Fund. Math. 44 (1957), 238 – 240 (French). · Zbl 0081.27902
[7] V. Jarnik, Sur les nombres dérivées approximatifs, Fund. Math. 22 (1934), 4-16. · JFM 60.0214.01
[8] R. L. Jeffery, The Theory of Functions of a Real Variable, Mathematical Expositions, no. 6, University of Toronto Press, Toronto, Ont., 1951. · Zbl 0043.27901
[9] C. Kuratowski, Topologie, Vol. I, 4th ed., Monogr. Mat., Tom 20, Warsaw, 1958. · Zbl 0078.14603
[10] I. Maximoff, Sur les fonctions ayant la propriété de Darboux, Prace Mat. Fiz. 43 (1936), 241-626. · Zbl 0013.25007
[11] S. Saks, On the functions of Besicovitch in the space of continuous functions, Fund. Math. 19 (1932), 211-219. · Zbl 0005.39105
[12] -, Theory of the integral, Monogr. Mat., Tom 7, Warsaw-Lwów, 1937.
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