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Book Review

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Book Information:

Author: Andrew M. Bruckner
Title: Differentiation of real functions
Additional book information: Lecture Notes in Math., vol. 659, Springer-Verlag, Berlin and New York, 1978, x + 246 pp., $12.00.

References [Enhancements On Off] (What's this?)

  • 1. A. Bruckner and K. Garg, The level structure of a residual set of continuous functions, Trans. Amer. Math. Soc. 232 (1977), 307-321. MR 476939
  • 2. A. Bruckner and C. Goffman, Differentiability through change of variables, Proc. Amer. Math. Soc. 61 (1976), 235-241. MR 432831
  • 3. R. Fleissner and J. Foran, Transformations of differentiable functions, Colloq. Math. 39 (1978), 277-284. MR 522368
  • 4. V. Jarnik, Sur les nombres dérivés approximatifs, Fund. Math. 22 (1934), 4-16.
  • 5. M. Laczkovich and G. Petruska, On the transformers of derivatives, Fund. Math. 100 (1978), 179-199. MR 509545
  • 6. J. Lipiński, Une propriété des ensembles {ƒ'(x)>a}, Fund. Math. 42 (1955), 339-342. MR 76842
  • 7. J. Marcinkiewicz, Sur les nombres dérivés, Fund. Math. 24 (1935), 305-308.
  • 8. I. Natanson, Theory of functions of a real variable, Vol. I, Ungar, New York, 1961. MR 148805
  • 9. C. Neugebauer, Darboux functions of Baire class 1 and derivatives, Proc. Amer. Math. Soc. 13 (1962), 838-843. MR 143850
  • 10. R. O'Malley, The set where the approximate derivative is a derivative, Proc. Amer. Math. Soc. 54 (1976), 122-124. MR 390143
  • 11. R. O'Malley and C. Weil, The oscillatory behavior of certain derivatives, Trans. Amer. Math. Soc. 234 (1977), 467-481. MR 453940
  • 12. D. Preiss, On the first derivative of real functions, Comm. Math. Univ. Carolinae 11 (1974), 817-822. MR 274669
  • 13. S. Saks, Theory of the integral, Mongrafie Mat., vol. 7, Warszawa, 1937.
  • 14. W. Sierpiński, Sur une propriété de fonctions quelconques d'une variable réelle, Fund. Math. 25 (1935), 1-14.
  • 15. C. Weil, On properties of derivatives, Trans. Amer. Math. Soc. 114 (1965), 363-376. MR 176007
  • 16. C. Weil, On approximate and Peano derivatives, Proc. Amer. Math. Soc. 20 (1969), 487-490. MR 233944
  • 17. H. Whitney, On totally differentiate and smooth functions, Pacific J. Math. 1 (1951), 143-159. MR 43878
  • 18. Z. Zahorski, Sur la première dérivée, Trans. Amer. Math. Soc. 69 (1950), 1-54. MR 37338

Review Information:

Reviewer: Daniel Waterman
Journal: Bull. Amer. Math. Soc. 2 (1980), 232-237
DOI: https://doi.org/10.1090/S0273-0979-1980-14733-3
American Mathematical Society